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UNIVERSITY OF ILLINOIS AT URBANACHAMPAIGN
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UNIVERSITY , OF ILLINOIS 1 UldiETIN
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T'lj;!ST 'IV D TJj(ERJINElJlMil
THE RIGIDITY OP RIVETED JOINTS
OF ýSTEEL STRUCTURES.
B3Y
<.WILBLTPl M. WVIL4ON
AND
HERBERT F. MOORE
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T HE Engineering Experiment Station was established by act of
the Board of Trustees, December 8, 1903. It is the purpose
o of the Station to carry on investigations along various lines
of engineering'and to study problems of importance to professional
engineers and to the mainufacturing, iailway, mining, constructional
and industrial interests of the State.
The control of the Engineering Experiment Station is vested
in the heads of the several departments of the College of Engineering.
These constitute the Station Staff and, with the Director, determine
the character of the investigations tobe undertaken. The work is
cearried on uinder the supervision of the Staff, sometimes by research
fellows as graduate work, sometimes by menmbers of the instructional
staf of the College of Engineering, but more frequently by investi
gators belonging to the Station corps
The results of these investigations are published in the form of
bulletins, which record nmostly the experiments of the Station's own
staff of investigators There will also be issuied from time to time, Iu
the, form of circulars, compilations giving the results of the experi
ments of engineers, industrial works, technical institutions, and gov
UNIVERSITY OF ILLINOIS
ENGINEERING EXPERIMENT STATION
BULLETIN NO. 104
DECEMBER, 1917
TESTS TO DETERMINE THE RIGIDITY OF
RIVETED JOINTS OF STEEL
STRUCTURES
BY
WILBUR M. WILSON
ASSISTANT PROFESSOR OF CIVIL ENGINEERING
AND
HERBERT F. MOORE
RESEARCH PROFESSOR OF ENGINEERING MATERIALS
ENGINEERING EXPERIMENT STATION
PUBLISHED BY THE UNIVERSITY OF ILLINOIS, URBANA
CONTENTS
I. INTRODUCTION . . . . . . . . . .
1. Object of Tests . . . . . . . .
2. Acknowledgments . . . . . . .
II. DESCRIPTION OF TESTS . . . . . . .
3. Description of Test Pieces . . . .
4. Apparatus and Methods of Testing .
PAGE
7
7
8
. 11
. 11
. 14
III. DISCUSSION OF RESULTS . . . . . . . . . . .
5. Definition of Slip . . . . . . . . . . .
6. The Effect of the Slip in Connections upon a Rec
tangular Frame . . . . . . . . . . .
7. Method of Determining the Magnitude of the Change
in the Deflection and in the Distribution of the
Stresses in a Rectangular Frame Due to Slip in
the Connections . . . . . . . . . . .
8. Graphic Records . . . . . . . . .
9. Strength of Test Pieces . . . . . . . . .
10. Interpretation of Results . . . . . . . . .
11. Test Piece Al . . . . . . . . . .
12. Test Piece A2 . . . . . . . . . . .
13. Test Piece A3 . . . . . . . . . . . .
14. Test Piece A4 . .. . . . .
15. Test Piece A5 . . . . . .
16. Test Piece A6 . . . . . . . . .
17. Comparison of Results of Tests of Different Test
Pieces . . . . . . . . . . . . . .
53
. . . 55
18. Conclusions .
LIST OF FIGURES
NO.
1. Diagram of Deformation of Rectangular Frame
2. Test Piece Al . . . . . . . . . . . .
3. Test Piece A2 . . . . . . . . . . . .
4. Test Piece A3 . . . . . . . . . . . .
5. Test Piece A4 . . . . . . . . . . . .
6. Test Piece A5 . . . . . . ........
7. Test Piece A6 . . . . . . . . . . . ..
8. Diagram of Test Pieces in Testing Machine . .
9. General View of Test Pieces Al in Testing Machine
10. Measurements of Rotation for Test Pieces Al
11. Measurements of Rotation for Test Pieces A2 . .
12. Measurements of Rotation for Test Pieces A3
13. Measurements of Rotation for Test Pieces A4
14. Measurements of Rotation for Test Pieces A .
15. Measurements of Rotation for Test Pieces A6
16. Diagram of Rectangular Frame with Pin Joints .
17. Diagram of Rectangular Frame with Slip at Joints .
PAGE
. . . . . . 7
. . . . . . 8
. . . . . 9
. . . . . . 9
. . . . . . 10
. . . . . . 10
. . . . . 11
. . . . 13
. . . . . 15
. . . . 18
. . . . 19
. . . . 20
. . . . 21
. . . . 22
. . . . . . 23
. . . . 25
. . . . . . 28
18. Error in Computations for Moment in Frame with Varying Values of n .
19. Error in Computations for Moment in Frame with Varying Values of K .
20. Test Results for Test Piece A1 . . . . . . . . . . . . .
21. Test Results for Test Piece A2 . . . . . . . . . . . . .
22. Test Results for Test Piece A3 . . . . . . . . . . . . .
23. Test Results for Test Piece A4 . . . . . . . . . . .. .
24. Test Results for Test Piece A5 . . . . . . . . . . . . .
25. Test Results for Test Piece A6 . . . . . . . . . . . . .
LIST OF TABLES
NO.
1. Properties of Columns and Girders . . . .
2. Loads on Test Pieces . . . . . . . . . .
3. Effect of Slip in Connections of Al upon Distribution
Rectangular Frame, case I, 37; case II . ....
4. Effect of Slip in Connections of A2 upon Distribution
Rectangular Frame . . . . . . . . . . .
5. Effect of Slip in Connections of A2 upon Distribution
Rectangular Frame .. . . . . . . . .
6. Effect of Slip in Connections of A6 upon Distribution
Rectangular Frame . . . . . . . . . . .
7. Effect of Slip in Connections of A6 upon Distribution
Rectangular Frame . . . . . . . . . . .
PAGE
. 14
qM
Moments
Moments
Moments
Moments
Moments
in
in
in
. 46
in
. 52
in
. . . . 53
8. Comparison of Effects of Slips in Connections upon Moments in Rec
tangular Frames . . . . . . . . . . . . . . . . .
in
TESTS TO DETERMINE THE RIGIDITY OF RIVETED
JOINTS OF STEEL STRUCTURES
I. INTRODUCTION
1. Object of Tests.The object of these tests was to determine
the rigidity of riveted joints which connect the members of steel
framed structures.
If the geometrical elemnent of a frame is a triangle, the members
may be joined with frictionless hinges and the frame will resist ex
ternal forces. If, however, the geometrical element of a frame is
a rectangle, shear in the frame due to external loads produces turning
moments on the connections, and in order to prevent the frame from
collapsing the connection must be designed to resist moment. The
distribution of the stresses in a rectangular frame depends upon the
rigidity of the connections. In analyzing the stresses in such a frame
it is customary to assume that the connections are perfectly rigid. If
the connections are not perfectly rigid, it is apparent that the actual
stress may not be equal to the computed stress. In addition to de
termining the rigidity of riveted connections, analyses have been
made to determine the effect of lack of rigidity upon the distribution
of stresses in a frame.
Although there are other structures in which the rigidity of
the connections affects the distribution of the stresses, the discussion
in this bulletin is limited to a discussion of the effect of the rigidity
FIG. 1. DIAGRAM OF DEFORMATION OF RECTANGULAR FRAME
of connections upon the distribution of the stresses in a rectangular
frame subjected to shear (Fig. 1). The most important example of
this type of frame is the wind brace in steel skeleton buildings.
i
ILLINOIS ENGINEERING EXPERIMENT STATION
2. Acknowledgments.The tests described in this bulletin were
made under the general supervision of Dr. F. H. Newell, head of the
Department of Civil Engineering, and of Dr. A. N. Talbot, head of
the Department of Theoretical and Applied Mechanics. The tests
formed a part of the regular research 'work of these Departments.
The specimens designated as Al, A2, and A3 were donated by
the American Bridge Company.
Camillo Weiss, Research Fellow in Civil Engineering, Bernard
Pepinsky, Research Fellow in Theoretical and Applied Mechanics,
and W. L. Parish, Graduate Student in Architectural Engineering,
rendered valuable serviee by assisting with the tests and with the cal
culations.
FIG. 2. TEST PIECE Al
THE RIGIDITY OF RIVETED JOINTS OF STEEL STRUCTURES 9
FIG. 3. TEST PIECE AZ
Tw5
0
S
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a
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FIG. 4. TEST PIECE A3
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10 ILLINOIS ENGINEERING EXPERIMENT STATION
FIG. 5. TEST PIECE 44
FIG. 6. TEST PIECE A
THE RIGIDITY OF RIVETED JOINTS OF STEEL STRUCTURES
FIG. 7. TEST PIECE A6
II. DESCRIPTION OF TESTS
3. Description of Test Pieces.The test pieces are shown in
Figs. 2 to 7, inclusive. Two pieces of each type were used, tests on
similar pieces being made simultaneously.
In selecting the test pieces it was the aim to use connections of
types which are common in engineering structures and which resist
loads and moments by methods which are fundamentally different.
