Analytical Study of Panel Zone Behavior in Beam-Column Connections.pdf

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ANALYTICAL STUDY OF PANEL ZONE BEHAVIOR

IN BEAM-COLUMN CONNECTIONS

• for

I THE AMERICAN INSTITUTE of

STEEL CONSTRUCTION, INC .

• • by

• Ralph M. Richard

and

• David R. Pettijohn

• • • • November 1981

Department of Civil Engineering

• and Engineering ~~chanics

The University of Arizona Tucson, Arizona

• RRIOOO

I 7125

•

I I I I I I I I I I I I I I I I I I


IN BEAM- COLUMN CONNECTIONS

for

IRE AMERICAN INSTITUTE of

STEEL CONSTRUCTION, INC .

by

Ralph M. Richar d

and

David R. Pettijohn

November 1981

Department of Civil Engineering and Engineering Mechanics

The Universtty of Arizona Tucson, Arizona



IN BEAM COLUMN CONNECTIONS

I. Introduction .

The panel zones of a series of four test specimens comprising a W14 x 90

column section and a W24 x 62 beam section were analyzed using the nonlinear

finite element program INELAS. The results of these analyses are compared

with those obtaiced experimentally by Dr. Roger C. Slutter of the Fr itz

Engineering Laboratory at Lehigh University (1). The test specimen config-

urations and designs are shown in Figure 1.

II. Program INELAS .

Program INELAS (2) is a finite element program written to analyze struc-

tural systems stressed into the inelastic range . This program was written

by Professor Ralph M. Richard of the University and has been used extensively

in the aerospace industry since the late 1960's and more recently in the

civil engineering profession in research studies for the analysis and design

of steel connections. Included in the program are the following elements:

1) A constant strain bar.

2) A constant strain plane triangle,

3) An orthotropic constant strain plane triangle .

4) A linear strain plane rectangle .

5) A plane linear strain q~drilateral.

6) A connector element to represent bolts, rivets or weldments.

Mixed boundary conditions may be treated; i . e., either forces or pre-

scribed displacements may be specified. Three-dimensional structures con-

sisting of two-dimensional (i.e., plane) elements may be modeled.

1

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I I

The nonlinear structural response for the two-dimensional elements is

calculated by a numerical algorithm that uses the VOn Mises yield c r iterion

I and the associated flow rule (3). Ordinary simultaneous first-orde r differ-

ential equations are generated to describe differential force-displacement

I relationships and are solved by the fourth-order Runge Kutta method.

I III. The Finite Element Models .

The general finite model of the test specimens and loading is shown in

I Figure 2. Specimen No. 1 (no doubler plate) consisted of 54 plane stress

finite elements (rectangles, quadrilaterals, and triangles) which s i mulated

I the beam and column webs and 46 bar elements which simulate the beam and

I column flanges and the beam flange continuity plates. A comparison of the

deflection at the applied load points as shown in Figure 1 obtained by beam

I theory with the deflection obtained by the finite element model indi cates

that the model predicts the elastic structural behavior of the test specimen

I within two percent.

I Specimens 2, 3, and 4 were modeled the same as Specimen 1 excep t

linear strain rectangular plate elements were added to simulate the doublers

I and weldment elements were used to attach these plates to the column web as

Shown in Figure 2.

I Material uniaxial stress- strain properties used to represent the A36

and Grade 50 steels are given in Figure 3 . Yield stresses of 42. ksi for

I the A36 steel and 56. ksi for the Grade 50 steel approximate the test

I coupon's values of the Lehigh specimens .

For the weldment elements, the results of the research of Butler and

I Kulak (4) are used. The force-deformation curve for fillet- welds in shear

I 2

I


is shown in Figure 4 . This curve is for a 1/4" E60 weld one-inch in length.

To obtain the strength and stiffnness of the welds of different weld sizes,

grades, and tributary lengths, the procedure given in Eighth Edition of the

AlSC Manual (see pp . 4-73) was used. The Richard Equation (4) was used to

analytically represent force-deformation curves and is plotted in Figure 4.

For the 1/4" E60 weld , this equation is

R -5000 x Il

(1 + 15000 . x Ill) 11.

where R is the load and Il is the deformation .

