Code-check of bolts according to Indian standard

Shear capacity of bolts

The design strength of the bolt, $V_{dsb}$, as governed shear strength is given by IS 800, Cl. 10.3.3:

$$V_{sb} \le V_{dsb}$$

where:

• $V_{dsb} = V_{nsb}/\gamma_{mb}$ – design shear capacity of a bolt
• $V_{nsb} = \frac{f_{ub}}{\sqrt{3}} A_e$ – nominal shear capacity of a bolt
• $f_{ub}$ – ultimate tensile strength of a bolt;
• $A_e$ – area for resisting shear; $A_e = A_n$ for shear plane intercepted by the threads, $A_e = A_s$ for the case where threads do not occur in shear plane
• $A_n$ – net tensile stress area of the bolt
• $A_s$ – cross-section area at the shank
• $\gamma_{mb} = 1.25$ – partial safety factor for bolts – bearing type – IS 800, Table 5; editable in Code setup

When the grip length of bolts $l_g$ (equal to the total thickness of the connected plates) is higher than $5d$, the design shear capacity $V_{dsb}$ is reduced by a factor $\beta_{lg}$ – IS 800, Cl. 10.3.3.2:

$$\beta_{lg} = \frac{8}{3+l_g/d}$$

According to IS 800, Cl. 10.3.3.3, the design shear capacity of bolts carrying shear through a packing plate with the thickness $t_{pk} \ge 6$ mm shall be decreased by a factor:

$$\beta_{pk} = (1-0.0125 t_{pk})$$

Each shear plane is checked separately, and the worst result is shown.

Bearing capacity of bolts

The design bearing strength of a bolt on any plate, as governed by bearing is given by IS 800, Cl. 10.3.4:

$$V_{sb} \le V_{dpb}$$

where:

• $V_{dpb} = V_{npb} / \gamma_{mb}$ – design bearing strength of a bolt
• $V_{npb} = 2.5 k_b d t f_u$ – nominal bearing strength of a bolt
• $k_b = \min \left \{ \frac{e}{3d_0}, \, \frac{p}{3d_0}-0.25, \, \frac{f_{ub}}{f_u}, \, 1.0 \right \}$ – factor for joint geometry and material strength
• $e$ – end distance of the fastener along bearing direction
• $p$ – pitch distance of the fastener along bearing direction
• $f_{ub}$ – ultimate tensile strength of the bolt
• $f_u$ – ultimate tensile strength of the plate
• $d$ – nominal diameter of the bolt
• $d_0$ – diameter of bolt hole
• $t$ – plate thickness
• $\gamma_{mb} = 1.25$ – partial safety factor for bolts – bearing type – IS 800, Table 5; editable in Code setup

Bearing on each plate is checked separately and the worst result is shown.

The bearing resistance is reduced for oversized and slotted holes by a factor:

• 0.7 – for oversized and short slotted holes
• 0.5 – for long slotted holes

Sizes of oversized, short slotted, and long slotted holes are determined according to IS 800, Table 19.

Tension capacity of bolts

A bolt subjected to a factored tensile force is checked according to IS 800, Cl. 10.3.5:

$$T_b \le T_{db}$$

where:

• $T_{db} = T_{nb} / \gamma_{mb}$ – design tensile capacity of the bolt
• $T_{nb} = \min \{ 0.9 f_{ub} A_n, \, f_{yb} A_s (\gamma_{mb} / \gamma_{m0}) \}$ – nominal tensile capacity of the bolt
• $f_{ub}$ – ultimate tensile strength of the bolt
• $f_{yb}$ – yield strength of the bolt
• $A_n$ – net tensile stress area of the bolt
• $A_s$ – cross-section area at the shank
• $\gamma_{mb} = 1.25$ – partial safety factor for bolts – bearing type – IS 800, Table 5; editable in Code setup
• $\gamma_{m0} = 1.1$ – partial safety factor for resistance governed by yielding – IS 800, Table 5; editable in Code setup

Bolt subjected to combined shear and tension

A bolt required to resist both design shear force and design tensile force at the same time shall according to IS 800, Cl. 10.3.6 satisfy:

$$\left( \frac{V_{sb}}{V_{db}} \right)^2 + \left( \frac{T_{b}}{T_{db}} \right)^2 \le 1.0$$

where:

• $V_{sb}$ – factored shear force
• $V_{db} = \min \{ V_{dsb}, \, V_{dpb} \}$ – design shear resistance of the bolt – IS 800, Cl. 10.3.2
• $V_{dsb}$ – design shear resistance
• $V_{dpb}$ – design bearing resistance
• $T_b$ – factored tensile force
• $T_{db}$ – design tensile capacity of the bolt