Test pieces Al and A2 are types of connections used when the mo
ment to be resisted is large; A4 is a type used when the moment is
comparatively small and when the center lines of the columns and
girdles do not intersect; A3, A5, and A6 are designed primarily to
resist shear and are not intended to resist moment. For all speci
mens except Al, relative rotation between the columns and girders can
occur by virtue of the deflection of a comparatively thin member in
crossbending. In the case of A3, for example, the portion of the
vertical leg of the top lug angle between the lower rivet and the
horizontal leg of the lug angle acts as a cantilever, and by bending
the vertical leg the angle pulls away from the column. In a similar
manner for A2, A4, A5, and A6, bending of the outstanding legs of
the connection angles permits the girders to rotate relatively to the
12 ILLINOIS ENGINEERING EXPERIMENT STATION
columns. The connection of test piece Al permits rotation of the
girder relative to the column only by virtue of the axial strain in the
metal or by virtue of the slip of the rivets.
Rivets which are usually driven in the shop were driven with
a press riveter; rivets which are usually driven in the field were driv
en with an air gun. Test pieces Al, A2, and A3 were fabricated by
the American Bridge Company; test pieces A4, A5, and A6 were fab
ricated by the Burr Company of Champaign, Illinois. The Ibeams
of A3 were used in making A4 and A6, and the girders and columns
of A2 were used in making A5. The rotation of the girders relative
to the columns in A4, A5, and A6 was due to the strain in the con
nection angles, and these connection angles had not been previously
stressed. It is therefore improbable that the rotation of the girders
relative to the columns in A4, A5, and A6 was affected in any way by
the fact that the main members of which the test pieces were com
posed had been stressed as members of pieces A2 and A3.
The structural details of the girders and columns of the test
pieces are given in Table 1.
THE RIGIDITY OF RIVETED JOINTS OF STEEL STRUCTURES
0
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ILLINOIS ENGINEERING EXPERIMENT STATION
TABLE 1
PROPERTIES OF COLUMNS AND GIRDERS
For Frame 15 Feet High and
Column Girder 20 Feet Wide. K =for
I
Test Girder, nK = for Column
Piece I for I for
Section Gross Section Gross
Section s Section ss K (for col.) K (for girder) n
Al 1Pl14x% 584 1P 24x% 1966 3.25 8.20 .4
4 Ls5x3x % 4 Ls5x3x%
A2 Same as Al 584 Same as Al 1966 3.25 8.20 .4
A3 12"131.5 215.8 12131.5 215.8 1.20 .90 1.33
A4 12" FlatI31.5 9.5 12131.5 215.8 .05 .90 .055
A5 Same as Al 584 Same as Al 1966 3.25 8.20 .4
A6 8"H39 139.5 12131.5 215.8 .78 .90 .86
4. Apparatus and Methods of Testing.The test pieces de
scribed were tested in pairs in a 300,000pound Olsen fourscrew
testing machine. Fig. 8 shows the arrangement of a pair of test
specimens, and Fig. 9 is a reproduction of a photograph of a pair of
test specimens in the machine. The column of each test specimen
was supported by a halfround piece of steel, F and J, (Fig. 8) which
in turn was supported by the table of the testing machine. Tie rods
at the bottom T, T, and a strut at the top, S, S, held the test pieces
in the position shown. Load was applied by the crosshead of the
testing machine through rollers, G and H, to the ends of the beams.
The halfround bearings, F and J, the knifeedge ends of the strut,
S, S, the flexibility of the long, slender tie rods, T, T, and the rollers,
G and H, permitted free rotation of the specimens and insured an
equal distribution of load between the two specimens.
The strain measurements include the rotation of the beam relative
to the column, the slip of rivets, and the deformation of angles used
in making the joint. The rotation of a beam with respect to a column
was measured by determining for one or more points the change of
slope of the beam with respect to the column and then comparing
this change of slope with the change in slope due to elastic strain.
The apparatus for measuring this change of slope is shown in Fig.
8. The arm, OE, is rigidly attached at 0, the junction of the axis
of the beam with the axis of the column, and the arm, AD, is attached
LU
FIG. 9. GENERAL VIEW OF TEST PIECES Al IN TESTING MACHINE
;;
THE RIGIDITY OF RIVETED JOINTS OF STEEL STRUCTURES
rigidly at A, some point on the neutral axis of the beam. AD and
OE are equal in length. If no rotation of A with respect to 0 takes
place, the ends D and E will remain a constant distance apart, but
if rotation does take place, the change of distance between D and E
will be a measure of this rotation, and if the magnitude of this change
of distance is denoted by AS, the angle of rotation is denoted by 0,
and the length of arm by q, then tan0
The motion of D with respect to E is measured by means of a
micrometer fastened at E. This micrometer consists of a drum one
inch in circumference carrying a pointer moving over a dial. Around
the drum is wound a No. 36 insulated copper wire kept taut by a
weight and fastened at D. The motion of the pointer over the dial
indicates the magnitude of movement of D with respect to E.* A
similar apparatus is used to measure the rotation of points in the
column. The arms carrying the dials are clamped to the webs of
the beams, or the columns, with bolts and pipe fittings as shown in
Fig. 8. Slip of rivets, change of form of connecting angles, and
other small deformations were measured by means of strain gages
and attached micrometer dials. f Figs. 10 to 15, inclusive, show the
location of the instruments for measuring changes of slope on the
specimens.
*For a more detailed description of the wirewound dial micrometer see Proc. A. S.
T. M., p. 607, 1907.
tFor a description of the strain gage and directions for its use see "Tests of Re
inforced Concrete Buildings under Load," Univ. of Ill., Eng. Exp. Sta., Bul. 64, 1918.
and Proc. A. S. T. M., p. 1019, 1913.
ILLINOIS ENGINEERING EXPERIMENT STATION
Ei
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0
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0
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4
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H
z
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THE RIGIDITY OF RIVETED JOINTS OF STEEL STRUCTURES
ILLINOIS ENGINEERING EXPERIMENT STATION
THE RIGIDITY OF RIVETED JOINTS OF STEEL STRUCTURES
1f I
22 ILLINOIS ENGINEERING EXPERIMENT STATION 
THE RIGIDITY OF RIVETED JOINTS OF STEEL STRUCTURES
ILLINOIS ENGINEERING EXPERIMENT STATION
III. DISCUSSION OF RESULTS
5. Definition of Slip.It is customary in analyzing the stresses
in a stiff structure to assume that the connections are perfectly rigid.
This assumption is equivalent to saying that if tangents are drawn
to the elastic curves of two intersecting members at the point where
the curves intersect, these tangents do not rotate relatively to each
other when the connection is stressed. If the tangents to the elastic
curves at their point of intersection rotate relatively to each other,
the connection is said to slip.
It is also customary in analyzing the stresses in a stiff structure
to consider that where a column and girder intersect, both members
maintain a constant crosssection up to the point of intersection of
the elastic curves of the members, a condition impossible to obtain
exactly, except for members having a width of zero.
If a column or a girder is subjected to flexure, a point in the
elastic curve rotates relatively to other points in the elastic curve by
virtue of the strain in the material even if the material is continuous.
For this reason, when the connection between a column and a girder
is subjected to a moment, a point in the elastic curve of the column
rotates relatively to the point of intersection of the elastic curves of
the two members. Similarly a point in the elastic curve of a girder
rotates relatively to the point of intersection of the elastic curves of
the two members; therefore the rotation of a point in the elastic curve
of the girder relative to a point in the elastic curve of the column
may be due partly to the slip in the joint and partly to the strain in
the material. In determining the slip in the connections from the
tests, the computed rotation of a point in the girder relative to a
point in the column due to the strain in the material was subtracted
from the measured rotation of one point relative to the other. In
computing the relative rotation of the two points due to the strain
of the material both members were considered as having constant
crosssections up to the point where the elastic curves of the two
members intersect; thus what is really obtained in the analysis is not
the error due to slip alone but rather the combined error resulting
from two assumptions, one that the connection is perfectly rigid, and
the other that both members maintain a constant crosssection up to
the point of intersection of the two elastic curves.
THE RIGIDITY OF RIVETED JOINTS OF STEEL STRUCTURES
The rotation of a point in the elastic curve of a member relative
to another point in the elastic curve of the same member due to the
strain of the material can be determined from the following propo
sition: For a member in flexure the change in slope between two
points in the elastic curve of the member is equal to the area of the
M
E diagram for the portion of the member between the two points.
6. The Effect of the Slip in Connections upon a Rectangular
Frame.Fig. 16 represents a rectangular frame subjected to a shear
9
FIG. 16. DIAGRAM OF RECTANGULAR FRAME WITH PIN JOINTS
parallel with one side of the frame. If the connections at the corners
of the frame are frictionless hinges, the frame will collapse as shown
by the dotted lines. If, however, the connections at the corners are
capable of resisting a moment, the frame will take the form shown in
Fig. 1. The rigid connections between the vertical and horizontal
members hold the ends of the vertical members in a nearly vertical
position and thus prevent the frame from collapsing.
If the connections at the corners of the frame represented by
Fig. 1 are not rigid but permit the vertical members to rotate slightly
relatively to the horizontal members, because of the slip in the con
nections, a vertical member will be deflected from a vertical through
its lower end more than if the connections are perfectly rigid. When
all the connections slip, moreover, by the same angular amount, the
stresses in the frame are the same as when all the connections are
perfectly rigid;* but if the angular slip is greater in one or more
connections than in the other connections, the stresses in the frame
* See page 80.
ti;
/
I/
ILLINOIS ENGINEERING EXPERIMENT STATION
are not the same as when all the connections are perfectly rigid, that
is, slip in the connections of a rectangular frame increases the de
flection of the frame and, unless all connections slip by the same
amount, makes the stresses in the frame different from the stresses
in a similar frame having rigid connections.
