8

CHAPTER 2

LITERATURE REVIEW

2.1 GENERAL

A brief review of the research carried out during the past years

related to the behaviour of bolted steel angle tension members is presented

herewith. Literature pertaining to both hot-rolled steel tension members and

cold-formed steel tension members is presented. The review includes

experimental, analytical and numerical investigations carried out in the past

years.

2.2 SHEAR LAG

Tension members are used in a variety of structures such as trusses,

transmission towers etc. The most widely used structural shapes are the angle

section and the channel sections. Angles may be used as single angles or

double angles and the connection may be bolted or welded. For practical

reasons, it is unusual to connect the entire cross-section to the gusset plate. As

a result, highly non uniform stresses will be generated near the connection

and this can cause localized yielding in parts of the cross-section. Thus, the

whole cross-section may not be fully utilized which causes a reduction in the

net section efficiency. This loss of efficiency of the section is due to “shear

lag effect”. An accurate estimation of this non–uniform stress distribution is

necessary for determination of load carrying capacity of angles under tension.

This non-uniform stress distribution across cross-section of the angle

9

connected by only one leg to the gusset is shown in Figure 2.1. The concept

of effective net area has been traditionally used to account for this non-

uniform stress distribution.

Less stressed material

Outstanding leg (A2)

More stressed material

Connected leg ( A1)

Figure 2.1 Non uniform stress distribution across the cross-section of

the angle

2.2.1 Effect of Shear Lag

Shear lag reduces the effectiveness of tension member components

that are not connected directly to a gusset plate or other anchorage. The

efficiency of a member can be increased by reducing the areas of such

components relative to the area of the member as a whole. The distance from

a fastener plane (gusset plate) to the C.G of the area tributary to it is a

convenient measure of the distribution of the cross-sectional area of a

member.

For example, the tributary area of an angle member of Figure 2.2 is

the entire area of the angle and the co-ordinate x from the fastener plane to

the centroid of the area is a measure of the efficiency of the cross section.

10

Figure 2.2 Tributary areas of angle section

2.2.2 Shear Lag Factor

Shear lag is influenced by the length and eccentricity of the

connection. The effect of these two parameters can be expressed as an

efficiency coefficient given by

K4 = 1- ( x / L) (2.1)

where K4 = Shear lag factor

x refers to the distance from the face of the connection to the

centre of gravity of the member,

L is the length of connection (distance from the first fastener to the

last one).

2.3 STUDIES ON HOT ROLLED MEMBERS

Chesson and Munse (1963) investigated a wide range of truss –

type tension members using both test results obtained from their own

experiments and from others. The parameters studied included different

cross–sectional configurations, connections, materials, and fabrication

methods. An empirical equation to calculate the net section efficiency was

11

proposed. It was based on the test results of 218 specimens among which

there were 56 single angles and 33 double angles. Both riveted and bolted

connections were examined. An empirical equation to calculate the net

section efficiency was proposed.

Chesson and Munse found that the net section efficiency of tension

members with bolted or riveted end connections was a function of a number

of factors and it could be expressed as follows:

Ane = K1K2K3K4An (2.2)

where Ane = effective net area of cross-section

An = net area of cross-section

K1 = 0.82 + 0.0032Q < 1

K2 = 0.85 for members with punched holes

= 1 for members with drilled holes

K3 = 1.6 – 0.7 An/Ag

Ag = gross area of cross-section

K4 = 1 – x /L .

K1 is the factor that accounts for the ductility of material, in which,

the term Q is the percent reduction in the area at rupture of a standard tensile

test coupon (51mm gauge length). K2 is the fabrication factor that accounts

for the reduction in efficiency due to the effect of punching the holes. K3 is a

geometry factor that accounts for the effect of hole spacing on the connection.

K4 is the shear lag factor. This factor takes into account for both the

eccentricity in the connected part and the connection length. In the expression

for K4, x refers to the distance from the face of the connection to the centre

of gravity of the member, and L represents the connection length and is taken

as the distance between extreme fasteners.

Kennedy and Sinclair (1969) investigated the influence of the edge

distance and the end distance on net section efficiency. In this investigation,

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721 single angle, single bolted connections were tested. In order to simulate

the fabrication of members in field conditions, all the specimens were cut to

length by shearing and all holes were punched. The test results showed that

minimum edge and end distances were required to develop the yield strength

of the cross section.