For the butt welds of Specimen 2 , the strength and stiffness of these

welds were taken equal to the doubler plate strength and stiffness.

IV . Analytical Results.

Shown in Figure 5 is a typical computer plot of the undeformed and

deformed shape of the test specimens as obtained from the finite element

analysis. The deformed shape is exaggerated to show the distortion pattern

of the specimens . It is of interest to note the general distorted shape

of the panel zone and also the kinking of the column flanges near the

corners of the panel. Both these features were observed and reported by

Krawinkler, Popov, and Bertero in their experimental studies at the

University of California at Berkeley (6, 7). This plot was generated from

the model of Specimen 3 and as a result the small distortion of the weldment

elements may also be observed.

Figures 6, 7, 8, and 9 show the shear stress distribution along the

vertical centerline of the panel as a function of the applied load. At low

loads the maximum shear stress occurs at the center of the panel, whereas

3

I ~ CO


near maximum load the shear stress is uniform across the panel. It is noted

that the shear stress in the doubler lags the shear stress intensity in

the column web until near maximum load is reached. This is a direct result

of the weldment distortions. Shown in Figure 10 is the panel zone deforma-

tion of Specimen 3 for a beam load of 110. kips . The average shear strain

is approximately 0.046 radians and is computed as follows:

y • 2 x 0 . 56" 24 II - 0.046

This value compares almost exactly with the value obtained by averaging all

of the panel zone element strains of the model .

The resultant loads and their directions on the weldment elements for

Specimen 3 (fillet welded Grade 50 doubler) are shown in Figures 11 through

15 where these figures are for 20%, 40%, 60%, 80%, and 100%, respectively,

for 102. kip beam loads. To compute the load per inch of weld , the load

values shown in these figures must be divided by their tributary areas.

For example, in Figure 15 the weldments at the corner have a load of 120 . 29

kips and have a total tributary length of 6 .86 inches. The strength of

these weldments is the~ computed as follows:

a) For a 1/4" weld one-inch long in shear R - 11.0 kips

(see Figure 4).

b) Hultiply 11.0 kips by the ratio of 70/60 to account for

E70 electrodes.

c) Multiply the result above by the ratio of 3/2 to account

for the 3/8" weld.

d) Multiply the result of (c) by 6.86 to account for this

tributary length.

That is, the corner weldments have a strength of

R -70 3

11.0 x 60 x 2 x 6. 86 • 132 . kips

4

I I

The deformation of these welds as determined from Program INELAS was

0.05 inches which is about one-half the total ductility available as reported

I by Butler and Kulak for welds in pure shear (see Figure 4). These results

support the use of the fillet weld for doubler plates in place of the more

I expensive full penetration welds .

In Figure 16 the experimental load-panel zone deformation curves are

I shown as solid lines. The dashed lines are the results obtained by Program

I INELAS. The agreement between these is very good especially in the Specimens

2, 3, and 4, which have the panel zone reinforced with doubler plates. The

I analytical study showed that the fillet - welded specimen performed essentially

identical to the butt- welded specimen.

I From these results it is apparent that the panel zone itself is con-

I strained Significantly by the column flanges and the beam web so that this

zone will carry a significantly greater shear load than predicted by the

I AISC plastic design formula

V D 0.55 F d t Y Y c

I where

v = shear force causing yielding in the panel zone y

F yield stress of steel in tension y I I

d = depth of column c

t = thickness of web

I This fact was observed and reported by Krawinkler, Berterro, and Popov

(6) . Krawinkler (7) presents a panel ultimate shear strength formula based

I upon a panel strain of four times the yield strain. This is Equation 10 on

I page 87 of this reference. If the panel strain is left arbitrary, this

I 5

I


formula becomes

v -u 0 . 55 F d t

Y c (1. +

where a is the ratio of the panel strain to the yield strain. For Lehigh

tests this reduces to

v - V (1. + 0 . 0575 (a - 1)) u y

A comparison of the Lehigh test results and this formula is given in the

table below:

SPECIMEN

Ul @ y = 1. 75%

02 @ Y = 2% (lst Cycle)