7. Method of Determining the Magnitude of the Change in the
Deflection and in the Distribution of the Stresses in a Rectangular
Frame Due to Slip in the Connections.In order to determine the
magnitude of the change in the deflection and in the distribution of
the stresses in a rectangular frame due to slip in the connections, the
following formulas are derived:
Let
MAB = moment at A in member AB.
OA = change in slope of the elastic curve of the member
at the point A.
0B = change in slope of the elastic curve of the member
at the point B.
d
R 1
d = deflection of one end of the member relative to the
other end, measured in a direction normal to the
original position of the member.
I = length of the member in inches.
E = modulus of elasticity of the material.
K I moment of inertia for the member.
I length
It has been proved that the moment at the end A of the member
AB, Fig. 1, is given by the equation *
MA 2EK (20A+OB3R) . . . . (1)
The moment at the end of a member may be expressed in terms of
the changes in the slopes of the ends of the member and the deflection
of one end of the member relative to the other end.
I
If the frame has perfectly rigid connections, and  for A B and
C D is represented by K, and  for A D and B C by nK, then, from
equation (1)
*See "Wind Stresses in the Steel Frames of Office Buildings," Univ. of Ill. Eng.
Exp. Sta., Bul. 80. Equation A, p. 13, 1915.
THE RIGIDITY OF RIVETED JOINTS OF STEEL STRUCTURES
MAB = 2 E K 2 0A + 0B  (3R 0)] . . (2)
MA=D 2 E nK 3 0A +  3R]. . . . . (3)
Mo= 2 E K [ 20, + c  (3R = 0) ] (4)
MDA = 2 E nK[ 20 + A  3R] . . . . . (5)
The point A is in equilibrium; therefore MAB + MAD = 0,
and likewise M DA + MDc = 0. Since the frame is symmetrical
about a vertical center line, the sum of the moments at the top and
at the bottom of AD is equal to onehalf of the shear in the frame
multiplied by the height of the frame, that is,
Ph
MAD+ MDA + 2 = 0 . ........ (6)
Equating the right hand members of equations (2) and (3) gives
20(1 +n) + OB + nO, 3nR = 0 . . . . . . (7)
Likewise from equations (4) and (5)
20D(1+ n) +Oc +nOA3nRn= .. 0 .. . ... . (8)
From the conditions assumed, 0. = OA and Oc = OD.
Substituting these values of 0, and 0c in equations (7) and
(8) gives.
0A (3+2n) + n0 3nR =0 . . . . . . .. (9)
nOA + OD (3 + 2n)3nR=0 . . . . . . .. (10)
Substituting the values of MAD and MDA from equations (3) and
(5) in equation (6) gives
OA +,B=2R 1 (11)
12 E nK
Solving equations (9), (10), and (11) for OA, 0D, and R gives
1 Ph
OA 24 EK . . . . . . . . . . . . (12)
1 Ph
OD * . ........ (13)
N  24 EK (13)
1 Ph 1
R  (1+) ...... ... (14)
24 EK n
ILLINOIS ENGINEERING EXPERIMENT STATION
Substituting these values of 0,, OD, and R in equations (2) and
(4) gives
MA =l 1/4 Ph . . . . . . . . . (15)
Mac = 1/4 Ph . ........ (16)
Assuming that each member maintains a constant section up
to the neutral axis of the member which it intersects, equations (14),
(15), and (16) give the deflection and the moments in the frame
when the connections are perfectly rigid.
FIG 17. DIAGRAM OF RECTANGULAR FRAME WITH SLIP AT JOINTS
Consider now a rectangular frame having connections which
slip. Such a frame is represented by Fig. 17. The changes in the
slopes at the ends of the member AB are represented by 0A at A
and GB at B; likewise for the member CD the change in slope at C
is represented by Oc and at D by 0,, for the member AD the
change in slope at A is represented by 0E and at D by O6, and for
the member BC the change of slope at B is represented by 0, and
at C by OG, that is, the angular slip at A equalt 0E  OA, the an
gular slip at B equals 0p  Os, the angular slip at C equals 0G
 0c, and the angular slip at D equals 0,  O0D.
I I
RepresentT for AB and CD by K, and for AD and BC by nK.
Applying equation (1),* equating the sum of the moments at each
of the points A, B, C, and D to zero, and equating the sums of the
moments at the ends of the two members AD and BC to zero gives
*The presence of slip does not invalidate equation (1).
THE RIGIDITY OF RIVETED JOINTS OF STEEL STRUCTURES
2EK (20A + OB)) +2EnK (20s + 3R) = 0 . . (17)
2EK (20B + OA ) +2EnK(20, + O03R) =0 . . (18)
2EK (20c + OD ) 2.EnK (20, + 0, 3R) ==0 . (19)
2EK (20, + 0 ) + 2EnK (2 0,+ OE  3R) = 0 . . (20)
2 EnK (20E + 0,  3R + 20, + 0,  3R + 20, + 0o
 3R + 20 + 0,3R) + Ph= 0. . . . . .. . (21)
Letting A represent the quantity, slip at A divided by R, and
letting B, C, and D represent the corresponding quantities at the
points B, C, and D, respectively, gives
R R
=O OF
0 R
C  0 O
D= OH OD
= k  R
R R
Substituting the values of OE 0F~, 0o, and 0, from these equations
in the preceding equations gives
S(1 +n) + + =n (32AD) . . (22)
20 OA nO0
(l+n) +  + =n (32BD) . . (23)
20B OD flOB
S(1 + n) +  + = n (32CB) . . (24)
20D +,'nOt
R (1 + n) + + n =n (32DA) . . (25)
2EnKR 1/3 Ph
CA O R O  O R
+A + + 4 (A+B+C +D). (26)
These five equations contain four unknown angles and one un
known deflection. Solving these equations and substituting the values
for the 0 's and R in the expressions for the moments gives
ILLINOIS ENGINEERING EXPERIMENT STATION
1 Ph
3 4(A+B+C+D)
n:(6A +3B9)+n(16A+5B+4C+5D30)+(6A+3D9) (27)
1 (n+3) (3n+1)
1 Ph
MDA= 4(A+B+C+D)
an(6D+3C9)+n(16D+5C+4B+5A30) + (6D+3A9)] (28)
1n ± (n + 3) (3n+l 1)
M 1 Ph
Bc 3 4(A+B+C+D)
n2(6B+3A 9)+n(16B+5A+4D+5C30)+(6B+3C9) (29)
[n 9 (n+3) (3n+1)  9)
M 1 Ph
UcB 3 4(A+B+C+D)
In2(6C+3D9)+n(16C+5D+4A+5B30)+(6C+3B9) (30)
[ (n+3) (3n+l) 1
The values of OA, OB, Oc, and 6D, determined from equations
R R R R
(22) to (25) substituted in equation (26) give
1 1 (n + 1)
R= (RA+RB+RC+RD)+ Ph EnK (31)
In this equation RA, RB, RC, and RD represent the slips in the con
nections at A, B, C, and D, respectively. If the slips are measured,
R can be computed from equation (31). Knowing R and the slip,
the values of A, B, C, and D can be computed. Substituting the
values of A, B, C, and D in equations (11) to (14), inclusive, the
moments in a frame having connections which are not rigid can be
determined.
A comparison of the moments given by equations (27) to (30)
with the moments in a similar frame having rigid connections, de
termined by equations (15) and (16), will give the changes in the
moments due to the slip in the connections. A comparison of the de
flection of the frame, as given by equation (31), with the deflection
in a similar frame having rigid connections, as given by equation
(14), will give the change in the deflection due to the slip in the
connections.
THE RIGIDITY OF RIVETED JOINTS OF STEEL STRUCTURES
If A, B, C, and D of equations (27) to (30), inclusive, are equal
to each other, that is, if the slips in all the connections of the rec
tangular frame represented by Fig. 17 are equal, equations (27) to
(30) reduce to the following forms:
MAD 1/4 Ph ......... . (27a)
MDA = 1/4 Ph . . . . . . . . . . (28a)
Mc= 1/4Ph . . . . . . . . . . (29a)
MO = 1/4 Ph . . . . . . . . . . (30a)
These moments are the same as the moments given by equations
(15) and (16).
That is, if the slips in all the connections of the rectangular
frame shown in Fig. 17 are equal, the stresses in the frame are the
same as they are in a similar frame having connections which are per
fectly rigid.
8. Graphic Records.The quantities measured in the tests
are recorded graphically in Figs. 20 to 25. In these diagrams, meas
ured quantities are represented by full lines, and computed quan
tities by broken lines.
9. Strength of Test Pieces.An engineer is interested in the
rigidity of a connection at usual working stresses or at stresses
slightly higher. In computing the allowable working loads upon
the test pieces the following unit stresses were used:
Axial bending stress . . . 16,000 pounds per square inch.
Shear on rivets . . . . 12,000 pounds per square inch.
Bearing on rivets . . .. 24,000 pounds per square inch.