March (1969) conducted a series of tests on single angle members

in tension and compression. The effects of plastic behaviour were studied

during ultimate loading of the sections. March stated that as the extreme

fibres of the section yield, the line of action of the load would move, as well

as the eccentricity. Based on these observations, he proposed that the net

effective area (Ane) could be calculated as follows:

2

c 0ne

c

(L L t)tA dtL 0.04L

(2.3)

where Lc = width of the connected leg

L0 = width of the unconnected leg.

t = thickness of the section

L = distance from the point of loading to the innermost bolt.

d = diameter of the bolt hole.

For unequal leg angles, this formula gave a good prediction if the

long leg was connected. However, the prediction was rather optimistic if the

short leg was connected.

Hardash and Bjorhovde (1985) tested 28 specimens to develop an

improved design method for gusset plates. Gage between lines of bolts, edge

distance, bolt spacing and number of bolts were considered as the strength

parameters. Gusset plates fastened with two lines of bolts were tested. Test

specimens had a gage length of 51, 76 and 101 mm, edge distance of 25, 38

13

mm, and pitch distance of 38 and 51mm. Connections had two to five bolts in

a bolt line and diameter of bolt holes were 14 and 17 mm. The average

material properties of 27 specimens had a yield strength of 229 MPa and an

ultimate strength of 323 MPa. One specimen had a yield strength value of 341

MPa and ultimate strength of 444 MPa. Test plates had a basic failure mode

consisting of tensile failure across the last row of bolts, along with an

elongation of the bolt holes.

Load deformation curves of each test specimen was obtained and it

was observed that the drop in strength from the ultimate load to second

strength plateau corresponded approximately to the ultimate strength of the

net area at the last row of bolts. Ultimate shear resistance was more difficult

to define, because, the shear stress behaviour varied among the test

specimens. Shear stress was found to be dependent on the connection length

and a new block shear capacity equation, which includes the connection

length factor, was developed.

Murty et al. (1988) summarized the design approaches for

computing the ultimate strength of bolted single angles in accordance with the

following five specifications: the American Association of State Highway and

Transportation Officials, the American Institute of Steel Construction,

American society of Civil Engineers, the Canadian Standards Association,

and the British Standards Institute. These specifications were compared with

the test results of Nelson (1953), and an experimental program carried out.

They observed that certain combinations of end distance, and pitch may cause

the block shear mode of failure instead of net section failure. Although there

was no specific design equation proposed, they concluded that a distinction

should be made when predicting the ultimate strengths of angles connected by

the long leg or short leg.

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Epstein (1992) performed an experimental study on double-row,

staggered, and unstaggered bolted connections of structural steel angles. The

basic connections to be tested were pairs of angles, 8 mm thick, connected by

two rows of 8 mm diameter bolts in two rows on a 150 mm leg. Outstanding

legs of the angles vary between 90, 210 and 150 mm. An end and edge

distances of 38 mm, a bolt diameter of 19 mm were used in the connections.

The effect of several parameters in the connection geometry was investigated.

Test results were compared with the current code provisions and a revised

treatment was suggested by inclusion of a shear lag factor to the equation.

Gaylord (1992) presented a similar equation as Munse and Chesson

(1963). He suggested that the effective net area of tension member was a

function of four factors: steel ductility, fabrication methods, connection

efficiency, and shear lag effects. Their expression was as follows:

Aeff = K1K2K3K4An (2.4)

where K1 = ductility factor = 0.82 + 0.0032 R < = 1.0

K2 = fabrication factor = 0.85 for punching effects

= 1.0 for drilling effects.

K3 = efficiency coefficient

K4 = shear lag factor.

R = percent reduction in the cross sectional area of a tensile

coupon at failure.

The efficiency coefficient and the shear lag factors were similar to

that presented by Munse and Chesson (1963). Gaylord suggested that the

effect of punched bolt holes reduced net section capacity by 15%. Also, they

suggest that the inclusion of ductility factor had an effect on connection

efficiency. The R value was determined experimentally from tensile coupon

15

tests. More ductile steels would allow for a better distribution of stress

concentrations along a cross sectional area than lower ductile steels.

Wu and Kulak (1993) conducted an experimental program to

investigate the shear lag effect on single and double angle tension members.

The parameters studied include length of members, length of the connection,

size and disposition of the cross-section, including angle thickness and

whether the long leg or short leg was connected, out of plane stiffness of the

gusset plate for the single angle cases. Based on the test results, the following

design formula was proposed:

Tr = 0.85 Φ (FuAcn + βFyAo) (2.5)

where Tr = factored resistance of the member

Φ = resistance factor =0.90

Fu = ultimate tensile strength of the material

Fy = yield strength of the material

Acn = net area of the connected leg at the critical cross-section,

computed by taking the diameter of holes 2mm larger than

the nominal size if the holes were punched.

