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 Æ’v (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.

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.