The computed working loads are given in Column 3 of Table 2.
Methods of computing the working loads' on connections of the types
used in the test pieces have not been standardized. The methods
used in computing the working loads given in Table 2 are as follows:
ILLINOIS ENGINEERING EXPERIMENT STATION
TABLE 2
LOADS ON TEST PIECES
Load at T Load at Moment
T Failure Working rTimes Failure on
Test on One Load Working Divided Connection Manner of Failure
Piece Girder Lb. I Load
Pece Girder Lb.1 L by Working at Failure
Lb. Load In. Lb.
(1) (2) (3) (4) (5) , (6) (7)
Al 44,450 17,500 26,250 2.54 5,334,000 Column buckled
A2 37,500 18,540 27,800 2.02 4,500,000 Gusset plate buckled
A3 10,250 3,030 4,545 3.38 537,000 Lug angle opened
Column buckled and
A4 13,550 5,000 7,500 2.71 570,000 angle opened
Connection angle
A5 19,000 3,400 5,100 5.59 1,860,000 opened. Rivet failed
in tension
A6 11,250 2,750 4,125 4.10 506,000 Conne dangles
1 Based upon the following unit stresses:
Axial bending stress, 16,000 lb;. per sq. in.
Shear on rivets, 12,000 " " " "
Bearing, Rivets, 24,000 " " " "
2 Corresponding to allowable working stresses for wind loads.
Al.The strength of the connection of test piece Al to resist
moment is considered to be the moment of a couple composed of two
horizontal forces, one force is applied at the centroid of each flange;
the magnitude of each force is the working strength in bearing of
the eleven rivets connecting each flange of the girder to the gusset
plate. The working load on the girder is the load which applied at
the outer end of the girder produces the given moment on a vertical
section through the outer row of rivets in the gusset plate. The
vertical shear is considered to be taken by the vertical splice plates
connecting the girder web to the gusset plate.
A2.The working load for test piece A2 was determined in the
same manner as for test piece Al.
A3.The strength of the connection of test piece A3 to resist
moment is considered to be the moment of a couple composed of two
horizontal forces; one force is applied at.the top surface of the girder
and the other at the bottom surface of the girder. The magnitude
of each force is the working strength in shear of the two rivets con
necting the lug angle to the girder. The working load on the girder
THE RIGIDITY OF RIVETED JOINTS OF STEEL STRUCTURES
is the load which applied at the outer end of the girder produces the
given moment on a vertical section through the rivets connecting
the lug angles to the girder.
A4.The strength of the connection of test piece A4 to resist
moment is determined by the same method as for test piece A3. The
working load on the girder is the load which applied at the outer end
of the girder produces the given moment on a vertical section through
the middle rivet connecting the lug angle to the girder.
A5.If the strength of the connection of test piece A5 to resist
moment is regarded as determined by the strength to resist moment
of the rivets attaching the connection angles to the girder, if the
outer rivet at each end of the connection angles is considered to be
in double shear, if the strength of the intermediate rivets is con
sidered as determined by bearing on the web plate of the girder, re
duced onethird for the loose fill, and if the stress in the rivets varies
as the distance from the center of gravity of all the rivets, the work
ing load on the girder is the load which applied at the outer end of
the girder produces the given moment on a vertical section through
the rivets attaching the connection angles to the girder. The vertical
stress upon the rivets is neglected.
A6.Consider the strength of the connection of test piece A6 to
resist moment to be determined by the strength of the rivets attach
ing the connection angles to the girder web, consider the stress on
each rivet due to moment to vary as the distance from that rivet to
the center of gravity of all the rivets, and consider the vertical shear
to be evenly distributed over all the rivets. The working load upon
the girder is the load which applied at the outer end of the girder
produces on a vertical section through the center of gravity of the
rivets attaching the connection angles to the girder web a moment
equal to the resisting moments of the rivets.
The unit stresses which have been used in determining the work
ing loads on the girders as given in Column 3 of Table 2 are the
usual allowable working stresses due to dead and to live loads. This
type of connections for the test pieces is used largely for building
frames in which the bending stresses are due to wind loads. When
wind load stresses are combined with dead and live load stresses, the
allowable working stresses are usually fifty per cent greater than
the allowable working stresses for dead and live loads alone. In dis
cussing the results of the tests, loads one and onehalf times the work
ing loads for dead and live loads alone, corresponding to wind load
ILLINOIS ENGINEERING EXPERIMENT STATION
working stresses, are used. These loads are given in Column 4 of
Table 2.
10. Interpretation of Results.For the curves of Figs. 20 to 25,
the relation of the deviation of the full lines from the dotted lines
to the deviation of the dotted lines from the vertical axis, that is, the
relation of the slip to the elastic strain, is meaningless inasmuch as
the direction of the dotted line, or the magnitude of the elastic strain,
is dependent upon the distances of the points A, B, and C from 0,
Fig. 8. In order to determine the practical significance of the slip
in the analysis of the wind stresses in the frame of an office building,
the deflection and the stresses in a rectangular frame were computed
for the case in which the connections are assumed to be perfectly
rigid and for the case in which the connections slip by the amounts
determined in the test.
The change in the deflection and the change in the distribution
I
of the moments in a frame due to slip depend upon the 1 of the mem
bers of the frame, that is, they depend upon the lengths as well as
upon the sections of the members. In the discussion of the effect of slip,
a frame fifteen feet high and twenty feet long is considered. This frame
corresponds to average practice in office building construction.
The effect of slip upon the distribution of stresses in a rectan
gular frame depends upon differences in the slips rather than upon
the slips themselves. If more specimens had been tested, it is prob
able that greater differences might have been found in slips than
in the slips obtained from the two specimens of each type tested.
This fact must be kept in mind in considering the interpretation of
the results.
Two methods have been used in interpreting the results of the
tests. In Sections 11 to 16, the stresses were determined in a rec
tangular frame for which the slips in the connections were taken
equal to the slips corresponding to the loads given in Column 4 of
Table 2, as measured in the tests. In Section 17 the stresses were
determined in a rectangular frame for which the slips in two con
nections were taken equal to the maximum slip corresponding to the
loads given in Column 4 of Table 2 as measured, and the slips in the
other two connections were taken equal to onehalf of the maximum
slip. In other words, the differences in the slips were taken equal to
onehalf of the maximum measured slip.
THE RIGIDITY OF RIVETED JOINTS OF STEEL STRUCTURES
The interpretation of the results in Sections 11 to 17, inclusive,
are therefore based upon arbitrarily fixed conditions, and that fact
must be kept in mind in considering the interpretations presented.
11. Test Piece Al.The angular strains for test piece Al are
shown graphically in Fig. 20. The strain measured by dial UN8
should equal the sum of the strains measured by dials N4 and UN1.
A similar relation exists between the strains measured by dials LN8,
N4, and LN1; US8, S4, and US1; and LS8, 84, and LS1. These
quantities which should be equal are approximately equal, indicating
that the angular strains as measured are at least reasonably accurate.
The fact that the observed quantities for UN8, LN8, US8, and LS8
are on smooth curves and the fact that the curves are so nearly alike
are additional reasons for believing that the angular strains meas
ured by these dials are reasonably accurate. The discussion which
follows is based upon the angular strains as measured by dials UNS,
LN8, US8, and LS8.
In Fig. 20, comparing the full line curves with the brokenline
curves, it is apparent that for small loads the angular strain of C
and B relative to A (Fig. 8), as measured and as computed, agree
very closely, but that as the load increases, the difference between
the measured and the computed strains increases very rapidly.
If the slip corresponds to a load one and onehalf times the usual
working dead and live loads, the load, as given in Column 4 of Table
2, is 26,250 pounds. Reading from the curves of Fig. 20, the slip
measured in radians, that is, the quantities represented by the hori
zontal distances between the full lines and the broken lines, corre
sponding to a load of 26,250 pounds are .0010 for UN8, .0013 for LN8,
and .0025 for US8 and LS8. The properties of the columns and
girders are given in Table 1.
A load of 26,250 pounds on the end of a girder, as tested, pro
duces a moment of 3,150,000 inchpounds on the connection between
the column and the girder. With a rectangular frame subjected
to a shear as shown in Fig. 1, if the moment on each connection is
3,150,000 inchpounds, since the total shear on the frame times the
height of the frame equals the sum of the moments on all four con
nections, Ph = 4 x 3,150,000 = 12,600,000 inchpounds.
From the tests the slips in the connections due to a load upon the
girder of 26,250 pounds as measured by dials UN8, LN8, US8, and
LS8 and as given previously are .0010, .0013, .0025, and .0025. These
ILLINOIS ENGINEERING EXPERIMENT STATION
quantities correspond to RA, RB, RC, and RD of equation (31).
From Table 1:
K = 8.2
nK = 3.25
n = .4
B = 1/4 [.0073 .0302 =.009375.
d = 180 X .009375 = 1.688 inches, horizontal deflection of
the top of the frame relative to the bottom.
If all the connections are perfectly rigid,
R = 1/4 X .0302 = .0075, and
d = 180 X .0075 = 1.35 inches.
The increase in the deflection of the columns from the vertical
due to the slip is therefore 1.688  1.350 = .338 inches, or 25 per
cent.