U2 @ y = 2% (7th Cycle)

114 @ Y = 2% (lst Cycle)

04 @ y = 2% (7th Cycle)

LEHIGH TEST LOAD

55 .k

100.k

100.k

TEST PANEL SHEAR

210 .6k

FORMULA

201. k

454. k

455.k

455. k

Krawinkler specifically states that his derivation should be valid for

(a - 1) values (his y/y values) up to 3; however, the agreement is fair for y

the Lehigh tests even for (a - 1) values of the order of 7. He also indi-

cates that the formula is in good argrement with experimental results for

joints with thin to medium-thick column flanges, but that for very th ick

flanges (greater than rwo inches), additional studies are required . It

should be noted that very significant increases in allowable panel shears

result when this method is used as is evident in his design aid given in

Figure 8 of his paper. These increases range from about 10% up to about

6

I I I I I I I I I I I I I I I I I

65% for the Wl4 sections shown. It is apparent from the proposed shear

strength equation that the increase in shear capacity is primary a function

of the panel zone aspect ratio and the column flange thicknesses .

Krawinkler further recommends that the effect of the normal stresses in

the panel zone due to the column axial load be accounted for by the factor,

a, where

This is his Equation 5 in which P is the axial column load and P is the y

yield axial load.

TWo additional studies were made using the finite element models for

Specimens I and 2 . These were (a) the flange continuity plates were removed

from the models and (b) the beam tip loads were removed and their effects

were introduced as concentrated flange forces at the column faces and a

concentrated shear in the beam web at the column faces. The panel zone

strain distribution obtained from these models did not vary significantly

from those obtained previously . Further study concerning the removal of

the flange continuity plates, however, should be made in the full scale

tests since the analytical model is a two-dimensional model and does not

account for out-af-plane bending of the beam flanges .

V. Summary and Conclusions.

This analytical study of the Lehigh test specimens indicates that the

finite element Program INELdS adequately predicts the first half cycle

behavior of the test specimens and provides valuable insight into the load

and strain distribution within the panel zone. These results are in

agreement with and support the analytical and experimental work at the

7

I I

University of California at Berkeley . This latter observation is significant

in that the California researchers have developed a panel shear strength

I formula which includes the beneficial effects of the boundary elements of the

panel zone ; i . e. , the column flanges and the beam web . This formula, with an

I allowable prescr ibed panel zone shear strain, makes it possible for the

I structur al designer to arrive at a panel shear strength in a rational way.

I I I I I I I I I I I I 8

I

I I I I I I I

REFERENCES

1. "Tests of Panel Zone Behavior in Beam-Column Connections" by Roger G.

Slutter, Report No. 200.81.403 . 1, Fritz Engineering Labora~ory, Lehigh

University.

2. "User's Manual for Nonlinear Finite Element Analysis Program INELAS", by

Ralph M. Richard, Department of Civil Engineering, The University of

Arizona, Tucson, Az, 1968.

3. "Finite Element Analysis of Inelastic Structures", by Ralph M. Richard

and James R. Blacklock, AIAA Journal, Vol. 7, No.3, March 1969.

4. "Strength of Fillet Welds as a Function of Direction of Load", by L. J.

Butler and G. L. Kulak, Welding Journal Research Supplement, May 1971.

5. "A Versatile Elastic-Plastic Stress-Strain Formula", by Ralph M. Richard, I Journal of the Engineering Mechanics Division, ASCE, August 1975.

I 6. "Shear Behavior of Steel Frame Joints", by H. Krawinkler. V. V. Bertero.

and E. P . Popov, Journal of th~ Structural Division, ASCE, November 1975.

7. "Shear in Beam-Column Joints in Seismic Design of Steel Frames", by H.

I Krawinkler. Engineering Journal, AISC, Third Quarter 1978.

I I I I I I I

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112" Grade 50 3/8" Fillet Welds

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112" X 4" With 7 <;t"

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15 20 Shear Stress (ksi)

Panel Zone Shear Stress

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------------------Sie e

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p: 99k tweb & doubler)

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Analytical Study of Panel Zone Behavior in Beam-Column Connections.pdf