Ao = gross area of the outstanding leg

β = 1.0 for members with four or more fasteners per line in the

connection.

= 0.5 for members with fewer than four fasteners per line in

the connection.

Gross et al (1995) tested ten A588 Grade 50 and three A36 steel

single angle tension members with various leg sizes that failed in block shear.

A588 Grade 50 steel had a yield and ultimate strength of 427 and 545 MPa

and A36 steel had a yield and ultimate strength value of 310 and 469 MPa,

respectively. Bolt holes having a diameter of 21 mm and a bolt hole spacing

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of 64 mm and an end distance of 38 mm were used in all specimens. The edge

distance was varied between 32, 38, 44 and 50mm. Test results were

compared with the AISC-ASD and AISC-LRFD equation predictions and it

was observed that code treatments accurately predict failure loads for A36 and

A588 specimens.

Cunnigham et al (1995) performed a statistical study to assess the

American block shear load capacity predictions. Even though, both ASD and

LRFD equations predicts the failure loads with a reasonable level of accuracy

on average, it was observed that both the ASD and LRFD block shear

predictions have drawbacks in terms of anticipated failure modes. It is evident

from the test results that tension and shear planes do not rupture

simultaneously as assumed in ASD specification. Thus, Cunnigham set the

geometric and material parameters that had been investigated, and studied

several other parameters such as in-plane shear eccentricity and tension

eccentricity. Some equations, which include different types of failure modes

and variables, were presented to predict block shear load capacity.

Kulak and Grondin (2001) performed a statistical study on

evaluation of LRFD rules for block shear capacities in bolted connections

with test results. It was stated that there were two equations to predict the

block shear capacity but the one including the shear ultimate strength in

combination with the tensile yield strength seemed unlikely. Examination of

the test results on gusset plates reveals that there is not sufficient tensile

ductility to permit shear fracture to occur.

Mohan Gupta and Gupta (2002) presented simple equations for

predicting the load carrying capacity of single and double angles in tension,

for net section failure based on previously published experimental results.

These experimental results were divided into two parts: first which follow all

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the following four conditions, and the second which violate one or more of

the following conditions. The conditions are: a) The pitch is not less than the

minimum and not more than the maximum, b) minimum edge distance is

provided, c) minimum end distance is provided and d) thickness of angle

sections is not less than that normally used in structural works. The following

conclusions are obtained.

1. There is no significant difference between the net section

efficiencies of single and double angle tension members,

because of the shear lag effect. As such, there is no need to

make any distinction between single and double angles in

working out the load carrying capacities.

2. The following equations, based on net section efficiency, may

be used to predict the load carrying capacity of single and

double angles with relatively longer connection lengths.

For unequal angles connected by their long length,

Rn = 0.85Anfu (2.6)

For equal angles Rn = 0.80Anfu (2.7)

For unequal angles connected by their short leg ,

Rn = 0.75Anfu (2.8)

where Rn = Net section strength

An = Net cross-sectional area

fu = Ultimate tensile strength of the material

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3. There is an acute shortage of test results with relatively shorter

connection lengths.

Gupta Mohan and Gupta (2005) analysed the Indian standard for

design of steel structures (IS 800-1984) which follows working stress method,

and found that the provisions for design of angle tension members were

conservative for single angles when the number of bolts were relatively more

and less conservative, for single angles and double angles with lesser number

of bolts. For block shear failures, these predictions were least conservative.

They adopted these provisions in the revision of the code in the limit state

format and in these, provisions were adequate for single angles with three or

more bolts.

The net section strength of single and double angle members was

adequately represented by the equation

Rn = fu (A1 +A2k) (2.9)

where k = 3A1/(3A1+A2) for three or more bolts per row.

k = A1/(A1+A2) for two bolts per row.

The equation to predict the block shear strength is

Rb = fuAnt +fys Agv (2.10)

The strength based on yielding of gross section is

Rg = fy.Ag (2.11)

where A1 = Net area of the connected leg

A2 = Gross area of the unconnected leg.

Ag = Gross cross-sectional area

Agv = Gross area subjected to shear

Ant = Net area subjected to tension

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Rn = Net section strength

Rg = Gross section strength

Rb = Block shear rupture strength

fu = Ultimate tensile strength of steel

fy = Yield strength of steel

fys = Shear yield strength of steel ( = 0.6fy)

k = Reduction factor, to account for the effects of connection

eccentricity and shear lag.