Referring to Equation (31), d, the horizontal deflection of the
frame which equals R X 1, is made up of two quantities, one quantity
contains the slip in the connections and the other quantity contains
n and K. The first quantity is the deflection due to slip; the second
quantity is the deflection due to the elastic strain of the material. The
first quantity is independent of the sections of the members; the sec
ond quantity decreases as both n and K increase. The actual deflection
of a frame due to slip in the connections is, therefore, independent of
the K's of the members, but the ratio of the deflection due to slip in
the connections to the deflection due to the elastic strain of the ma
terial increases as the K's of the members increase.
If the slips in all the connections are equal, the distribution of
the stresses is the same as if the connections were perfectly rigid.*
If the slips in the connections are not equal, the effect of the slip
upon the distribution of the moments depends upon the location of
the connections at which the different slips occur. The three follow
ing distributions of the slips have been considered:
Case I
RA = .0025, slip at A in radians
RB = .0025, slip at B in radians
RC= .0010, slip at C in radians
RD = .0013, slip at D in radians
* See page 30.
THE RIGIDITY OF RIVETED JOINTS OF STEEL STRUCTURES
Case II
RA = .0025, slip at A
RB = .0010, slip at B
RC = .0025, slip at C
RD = .0013, slip at D
radians
radians
radians.
radians
Case III
RA = .0025,
RB = .0010,
RC = .0013,
RD = .0025,
slip at A in
slip at B in
slip at C in
slip at D in
For Case I the large slips occur at the tops of the columns, for
Case II one large slip occurs at the top of one column, and the other
large slip occurs at the bottom of the other column, and for Case
III one large slip occurs at the top of one column, and the other large
slip at the bottom of the same column. The moments MaD, MDa,
Mac, and MCB, as given by equations (27) to (30), are given in
Table 3.
TABLE 3
EFFECT OF SLIP IN CONNECTIONS OF Al UPON DISTRIBUTION OF MOMENTS IN
RECTANGULAR FRAME
CASE I
K =8.2, n =.4 (See Table 2)
Moment Errorl
MAD =3,030,000 in. lb. 3.8 per cent
MDA =3,240,000 in. lb. +3.0 per cent
MBC =3,050,000 in. lb. 3.0 per cent
MCB =3,300,000 in. lb. +4.6 per cent
radians
radians
radians
radians
ILLINOIS ENGINEERING EXPERIMENT STATION
TABLE 3 (Continued)
CASE II
K = 8.2, n = .4 (See Table 2)
Moment
MAD =3,050,000 in. lb.
MDA =3,225,000 in. lb.
MBC =3,275,000 in. lb.
MCB =3,060,000 in. lb.
Error1
3.2 per cent
+2.0 per cent
+4.0 per cent
3.0 per cent
CASE III
MAD =2,980,000 in. lb.
MDA =2,978,000 in. lb
MBC =3,360,000 in. lb.
MCB =3,308,000 in. lb.
5.4 per cent
5.5 per cent
+6.8 per cent
+5.0 per cent
1 "Error" in this table means the difference between the moments determined from
equations (27) to (30) and the moments based upon the assumptions that the connections
are perfectly rigid and that each member maintains a constant section up to the neutral
axis of the member which it intersects.
It is apparent from Table 3 that for the frame considered the
slip does not materially affect the distribution of the stresses. It re
mains to determine the effect of the size of the section of the mem
bers upon the change in the distribution of the stresses resulting from
the slip. It is to be expected that slip in the connections of a rec
tangular frame will have a greater effect upon the distribution of
the stresses if the members of the frame are short and stiff than if
they are long and flexible. Consider a frame exactly like the one
for which the moments have been determined except that the I's
of the columns are changed. That is, n of equations (27) to (30) is
assigned different values. The moments in frames having values of
n equal to 1 and 2 were computed on the basis that the connections
are perfectly rigid, and also upon the basis that the slip is the same
as specified for Case I, Case II, and Case III (page 34). The dif
ferences in results obtained by the two methods are designated as the
errors due to the assumptions that the connections are perfectly
rigid and that each member maintains its section up to the axis of
the member which it intersects. The errors are represented graph
ically in Fig. 18.
THE RIGIDITY OF RIVETED JOINTS OF STEEL STRUCTURES
VALUE OF n K=8.2
FIG. 18. ERROR IN COMPUTATIONS FOR MOMENT IN FRAME WITH VARYING
VALUES OF n
ILLINOIS ENGINEERING EXPERIMENT STATION
In order to study further the effect of the stiffness of the mem
bers of a frame upon the error due to slip in the connections, the
moments were determined in frames for which the columns and the
k.
C
0
VALUE OF K n=1
FIG. 19. ERROR IN COMPUTATIONS FOR MOMENT IN FRAME WITH VARYING
VALUES OF K
THE RIGIDITY OF RIVETED JOINTS OF STEEL STRUCTURES
girders have the same values of K, that is, n is made equal to 1, and
for which K for both columns and girders has the values 4, 8, 12, and
16. The slips in the connections and the total moment upon the
frame were taken the same as in Case I, II, and III. The magnitude
of the errors due to slip is represented in Fig. 19.
It is apparent from Figs. 18 and 19 that in judging the serious
ness of the error in the moments in a frame due to slip in the con
nections, it is necessary to consider the K's of the members. The
girder of Al is about 8.5 per cent stronger in moment than the con
nection. The distances between columns of bents of officebuilding
frames are usually between fifteen feet and twentyfive feet. It,
therefore, seems that the value of K equaling 8.2 for the girder of
Al, corresponding to a distance between columns of twenty feet, is
as large as would be used in an office building in conjunction with
the connection of test piece Al.
The size of a column of an office building is usually determined
by the axial load rather than by the bending moment due to the wind
load. The relation between the axial stress in a column due to dead
and to live load and the bending stress in the column due to the wind
load depends upon many features of the building and is distinct for
each building.
Taking a position intermediate between the two extremes, a col
umn section consisting of one web plate 14 by 5/8, four flange angles
5 by 4 by 5/8 and two cover plates 14 by 11/8, having a moment of
inertia of 3006 in.4, was used at a point on the column where the
moment on the connection corresponded to a load of 26,250 pounds
3006 X 20
upon the girder of Al as tested. For this column n 6
1966 X 15
= 2. With K equal to 8.2 and n equal to 2, the maximum error is
in McB under Case I and is slightly less than 15 per cent.
In the tests, furthermore, the loads were so applied that slip
in a connection did not reduce the moment to which the connection
was subjected, whereas in engineering structures the moment is au
tomatically transferred from a connection which slips to the more
rigid connections. The addition to the moment on the more rigid
connections and the reduction of the moment on the less rigid con
nections tend to make the slip on all the connections more nearly
equal than in the ease of the specimens tested.
It seems, therefore, that the tests of the two specimens marked
Al support the following statement:
ILLINOIS ENGINEERING EXPERIMENT STATION
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FIG. 20. TEST RESULTS FOR TEST PIECE Al
NOTE.In Figs. 20 to 25 the location of the measurements is given by a combination of
letters and numbers. The letters refer to general location. U, upper side ; L, lower side;
N, north end; S, south nd; E, east side; W, west side. The numbers refer to the location
of the measurements on the test piece as shown by Figs. 10 to 15, inclusive.
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THE RIGIDITY OF RIVETED JOINTS OF STEEL STRUCTURES 43
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FIG. 21. TEST RESULTS FOR TEST PIECE A2
For rectangular frames having opposite sides alike, the assump
tions that the connections are perfectly rigid and that each member
maintains its section up to the neutral axis of the member to which
it is connected produce errors in the moments which are dependent
upon the stiffness of the members. The magnitude of the error de
pends upon the K's of all the members of the frame. For wind
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ILLINOIS ENGINEERING EXPERIMENT STATION
braces for office buildings the maximum error usually will be con
siderably less than 15 per cent.
12. Test Piece A2.Referring to Fig. 8, the slip in the con
nection which affects the stresses in a frame can be obtained from
the rotation of the points B and C relative to the point A. The ro
tation of B relative to A equals the rotation of B relative to 0 plus
the rotation of A relative to 0. Similarly, the rotation of C, relative
to A equals the rotation of C relative to 0 plus the rotation of A
relative to 0. Referring to Fig. 21, for the north specimen, the ro
tation of B relative to 0 is represented graphically by curve UN1,
A relative to 0 by curve N4, and C relative to 0 by curve LN1. For
the south specimen, the rotation of B relative to 0 is represented
graphically by curve US1, A relative to 0 by curve 84, and C rela
tive to 0 by curve LS1. The slip of B relative to A is represented
by the sum of the horizontal distances between the full lines and the
broken lines for curves UN1 and N4 for the north specimen, and by
the sum of the corresponding distances for curves US1 and S4 for
the south specimen. Similarly the slip of C relative to A is repre
sented by the sum of the horizontal distances between the full lines
and the broken lines of curves LN1 and N4 for the north specimen,
and by the sum of the corresponding distances for curves LS1 and
S4 for the south specimen.
With a load of 27,800 pounds on the girder (see Column 4,
Table 2), the rotation of B relative to A due to slip, obtained as out
lined previously, is .0018 for the north specimen and .002 for the
south specimen. The rotation of C relative to A due to slip is .0013
for the north specimen and .0014 for the south specimen. The dif
ferences between the slips for specimen A2 are only about 42 per
cent as great as the differences in the slips for Al, and the errors in
the moments based upon the assumption that the connections are per
fectly rigid are accordingly less for A2 than for Al.
