Tension Members

SECTION  6   DESIGN OF TENSION MEMBERS

6.1 Tension Members
Tension members are linear members in which axial forces act causing elongation (stretch). Such members can sustain loads upto 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 nonfunctional due to the excessive elongation. Plates and other rolled sections in tension may also fail by block shear of end bolted regions, under combined shear along longitudinal sections along bolt lines and normal tensile stresses on a transverse section across a bolt line.
The factored design tension T, in the members shall satisfy the following requirement
T < Td
where
Td = design strength of member as given below
The design strength of a member under axial tension, Td, is the lowest of the design strength due to yielding of gross section, Tdg, rupture of critical section, Tdn and block shear Tdb.

• Design Strength due to Yielding of Gross Section

The design strength of members under axial tension Tdg, as governed by yielding of gross section, is given by
Tdg = fy Ag /gm0
where
fy = yield strength of the material in MPa
    Ag = gross area of cross section in mm2
gm0  = partial safety factor for failure in tension by yielding

• Design Strength due to Rupture of Critical Section

6.3.1 Plates - The design strength in tension of a plate, Tdn, as governed by rupture of net cross sectional area, An, at the holes is given by
Tdn =0.9 fu An / gm1
where             
gm1 = partial safety factor
 fu = ultimate stress of the material in MPa
An = net effective area of the member,          =

where
     b, t = width and thickness of the plate respectively
      dh = diameter of the bolt hole (additional 2 mm to the diameter in case the directly punched holes)
  g = gauge length between the bolt holes as shown in Fig 6.1
       ps = staggered pitch length between line of bolt holes as shown in Fig 6.1
  n = number of bolt holes in the critical section
6.3.2 Threaded Rods - The design strength of threaded rods in tension, Tdn, as governed by rupture is given by
Tdn =0.9 fu An / gm1
where
An = net root area at the threaded section
6.3.3 Single Angles - The tearing strength of an angle connected through one leg is affected by shear lag. The design strength, Tdn, as governed by tearing at net section is given by
Tdn      = 0.9 fu Anc / gm1 +b Ago  fy /gm0
where
b= 1.38 – 0.076(w/t)(fy/fu)(bs/L )≈1.4-0.54(bs/L)
where w and bs are as shown in Fig 6.2
L = Length of the end connection, i.e., distance between the outermost bolts in the joint along the length direction or length of the weld along the length direction
Alternatively, the tearing strength of net section may be taken as
Tdn = a An fu /gm1
where
a = 0.6 for one or two bolts, 0.7 for three bolts and 0.8for four or more bolts in the end connection or equivalent weld length
An = net area of the total cross section
Anc= net area of the connected leg
Ago= gross area of the outstanding leg
   t = thickness of the leg

6.3.4 Other Sections – The tearing strength, Tdn, 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 b is calculated based on the shear lag distance, bs taken, from the farthest edge of the outstanding leg to the nearest bolt/weld line in the connected leg of the cross section.
6.4 Design Strength due to Block Shear ─ The block shear strength at an end connection is calculated as given below:
6.4.1 Plates –The block shear strength, Tdb, of connection shall be taken as the smaller of
Tdb =   ( Avg  fy /(gm0) + fu  Atn /gm1 )
or
Tdb =   ( fu Avn /(gm1) + fy Atg /gm0 )
where
Avg, Avn = minimum gross and net area in shear along a line of transmitted force, respectively (1-2 and 4 –3 as shown in Fig 6.3 and 1-2 as shown in Fig 6.4)
Atg, Atn = minimum gross and net area in tension from the hole to the toe of the angle or next last row of bolt in plates, perpendicular to the line of force, respectively (2-3) as shown in Fig 6.3 and Fig 6.4
   fu, fy  = ultimate and yield stress of the material respectively
 

6.4.2 Angles – Strength as governed by block shear failure in angle end connection shall be calculated as given in Section 6.4.1 by using appropriate areas in shear and tension as shown in Fig 6.4.