They also reported that design strengths were obtained by using

specified minimum values of yield stress and ultimate stress in association

with partial safety factors. The lower of these gave the maximum factored

load carrying capacity of angles in tension. The factor of safety obtained as a

result indicated adequate representation of the design strengths.

The above research studies reveals that the effect of shear lag on

hot-rolled steel structural connections was well understood. Hence most of the

codal provisions had already incorporated necessary design guidelines.

2.4 STUDIES ON COLD-FORMED STEEL TENSION MEMBERS

Bryan (1993) presented a paper on the design of bolted joints in

cold-formed steel sections. Design expressions using joint flexibility for the

bearing strength of bolted joints and for the joint moment under load were

given. It was shown how the design expressions may be used to estimate the

moment capacity and moment/rotation relationship of bolt groups, and how

this information may be used to give an economical design of structural

assemblies.

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La–Boube and Yu (1995) conducted an experimental and analytical

study at the University of Missouri–Rolla, to expand the knowledge and

understanding of the behaviour of cold-formed steel bolted connections. This

research consisted of two parts. The first part concentrated on the tensile

capacity, bearing capacity and the interaction of tension and bearing

capacities of flat sheet cold-formed steel bolted connections. For the

specimens that failed in bearing, the results showed that the AISI specification

was a good predictor of the ultimate strength while the AISC specification

was not. For the specimens that failed in net section, both the AISI and AISC

specifications were deemed to be good predictors. In the second part, the

tensile capacity and bearing capacity of bolted connections of flat sheet, angle

and channel cold-formed steel members were addressed. For the angle and

channel sections that failed by net section fracture, the studies had shown that

the current AISC specification formulation for addressing the influence of

shear lag was unacceptable for cold-formed steel connections. Based on the

tests results, the equations that could estimate the influence of shear lag on the

tensile capacity of bolted connections were derived for cold-formed angle and

channel sections and were stated as follows:

For angle sections,

U = 1 – 1.2 x /L ≤ 0.9 (2.12)

For channel sections,

U = 1 – 0.357 x /L ≤ 0.9 (2.13)

where U = net section efficiency,

x = distance from the face of the connection to the center of

gravity of the member

L = connection length

Seleim and LaBoube (1996) studied the behaviour of low ductility

steel in cold-formed steel connections. Single lap bolted connections were

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studied to assess the influence of steels not meeting the specified ductility

requirements. The conclusions obtained from forty-seven tests results were:

AISI equations provide conservative strength prediction for the limit state

edge shearing parallel to the direction of loading, specimens that failed in a

bearing type mode were subjected to small deformation prior, out-of-plane

shearing and fracture in the net section did not occur for specimens governed

by net-section failure as per AISI provisions. Test results indicated that failure

modes in low ductility steels were inconsistent with observed failure modes in

adequate ductility steels.

Chung and Lau (1999) conducted an experimental investigation on

cold-formed steel members with bolted moment connections. Two lipped C

sections back to back with four bolts per member were used as beam and

column members. Four modes of failure such as bearing failure in section

web around bolt hole, lateral torsional buckling of gusset plate, flexural

failure of connected member and combined compression and bending failure

of column member were identified. Among sixteen tests, the moment

resistance of bolted moment connections with four bolts per member was

found to lie between 42% and 84% of the moment capacities of the connected

members. It was observed that moment connections among cold-formed steel

members were structurally feasible and economical through rational design.

Yip and Cheng (2000) performed an experimental program

consisting of 23 angle and channel specimens to study the shear lag effect.

The connection length and cross sectional geometry are two major parameters

studied. With the test results, the net section efficiency(U) and the behaviour

of the specimen were discussed. Finite element method was used to model

and analyze the test specimens. A parametric study was also set up using the

developed finite element models to investigate the factors affecting the net

section efficiency of angle and channel sections. With the results obtained

22

from the parametric study, it was concluded that the current design equations

give inconsistent predictions on the net section efficiency of cold-formed

tension members. It was found that the net section efficiency does not only

depend on the connection length(L) and eccentricity( x ), but also the flat

width to thickness(w/t) and flat width to bolt diameter (w/d) ratios. Based on

this observation, new net section efficiency equations were developed using

non-linear regression analysis for both angle and channel sections as

a) For equal leg angle members connected by one leg or unequal

leg angles with long leg connected

i) with one bolt in the line of force

U = 1-0.11(w/t)0.3(w/d)0.42≤1.0 (2.14)

ii) with two or more bolts in the line of force

U = 1-0.085( x /L )0.41(w/t)0.36(w/d)0.51≤1.0 (2.15)

b) For channel members connected by the web

i) with one bolt in the line of force

U = 1-0.11(w/t)0.4(w/d)0.07≤1.0 (2.16)

ii) with two or more bolts in the line of force

U = 1-0.04( x /L )0.85(w/t)0.54(w/d)1.02≤1.0 (2.17)

