The factored design tension, T, in the members shall satisfy T<=Td as detailed in Cl. 6.1 of IS 800:2007 where Td = design strength of the member.

**FAILURE MODES FOR TENSION MEMBERS**

Tension members, as described in IS 800:2007, can sustain
loads up to the ultimate load, at which stage they may fail by rupture at a
critical section. However, if the gross area of the member yields over a major
portion of its length before the rupture load is reached, the member may become
non-functional due to excessive elongation. Plates and other rolled sections in
tension may also fail by block shear of end bolted regions also. The design
objective is basically to check these three failure modes under prescribed
loads or combination of loads.

** DESIGN
CONSIDERATION OF TENSION MEMBERS**

The
factored design tension, T, in the members shall satisfy T<=Td as detailed
in Cl. 6.1 of IS 800:2007 where Td = design
strength of the member. The design strength of a member under axial tension,Td
, is
the lowest of the design
strength due to
yielding of gross section ,rupture strength of critical section (Tdn ),and block
shear strength (Tdp), given in
clauses 6.2, 6.3 and 6.4 of IS 800:2007
respectively.

**1. Design Strength due to Yielding of Gross
Section **

The
design strength of members under axial tension as governed by yielding of gross section, as
per IS 800:2007, is given by A_{g}/t_{y}/r_{mo} where is the yield stress of the material, Ag is the
gross area of cross-section, and r_{mo }is the partial safety factor
for failure in tension by yielding as given in Table 5 of IS 800:2007. This
table is reproduced here as Table 8.

** Table
8 Partial Safety Factors for Materials **

**Sl No Definition Partial safety factor**

1 Resistance, governed by yielding, ?? 1.10

2 Resistance of member to buckling, ?? 1.10

3 Resistance, governed by ultimate stress,
?? 1.25

4 Resistance of connection Shop Fabrications Field Fabrications

4(a) Bolts-Friction Type, ?? 1.25 1.25

4(b) Bolts-Bearing Type, ??? 1.25 1.25

4(c) Rivets, ??? 1.25 1.25

4(d) Welds, ?? 1.25 1.50

**2. Design
Strength due to Rupture Strength of Critical Section**

The rupture strength of the critical section is
also a governing criterion for the design of tension members. Cl. 6.3 of IS
800:2007 deals with the rupture strength of critical section. The critical
section has to be carefully evaluated as the section which is having the least
net cross sectional area out of the various possible failure planes. The
evaluation of the strength of critical sections depends on the type of cross
section. The calculation will be based on Cl. 6.3.1 (Plates), Cl. 6.3.2
(Threaded rods), Cl.

6.3.3 (Angles) and Cl. 6.3.4 (Other sections) of IS 800:2007.
Our discussion will be limited to that of plates and angles in this section.

**2.1.
Design Strength due to Rupture Strength of Critical Section for plates**

Cl. 6.3.1 of IS 800:2007 gives the design strength in tension
of a plate, T_{dn}, as governed by rupture of net cross-sectional area,
An, at the holes is T_{dn}= 0.9Anfu/rms where r_{ms} is the
partial safety factor for failure at ultimate stress as given in Table 8 above
or Table 5 of IS 800:2007, A_{n} is the ultimate stress of the
material, andis the net effective area of the member given by,| b-nd_{n}
+ Ew| t where b and t are the width and thickness of the plate, dh is
the diameter of the bolt hole (2 mm in addition to the diameter of the hole, in
case the directly punched holes), g is the

gauge length between the bolt holes, as shown in Fig. 5 of IS
800:2007. This figure is reproduced here as Figure 27. 'p' is the
staggered-pitch length between line of bolt holes, as shown in Fig. 5
of IS

800:2007, n is the number of bolt holes in the critical
section and i is the subscript for summation of all the inclined legs.

**2.2.
Design Strength due to Rupture Strength of Critical Section for plates**

Cl. 6.3.3 of IS 800:2007 gives the rupture strength of angles
connected through one leg. This strength will be affected by shear lag and is
given by T_{dn}. This should be limited by a maximum value given by and
by a minimum value of 0.7 where w is the outstand leg width, bs is the shear
lag width, as shown in Fig. 6 of IS800:2007 (Reproduced here as Figure 28), Lc_{
}is the length of the end connection, that is the distance between the
outermost bolts in the end joint measured along the load direction or length of
the weld along the load direction, An is the
net area of the total cross-section, _{Ago} is the
gross area of the outstanding leg, _{Anc} is the
net area of the connected leg and t is the thickness of the leg.

In the
case of design of tension members, the IS800:2007 permits to use a simpler
expression for preliminary sizing. The approximate rupture strength of net
section to be taken as T_{dn} = aA_{n}f_{u}/rms where
acan be taken as 0.6 for one or two bolts, 0.7 for three bolts and 0.8 for four
or more bolts along the length in the end connection or equivalent weld length.

**2.3.
Design Strength due to Rupture Strength of Critical Section for Other Section**

According
to Cl. 6.3.4 of IS800:2007, the rupture strength, , of the double angles, channels, I-sections
and other rolled steel sections, connected by one or more elements to an end
gusset is also governed by shear lag effects. The design tensile strength of
such sections as governed by tearing of net section may also be calculated
using equation in 6.3.3, where is calculated based on the shear lag distance, , taken from the farthest edge of the
outstanding leg to the nearest bolt/weld line in the connected leg of the
cross-section.

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