Combined Tension and Shear

Combined tension and shear stresses are of concern principally for fasteners, plate-girder webs, and ends of coped beams, gusset plates, and similar locations.

Tension and Shear in Bolts

The AISC ‘‘Load and Resistance Factor Design (LRFD) Specification for Structural Steel Buildings’’ contains interaction formulas for design of bolts subject to combined tension and shear in bearing-type connections. The specification stipulates that the tension stress applied by factored loads must not exceed the design tension stress Ft (ksi) computed from the appropriate formula (Table 6.24) when the applied shear stress ƒv (ksi) is caused by the same factored loads. This shear stress must not exceed the design shear strength.
For bolts in slip-critical connections designed by LRFD for factored loads, the design slip resistance @Rstr (kips) for shear alone given in Art. 6.14.2 must be multiplied by the
factor

Tension and Shear in Girder Webs

In plate girders designed for tension-field action, the interaction of bending and shear must be considered. Rules for considering this effect are given in the AISC LRFD and ASD Specifications.

Block Shear

This is a failure mode that may occur at the ends of coped beams, in gusset plates, and in similar locations. It is a tearing failure mode involving shear rupture along one path, such as through a line of bolt holes, and tensile rupture along a perpendicular line.

  1. gm0 = 1.10 gm1 = 1.25
    Consider the vertical plane to be primarily in tension and the horizontal planes to be primarily in Shear
    Edge Distance (d2) = 40 mm No. of Shear Planes (n1) = 1
    Vertical edge Distance (de1) = 40 mm No. of Tensile Planes (n2) = 1
    Avn = Net Shear area Atn = Net tension area
    Avg = Gross Shear area Atg = Gross tension area
    Case i) For vertical shear :
    Avn = n2(de1 + (nv – 1)sv – (nv – 0.5)dh)twb
    = 1 x( 40 mm+( 4 ) x 70 mm-( 5.50 ) x 24 mm)x 9.4 mm = 1767 mm2
    Avg = n2(de1 + (nv – 1)sv)twb
    = 1 x( 40 mm+( 4 ) x 70 mm) x 9.40 mm = 3008.0 mm2
    Atn = n1(de2 + (nh – 1)sh – (nh – 0.5)dh)twb
    = 1 x ( 40 mm+ 1 x 70 mm- 2.5 x 24 mm) x 9.40 mm = 470 mm2
    Atg = n1(de2 + (nh – 1)sh)twb
    = 1 x ( 40 mm+ 1 x 70 mm)x 9.40 mm= 1034 mm2
    Rn = 0.9 Fub Avn / (gm1 ?3)+ Fy Atg / gm0 = 527 kN
    min Fyb Avg / (gm0 ?3) + 0.9 Fub Atn / gm1 = 518 kN
    Rn = 518 kN > V = 40 kN OK
    Case ii) For Horizontal load :
    Avn = Atn of case i = 470 mm2
    Avg = Atgof case i= 1034.0 mm2
    Atn = Avn of case i= 1767 mm2
    Atg = Avgof case i= 3008 mm2
    Rn = 0.9 Fub Avn / (gm1 ?3)+ Fy Atg / gm0 = 736 kN
    min Fyb Avg / (gm0 ?3) + 0.9 Fub Atn / gm1 = 652 kN
    Rn = 651.9 kN > H = 250 kN OK
    Case iii) For combined Vertical shear and Horizontal load (Axial) :
    To discuss on interaction when both are acting together.