Rogers and Hancock (2000) investigated the failure modes of

bolted sheet steel connections loaded in shear. The load capacity formulations

presented in the American Iron and Steel Institute specification could not

accurately predict the failure modes of these connections when loaded in

shear. A modification to the bearing coefficient provisions to account for the

reduced bearing resistance of the materials was necessary and was suggested.

A revision of the net section fracture design method was also required.

23

Recommendations concerning the procedure used to identify the net section

fracture and bearing failure modes were also made.

Chi–Ling pan (2004) investigated the shear lag effect on bolted

cold formed steel tension members. Fifty four Channel sections with different

dimensions tested by using bolted connections were discussed. The

comparisons were made between test results and predictions computed based

on several specifications such as AISC, AISI, AS/NZS etc. The predictions

according to AISI and AS/NZS seemed to be overestimating as compared to

the test results. The computed values based on the AISC specification

provided good correlation with the test results. To study the stress distribution

at the various locations of the cross-section of specimen, finite element

software ANSYS was used. It was observed that stress distribution over the

entire section of the specimen was not uniform. The stresses in the connected

element (web) were larger than the stresses in the unconnected elements

(flanges). He also observed that the ratio of connection eccentricity to

connection length x /L, and the ratio of unconnected element width to

connected element width Wu/Wc were the two factors which had mainly

influenced the tensile strength of channel sections.

The tensile strength may be estimated by applying the following

empirical equation for the channel section,

P = UAnFu (2.18)

where U = 1.15 – 0.86( x /L) – 0.14 (Wu/Wc) (2.19)

x = Connection eccentricity

L = Connection Length

Wu = width of unconnected elements

Wc = width of connected elements

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Valdier Francisco de paula et al (2008), presented experimental

results of 66 specimens carried out on cold-formed steel angles fastened with

bolts under tension. Out of the 66 specimens, four angles have one bolt and

remaining 62 specimens have more than one bolt per line. These 66

specimens showed net section failure with two or more bolts in the cross-

section of cold-formed angles. The specimens tested had equal or different

legs, different cross-sections, various thicknesses and a varied number of bolts

and bolt lines. He conducted multiple linear regression analysis and suggested

the expression for net section efficiency (U) which depended on the

geometrical factors such as connection eccentricity ( x ), connection length

(L), width of connected leg of the angle (bc), net width of the angle with

connected leg (bcn), width of unconnected leg (bd), nominal bolt diameter (d)

and angle thickness (t).

The proposed equation is

U = 1.19 – 0.26 ( x /L) – (0.63bcn + 0.17bd – 0.47d-1.70t)/bc (2.20)

The effect of shear lag on cold-formed steel sections were much

limited when compared to studies on hot-rolled steel sections. The American

Iron and Steel Institute, Australian/ New Zealand and British Standard codes

were recently revised and incorporated the provisions. Hence there is a need

to investigate the behaviour of cold-formed steel angles under tension.

2.5 STUDIES ON NUMERICAL INVESTIGATION

Epstein and Chamarajanagar (1996) developed analytical model for

a series of single angle tests with staggered bolted connections. A 20 node

brick element was used in the finite element modeling of the angle sections to

capture the stress concentration effect in the vicinity of bolt holes. The

material nonlinear effects were modeled using the von Mises yield criterion

25

and the material stress-strain curve was assumed to be elastic–perfectly

plastic. In this study, a strain based failure criterion in which failure was

assumed to have occurred once the maximum strain reached five times the

initial yield strain was employed to capture the failure load.

The bolts were assumed to be rigid and the load was transferred

from the gusset plate to the angle fully by the bearing of bolts. The

longitudinal and the in-plane transverse displacements of the nodes attached

to the bearing surfaces were coupled to one another. This finite element study

included only the material non-linear effects and the geometric non-linear

effects were considered to be negligible.