The fact that the lower part of the connection is more rigid than
the upper part is due to the fact that the lower part is in compression
and the upper part is in tension. The lug angles of the connection
and the flange angles of the column are more rigid to resist com
pression than tension. If the frame represented by Fig. 1 has connec
tions like A2, the lug angles and flange angles are in compression for
connections at B and D and are in tension for connections at A and C.
In order to determine the error in the moments in a frame due
THE RIGIDITY OF RIVETED JOINTS OF STEEL STRUCTURES
to slip in the connections of the type used for A2, a, frame fifteen
feet high and twenty feet long with column and girder sections the
same as for specimens A2 was used. For a moment on each connec
tion corresponding to a load of 27,800 pounds on a girder as the speci
mens were tested, let the slip at A and C equal the average slips of
the two connections having lug angles in compression and let the
slip at B and D equal the average of the slips of the two connections
having the lug angles in tension. That is,
RC = RA ' 0018+ .0020 .0019, slips at A and C in radians.
2
RD B 013 .0014 .00135, slips at B and D in radians.
Ph = 4 X 27,800 X 120 = 13,350,000 inchpounds.
From Table 1,
K = 8.2 in.3
nK S 3.25 in.3
n= .4
Substituting these values in equations (27) to (30) gives the
moments in the frame. The moments and the errors due to slip are
given in Table 4.
TABLE 4
EFFECT OF SLIP IN CONNECTIONS OF A2 UPON DISTRIBUTION OF MOMENTS IN
RECTANGULAR FRAME
K =8.2, n =.4 (See Table 2.)
Moment
MAD =3,300,000 in. lb.
MDA =3,375,000 in. lb.
MBC = 3,375,000 in. lb.
MCB =3,300.000 in, lb.
Errorl
1 per cent
+1 per cent
+1 per cent
1 per cent
1"Error" in this table means the difference between the moments determined from
equations (27) to (30) and the moments based upon the assumptions that the connec
tions are perfectly rigid and that each member maintains a constant section up to the
neutral axis of the member which it intersects.
Comparing Table 4 with Table 3 it is apparent that with n =
.4 the maximum error in the moments due to slip is much less for
A2 than for Al.
ILLINOIS ENGINEERING EXPERIMENT STATION
The horizontal deflection of the frame with connections like the
connections used for A2 as given by equation (31) is 1.728 inches, of
which .288 inches or 20 per cent are due to the slip in the connections.
With n  2 and all other quantities the same as before, the mo
ments are as given in Table 5.
TABLE 5
EFFECT OF SLIP IN CONNECTIONS OF A2 UPON DISTRIBUTION OF MOMENTS IN
RECTANGULAR FRAME
K =8.2, n =2.0 (See Table 2.)
Moment Errorl
MAD =3,250,000 in. lb. 2.7 per cent
MDA =3,430,000 in. lb. +3 per cent
MBC =3,430,000 in. lb. +3 per cent
MCB =3,250,000 in. lb. 2.7 per cent
1 "Error" in this table means the difference between the moments determined from
equations (27) to (30) and the moments based upon the assumptions that the connections
are perfectly rigid and that each member maintains a constant section up to the neutral
axis of the member which it intersects.
Comparing Table 5 with Table 3, with n  2.0, the maximum
error in the moments due to slip is 3 per cent for A2; whereas the
corresponding error due to slip for Al is 9.5 per cent.
Although sufficient tests have not been made to justify a final
conclusion, the tests of the two specimens indicate that the type of
connection used for specimen A2 is more rigid than that used for Al.
The relation between moment and slip was, moreover, more nearly
the same for the two specimens A2 than for the two specimens Al.
Inasmuch as the strain for A2 was largely due to the elastic strain
of the material, a quantity independent of the workmanship of the
assembler, whereas the strain for Al was largely due to slip of rivets,
a quantity dependent upon the workmanship of the assembler, it is
reasonable to expect the connections of A2 to behave more consist
ently than the connections of Al. Since it is differences of slips rather
than absolute slips which affect the distribution of moments, slip of
the connections A2 will cause less error in the analysis of the stresses
than slip of the connections Al. With the type of connection used
for specimen A2, for frames of usual proportions, furthermore, the
assumptions that the connections are perfectly rigid and that a mem
ber maintains its section up to the neutral axis of the member to
which it is connected produce a very small error in the moments in
the frame.
THE RIGIDITY OF RIVETED JOINTS OF STEEL STRUCTURES
13. Test Piece A3.Referring to Fig. 22 the rotation of the
girder relative to the column is measured by dial N for the north
8100C
6POOC
,ooc
4,OOC
zpoc
4.C
6POC
p000
4,00C
?_0.C
doo
o, ooo
6,000
4,000
. 2,000
Aq
ý,/00o
"ooo
.,000
4000
11~r
...~~ _3 2 5 .= IM
S'I" J I '
1 1 1 1 ;LT ^ I I I ]III1^ ' I I IY l
L.3 1 ,3a , ,
z=(51:p ==^ = AE==Am=
^^~~~~~_ q_,: ^ ^:I:
S One D/lsion = 0.005 inrx h.5rn
8
U
I
/
A
the O/volor; = Goorrad&n C
/wnge of age
FIG. BB. TEST RESITLTS FOR TEST PIECE Af$
specimen and by dial S for the south specimen. The slips in the con
nections are measured by the horizontal distances between the full
line and the brokenline curves.
I
,,,,.
a
I






ILLINOIS ENGINEERING EXPERIMENT STATION
Referring to Table 2, one and onehalf times the working load
for usual dead and live load stresses is 4,545 pounds. From Fig. 22,
a load of 4545 pounds on a girder produces a slip in the connection
of .0028, the same for both specimens, as near as it is possible to read
from the curves. If the slips in all the connections of a frame are
6U1 2 L. .1 L. 2
10,000 LC J ..
50W
r _7_ I I I J
One wlision = 0.002 inch ets on
k 50  E# fr IL
FIG. 23. TES RESULTS FOR TEST PIECE A4
affect the dOne istribution of the0.00 rmoments,  a large slip in the conne
0teen feet high and twenty feet long made up of 12 inch31 1/2
Jo!0, J_L  1 VV+
One Dvision = 0.002 inch Defruwrlon
FIG. 23. TEST RESULTS FoR TEST PIECE A4
equal, the distribution of the moments is the same as if the connec
tions were perfectly rigid.
Although large equal slips in the connections of a frame do not
affect the distribution of the moments, a large slip in the connec
tions does seriously affect the stiffness of the frame. If a frame fif
teen feet high and twenty feet long made up of 12 inch 31 1/2
THE RIGIDITY OF RIVETED JOINTS OF STEEL STRUCTURES 49
pound Ibeams is joined with connections like the ones used for A3,
the horizontal deflection of the columns due to horizontal shear on
the frame producing a slip of .0028 in the connections, as given by
equation (31), is 1.260 inches, of which .672 inches or 53.4 per cent
are due to the slip in the connections.
14. Test Piece A4.Referring to Fig. 23, rotation of the girder
relative to the column is measured by dial N for the north specimen
and by dial S for the south specimen. The slips in the connections
are measured by the horizontal distances between the fullline and
the brokenline curves.
Referring to Table 2, one and onehalf times the working load
for usual dead and live load stresses is 7,500 pounds.
From Fig. 23, a load of 7,500 pounds on a girder produces a
slip in the connection of .00144 radians for the north specimen and
.00072 radians for the south specimen. In each case the angle given
is the slip between A and 0. The slip upon which the distribution
of the moments depends is the slip between A and B, and between A
and C. This slip was not determined for these specimens, and it is
therefore impossible to determine the effect of the slip upon the dis
tribution of the moments. Judging from the results of this test,
however, for connections which are apparently alike, a given moment
produces radically different slips in different connections, and the
distribution of the moment is therefore seriously affected by the slip
in the connections.
15. Test Piece A5.Referring to Fig. 24, rotation of the girder
relative to the column is measured by dials UN, LN, and N3 for the
north specimen, and by dials US, LS, and S3 for the south specimen.
The total slip in the connection for the upper part of the column is
the slip between B and 0 plus the slip between A and 0. This is
represented graphically by the sum of the horizontal distances be
tween the fullline and the brokenline curves for UN and N3. The
total slip in the connection for the lower part of the column is the
slip between C and 0 plus the slip between A and 0. This is repre
sented graphically by the sum of the horizontal distances between
the fullline and brokenline curves LN and N3.
Referring to Table 2, one and onehalf times the working load
for usual dead and live load stresses is 5,100 pounds. Referring to
Fig. 24, the slips in the connections for a load of 5,100 pounds are
ILLINOIS ENGINEERING EXPERIMENT STATION
5000
0
15,000
n000
n
4 o50C
I
NU
7m
2'
7'
7
LNW:
2
/
One DPi/
7
7
(
VE2 LNEi

I
I
UJ/ EZ L5E2
U
L I I I
_4T
'0/n = . Ub I/ncn .'rraln
S1 1
K
"i
7
2i

;.
jiiiiiIIi
One Divi/.ion = 0.002 rodian  Changqe of i/cpe
FIG. 24. TEST RESULTS FOR TEST PIECE A5
equal for all connections as nearly as can be determined from the
curves, but for larger loads the slip in the south specimen is a little
greater than in the north specimen. That is, although the connec
tions slip, the slips in the different connections at working loads arc
so nearly alike that the moment in a rectangular frame is distributed
almost exactly the same as it is when all the connections are per
fectly rigid.
