# 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