Kulak and Wu (1997) conducted a finite element analysis to

evaluate the stress distribution of the critical cross section at ultimate load. A

large strain four-node quadrilateral shell element with six degrees of freedom

per node was used in the finite element modeling of the double angle

members. The gusset plate was modelled using elastic four–node quadrilateral

shell element as yielding of the gusset plate was not observed in the

experimental tests. An elasto–plastic von Mises yield criterion was adopted to

represent the material non-linear effects. The material stress-strain curve was

described by a multilinear isotropic hardening behaviour. Based on the

symmetry consideration of the specimen, only half the length of the specimen

was modelled. Similarly, due to the symmetry of the double angle members

about gusset plate, only one of the pair angles was modelled. In the finite

element model, the effect of bolts was modelled by coupling the longitudinal

and in-plane transverse degrees of freedom of the nodes attached to the hole

surfaces on which the bolts bear against during deformation. The finite

element model included both geometric as well as material non-linear effects.

In the analysis, the failure load of the angle section was taken as the load

corresponding to the last converged step. At failure, significant necking of the

net area between the leg edge and lead bolt hole was observed.

26

Epstein McGinnis (2000) conducted a second study aimed at

refining the tools developed in Epstein’s 1996 work. The boundary conditions

and the solution procedure were identical to the 1996 Epstein study. Although

this finite element study included only the material nonlinearity as represented

by a simple elastic-perfectly-plastic yield criterion, the finite element results

indicated a reasonably good correlation with the experimental results.

Chung and Ip (2000) investigated the finite element modeling of

bolted connections between cold-formed steel strips and hot-rolled steel plates

under shear. The modeling was done with three-dimensional solid elements

using the results of the coupon tests. Twelve lap shear tests with two steel

grades, one bolt diameter and two washer sizes were carried out to caliber the

finite element models. The load-extension behaviour of the bolted

connections agreed well with the test data for extensions upto 3mm in terms

of both initial and the final slopes and also the maximum load carrying

capacities. The patterns of yielding, strength degradation and the strain

distribution the connections were established in detail using finite element

modeling. Typical strain levels in cold-formed steel strips in the vicinity of

bolt holes were found to be 40%. Therefore it is important to incorporate

reduced strength at larger strains for accurate prediction of the load-carrying

capacities of bolted connections.

Cem Topkaya (2004) aimed to develop simple block shear capacity

equations that are based on principles of mechanics in this study. A

parametric study was conducted to identify important parameters that

influence the block shear response. Specimens tested by three independent

research teams were modeled and analyzed. Analysis was performed with a

finite element program “ANSYS”. Gusset plates were modeled with six node

triangular plane stress elements, whereas angles and tee sections were

modeled with ten node tetrahedral elements. These element types were

27

capable of showing high material and geometric nonlinearities. The nonlinear

stress strain behavior of steel was modeled using von Mises yield criterion

with isotropic hardening. A generic true stress- true strain response was used

in all analysis.

Throughout the analysis the Newton-Raphson method is used to

trace the entire nonlinear load-deflection response and failure load was

assumed to be the maximum load reached during the loading history. He

presented three equations based on the analysis performed to predict block

shear load capacity

Gupta Mohan and Gupta (2004) conducted finite element analysis

to evaluate the stress distribution in the angle at design loads predicted by

equations developed earlier on the basis of experimental results. Detailed

finite element analysis was conducted on three bolted angle specimens. These

three angle specimens had two, three and four bolts at each end respectively.

Since the thickness of the angles and the gusset plates used were all less than

one inch, shell elements were used to represent all of the connection and

member components. A plastic quadrilateral shell element was used to model

the angles and the gusset plates. This element had six degrees of freedom at

each of the four nodes. Yielding was determined using the von Mises yield

criteria. From the analysis it was observed that in three bolts and four bolts

connections, the zones of high stresses lay along the critical section in the

connected and the un-connected leg. In a two bolt connection, the stresses

were mainly concentrated on the connected leg only, and in the un-connected

leg, the stresses were relatively low. The magnitude and the distribution of

stresses at critical section for three bolts and four bolts connection was almost

the same. The resulting stress distribution justified the use of area along the

gross shear plane in block shear strength prediction equation. The distribution

and concentration of von Mises stresses indicated that block shear failure

28

might occur in a two bolt connection, and net section failure might occur in

three and four bolts connection.

Only limited studies are reported on the numerical investigation of

steel angle sections connected to gusset plate. It is very difficult to model the

specimens because behaviour depends on a number of parameters like

geometry of section, material properties etc. But numerical analysis using

finite element method will be useful to investigate the behaviour and to

predict the modes of failure.