To determine the effect of the slip in the connections upon the
horizontal deflection in a rectangular frame, consider a frame fifteen
feet high and twenty feet long having column and girder sections
and connections, like the ones used for A5. As determined from
equation (31) the deflection of the frame when the moment in each
connection equals the moment in the connection of A5 due to a load
LJW/ t/J / LSE/ 1/JE/ LN /
I LUI # F I a
i .....
i
i
2
<
i
1
JL UL I LY7Ir Y#VIl LII~ YL • #1.
6
?
PIZ 
>~
H
i
i
^
1
L
/Wi

/3
' ^'
UN LN L3 UV5 1N3 53
~ Y I 1 I I  1!I
Ij I J I ii y I  14 1 1 1 1
1 l 1 ! I 1 ,. .1 li 1 z l I i l
:u :=I 1 1 I F7=:=F:
,. ,.f r_ _ _ _ _ i _._ _ _ _ . _ _ _ _
THE RIGIDITY OF RIVETED JOINTS OF STEEL STRUCTURES
of 5,100 pounds is .339 inches of which .122 inches, or 36 per cent,
are due to slip in the connections.
16. Test Piece A6.Referring to Fig. 25, the rotation of the
10,000
5,006
C
So, ox
Iso,00
j One D/i,/lion = 0.000 inch fraln
N s
5000  119
0 i 1 T I I I I I 1 _ 1 1
.J One Div,7i1on = 0.02 rcd/an  Chanqe of 5/ope
FIG. 25. TEST RESULTS FOR TEST PIECE A6
girder relative to the column is measured by dial N for the north
specimen and by dial S for the south specimen. The slip is repre
sented graphically by the horizontal distance between the fullline
and the brokenline curves marked N, for the north specimen and by
the corresponding distance on the curves marked S, for the south
specimen.
From Table 2, one and onehalf times the working load for usual
dead and live load stresses is 4,125 pounds.
Referring to Fig. 25 for a load of 4,125 pounds on one girder
the slip in the connection for the north specimen is .0052 radians, and
the slip for the south specimen is .0033 radians.
Let a rectangular frame similar to Fig. 1, fifteen feet high
and twenty feet, long be made up of girders and columns having the
same section as the corresponding members of specimen A6 and
joined with the type of connection used for A6. If the average mo
LS W1 USlWIl LJE/ USE/ LNW' UINWI L/NE U/NE
One Dlivsion = 0.05 inch S.rain
LN'2 OL/iWV LVEZ L3E2 U/E2 LSW2 USE USVZ2
_ _ _ ,^ _ Q: _'*D _ _ _ S^^ _ _ _S^ fi'']^_0
ILLINOIS ENGINEERING EXPERIMENT STATION
ment at each connection of the frame is equal to the moment pro
duced in the connection of A6 due to a load of 4,125 pounds on one
girder, the quantity Ph = 743,000 inchpounds. Consider the slip
at A and D to be .0052 radians and at B and C to be .0033 radians.
K =.9
nK = .755
n = .86
Ph = 743,000 in. lb.
RA = .0052 slip at A in radians
RB = .0033 slip at B in radians
RC = .0033 slip at C in radians
RD = .0052 slip at D in radians
The horizontal deflection of the frame as given by equation (31)
is 1.211 inches of which .765 inches or 63 per cent are due to slip in
the connections.
The moments in the frame, as given by equations (27) to (30),
are given in Table 6.
TABLE 6
EFFECT OF SLIP IN CONNECTIONS OF A6 UPON DISTRIBUTION OF MOMENTS IN
RECTANGULAR FRAME
K = .9, a = .86 (see Table 2)
Moment Errorl
MAD = 150.000 in. lb. 19.4 per cent
MDA =150,000 in. lb. 19.4 per cent
MBC =222,000 in. lb. +19.4 per cent
MCB = 222,000 in. lb. +19.4 per cent
1"Error" in this table means the difference between the moments determined from
equations (27) to (30) and the moments based upon the assumptions that the connections
are perfectly rigid and that each member maintains a constant section up to the neutral
axis of the member which it intersects.
If the frame is 7.5 feet high and 10 feet long,
K = 1.8 in.3
nK = 1.55 in.3
n= .86
Ph = 743,000 in. lb.
RA = .0052 slip at A in radians
RB = .0033 slip at B in radians
BC = .0033 slip at C in radians
RD = .0052 slip at D in radians
THE RIGIDITY OF RIVETED JOINTS OF STEEL STRUCTURES 53
The horizontal deflection of the frame as given by equation (31)
is .495 inches of which .382 inches or 77 per cent are due to slip in the
connections.
The moments in the frame are given in Table 7.
TABLE 7
EFFECT OF SLIP IN CONNECTIONS OF A6 UPON DISTRIBUTION OF MOMENTS IN
RECTANGULAR FRAME
K= 1.8, n .86 (see Table 2)
Moment Errorl
MDA =113,000 in. lb. 39.0 per cent
MDA = 113,000 in. lb. 39.0 per cent
MBC =260,000 in. lb. +40.0 per cent
MCB =260,000 in. lb. +40.0 per cent
1"Error" in this table means the percentage of difference between the moment de
termined from equations (27) to (30) and the moments based upon the assumptions that
the connections are perfectly rigid and that each member maintains a constant section
up to the neutral axis of the member which it intersects.
17. Comparison of Results of Tests of Different Test Pieces.
Since the effect of slip in the connections upon the distribution of
the stresses in a rectangular frame depends upon quantities independ
ent of the type of connection used, in making any comparison of the
different types of connections certain quantities must be fixed arbi
trarily. It must be clearly borne in mind that the results of the
comparison are true only under the conditions specified. Analyses
of the effect of slip in the connections upon the stresses in a rectan
gular frame under certain arbitrary fixed conditions are presented
in Sections 10 to 15, inclusive. As a further study, the effect of slip
has been determined under the following arbitrarily fixed condi
tions:
(1) The moment on the connection is the moment due to a
load one and onehalf times the working load corresponding to usual
dead and live load stresses; that is, it is the moment to which the
connection would be subjected as a part of wind bracing. This load
is given in Column 4 of Table 2 and is repeated in Column 2 of
Table 8.
(2) The slips at A and B are taken equal to each other and
equal to the maximum slip measured at the load specified. The
ILLINOIS ENGINEERING EXPERIMENT STATION
slips at C and D are taken equal to each other and equal to one half
of the slips at A and B. Differences in slips rather than slips them
selves affect the distribution of the stresses in the frame. The arbi
trarily fixed differences in the slips are used rather than the dif
ferences obtained in the tests because it is considered that tests of
two specimens cannot be relied upon to bring out the differences in
the behavior of connections which are supposed to be identical. It is
only fair, however, to point out that for Al the differences in the
slips for the two specimens as determined by tests were a little great
er than onehalf the maximum slip; whereas for A2 the differences
in the slips were less than one half of the maximum slip as determined
by the tests.
(3) The K's of all members of the frame are taken equal to
10, that is, if the moment of inertia of the member is small the
member is short, whereas if the moment of inertia of the member is
large the member is long, a condition prevalent in structures.
The quantities used in the determination of the moments are
given in Columns 2 to 4 of Table 8; the moments in the frames are
given in Columns 5 and 6. The errors in the calculated moments
resulting from the slip, due to the assumptions that the connections
are perfectly rigid and that the member maintains its section up to
the neutral axis of the member to which it is connected, are given
in Column 7, all in Table 8.
From Column 7, Table 8, it is apparent that under the condi
tions assumed, the connections for specimens Al and A2 can, for the
purpose of analyzing stresses in a rectangular frame, be considered
perfectly rigid without introducing prohibitive error, but the con
nections for specimens A3, A4, A5, and A6, for the purpose of an
alyzing stresses, cannot be considered perfectly rigid.
The error due to slip cannot exceed one hundred per cent of the
computed moment. Errors greater than one hundred per cent given in
Column 8 of Table 8 were obtained because, for the conditions upon
which the error due to slip is based, slip in a connection is not con
sidered as reducing the moment which produces the slip. As a
matter of fact if a connection slips, the moment to which it is sub
jected is automatically transferred to other connections. The error
in a frame due to slip in the connections is therefore less than the
values given in Column 8 of Table 8, the difference between the true
error and the values given in Table 8 depending upon the size of
the error. The values given in Column 8 of Table 8 are therefore
THE RIGIDITY OF RIVETED JOINTS OF STEEL STRUCTURES
relative rather than actual errors. The actual errors are less than
the values given in the table.
TABLE 8
COMPARISON OF EFFECTS OF SLIPS IN CONNECTIONS UPON MOMENTS IN RECTANGU
LAR FRAMES
K=10, n=l.
Slip at A and B is maximum slip as determined by tests at a load corresponding to
one and onehalf times the usual dead and live working loads. Slip at 0 and D is taken
as onehalf of the slip at A and B.
Test 1.5 Times Slip at A Slip at C MAD =MBC MDA =MBC Errors Due PXh
iece Load RA =RB RC =RD in Lb. in Lb. to Slip in Lb.
Al 26,250 .0025 .00125 2,870,000 3,434,000 9 per cent 12,600,000
A2 27,800 .0020 .0010 3,095,000 3,560,000 7 per cent 13,300,000
A3 4,545 .0028 .0014 88,000 541,000 138 per cent 910,000
A4 7,500 .00144 .00072 161,000 483,300 50 per cent 1,290,000
A5 5,100 .0046 .0023 22,700 1,023,000 104 per cent 2,000,000
A6 4,125 .0052 .0026 439,000 805,000 435 per cent 742,000
18. Conclusions.The main object of these tests was to deter
mine whether serious error is introduced into computations for stress
es in steel frames by the assumption that the joints are perfectly
rigid.
The rigidity of various types of joints has been studied by means
of tests, and the error introduced into computations studied by means
of mathematical analysis of the action of frames with slip at the
joints of a magnitude such as was observed in these tests. The action
under a load producing stresses equal to one and onehalf times the
working stress has been taken as a criterion, and for the joints stud
ied the following conclusions reached:
Connections of the type used for specimens Al and A2 are so
rigid that for the purpose of analyzing stresses in rectangular frames
the connections can be considered as perfectly rigid without intro
ducing serious errors into the results.
The errors due to slip in the connections is less for A2 than for
Al.
Connections of the type used for specimens A3, A4, A5, and A6
for the purpose of analyzing stresses cannot be considered perfectly
rigid.
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Bulletin No. 71. Tests of Bond between Concrete and Steel, by Duff A. Abrams. 1913. One
dollar.
*Bulletin No. 7X. Magnetic and Other Properties of Electrolytic Iron Melted in Vacuo, by Trygve
D. Yensen. 1914. Forty cents.
Bulletin No. 73. Acoustics of Auditoriums, by F. R. Watson. 1914. Twenty cents.
*Bulletin No. 74. The Tractive Resistance of a 28Ton Electric Car, by Harold H. Dunn. 1914.
Twentyfive cents.
Bulletin No. 75. Thermal Properties of Steam, by G. A Goodenough. 1914. Thirtyfive cents.
Bulletin No. 76. The Analysis of Coal with Phenol as a Solvent, by S. W. Parr and H. F. Hadley.
1914. Twentyfive cents.
*Bulletin No. 77. The Effect of Boron upon the Magnetic and Other Properties of Electrolytic
Iron Melted in Vacuo, by Trygve D. Yensen. 1915. Ten cents.
*Bulletin No. 78. A Study of Boiler Losses, by A. P. Kratz. 1915. Thirtyfive cents.
*Bulletin No. 79. The Coking of Coal at Low Temperatures, with Special Reference to the Prop
erties and Composition of the Products, by S. W. Parr and H. L. Olin. 1915. Twentyfive cents.
*Bulletin No. 80. Wind Stresses in the Steel Frames of Office Buildings, by W. M. Wilson and
G. A. Maney. 1915. Fifty cents.
*Bulletin No. 81. Influence of Temperature on the Strength of Concrete, by A B. McDaniel.
1915. Fifteen cents.
Bulletin No. 82. Laboratory Tests of a Consolidation Locomotive, by E. C. Schmidt, J. M. Snod
grass, and R. B. Keller. 1915. Sixtyfive cents.
*Bulletin No. 83. Magnetic and Other Properties of IronSilicon Alloys. Melted in Vacuo, by
Trygve D. Yensen. 1915. Thirtyfive cents.
Bulletin No. 84. Tests of Reinforced Concrete Flat Slab Structure, by A. N. Talbot and W. A.
Slater. 1916. Sixtyfive cents.
*Bulletin No. 85. The Strength and Stiffness of Steel Under Biaxial Loading, by A. T. Becker.
1916. Thirtyfive cents.
*Bulletin No. 86. The Strength of IBeams and Girders, by Herbert F. Moore and W. M. Wilson.
1916. Thirty cents.
*Bulletin No. 87. Correction of Echoes in the Auditorium, University of Illinois, by F. R. Watson
and J. M. White. 1916. Fifteen cents.
Bulletin No. 88. Dry Preparation of Bituminous Coal at Illinois Mines, by E. A. Holbrook. 1916.
Seventy cents.
* A limited number of copies of bulletins starred is available for free distribution
60 PUBLICATIONS OF THE ENGINEERING EXPERIMENT STATION
*Bulletin No. 89. Specific Gravity Studies of Illinois Coal, by Merle L. Nebel. 1916. Thirty
cents.
*Bulletin No. 90. Some Graphical Solutions of Electric Railway Problems, by A. M. Buck. 1916.
Twenty cents.
*Bulletin No. 91. Subsidence Resulting from Mining, by L. E. Young and H. H. Stoek. 1916.
One dollar.
*Bulletin No. 92. The Tractive Resistance on Curves of a 28Ton Electric Car, by E. C. Schmidt
and H. H. Dunn. 1916. Twentyfive cents.
*Bulletin No. 98. A Preliminary Study of the Alloys of Chromium, Copper, and Nickel, by
D. F. McFarland and 0. E. Harder. 1916. Thirty cents.
*Bulletin No. 94. The Embrittling Action of Sodium Hydroxide on Soft Steel, by S. W. Parr
1917. Thirty cents.
*Bulletin No. 95. Magnetic and Other Properties of IronAluminum Alloys Melted in Vacuo, by
T. D. Yensen and W. A. Gatward. 1917. Twentyfive cents.
*Bulletin No. 96. The Effect of Mouthpieces on the Flow of Water Through a Submerged Short
Pipe, by Fred B. Seely. 1917. Twentyfive cents.
*Bulletin No. 97. Effects of Storage Upon the Properties of Coal, by S. W. Parr. 1917
Twenty cents.
*Bulletin No. 98. Tests of Oxyacetylene Welded Joints in Steel Plates, by Herbert F. Moore
1917. Ten cents.
Circular No. 4. The Economical Purchase and Use of Coal for Heating Homes, with Special
Reference to Conditions in Illinois. 1917. Ten cents.
*Bulletin No. 99. The Collapse of Short Thin Tubes, by A. P. Carman. 1917. Twenty cents
*Circular No. 5. The Utilization of Pyrite Occurring in Illinois Bituminous Coal, by E. A.
Holbrook. 1917. Twenty cents.
*Bulletin No. 100. Percentage of Extraction of Bituminous Coal with Special Reference to
Illinois Conditions, by C. M. Young. 1917.
*Bulletin No. 101. Comparative Tests of Six Sizes of Illinois Coal on a Mikado Locomotive, by
E. C. Schmidt, J. M. Snodgrass, and 0. S. Beyer, Jr. 1917. Fifty cents.
*Bulletin No. 102. A Study of the Heat Transmission of Building Materials, by A. C. Willard
and L. C. Lichty. 1917.
*Bulletin No. 108. An Investigation of Twist Drills, by Bruce W. Benedict and W. Penn Lukens.
1917.
*Bulletin No. 104. Tests to Determine the Rigidity of Riveted Joints of Steel Structures by
Wilbur M. Wilson and Herbert F. Moore. 1917. Twentyfive cents.
*A limited number of copies of bulletins starred is available for free distribution.
THE UNIVERSITY OF ILLINOIS
THE STATE UNIVERSITY
Urbana
EDMUND J. JAMES, Ph. D., LL. D., President
THE UNIVERSITY INCLUDES THE FOLLOWING DEPARTMENTS:
The Graduate School
The College of Liberal Arts nd Sciences (Ancient and Modern Languages and
; Literatures; History, Economics, Political Science, Sociology; Philosophy,
:. Psychology, Education; Mathematics; Astronomy; Geology; Physics;Chemistry;
Botany, Zoology, Entomology; Physiology; Art and Design)
The College of Commerce and Business Administration (General Business, Bank
ing, Insurance, Accountancy, Railway Administration Foreign Commerce;
Courses for Commercial Teachers and Commercialand Civic Secretaries)
The College of Engineering (Architecture; Architectural, Ceramic Civil, Electrical,
Mechanical, Miing, Municipal and Sanitary, and ailway Enginering)
The College of Agriculture (Agronomy; Animal Hsbandry Dairy Husbandry,
Horticulture and Landscape Gardening; Agricultural xtension; Teacher
Course; Household Science)
The College of Law (three years' course)
The School of Education
The Course In Journalism
The Courses in Chemistry and Chemical Engineering
The School of Railway Engineering and Administration
The School of Music (four years' course) 
The School of Library Science (two years' course)
The College of Medicine (in Chicago)
The College of Deti stry (in Chicag o)
The School of Pharsmacy (in Chicago; Ph. G. and Ph. C. courses)
The Summer Session (eight weeks
Experiment Stations and Selentific Bureaus: U. 8. Agricultural Experiment
Station; Engineering Experiment Statioi; State Laboratory of Natural His
toryi State Entoiologist's Office; Biological Experhnent Station on Illinois
kiver; State Water Survey; State Geological Survey; UT. S. Bureau of Mines
Experient Station.
The i lbrar collections contain (December 1, 1917) 411,737 vohltmes and 104,524
For cstalogs and information address
THE REGSTR.AR
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