### SHEAR STRESS IN STEEL BEAM

This beam, supporting a column point load of 96 k over a door, is a composite beam consisting of a wide-flange base beam with 8x½ in plates welded to top and bottom flanges. The beam is analyzed with and without plates. As shown before, for steel beams shear stress is assumed to be resisted by the web only, computed as fv = V/Av. The base beam is a W10x49 [10 in (254 mm) nominal depth, 49 lbs/ft (6.77 kg/m) DL] with a moment of inertia Ixx= 272 in^4 (11322 cm^4). Shear in the welds connecting the plates to the beam is found using the shear flow formula q = VQ/(I).

1 Beam of L= 6 ft (1.83 m) span with P = 96 k point load

2 Composite wide-flange beam W10x49 with 8x½ inch stiffener plates

Shear force V = P/2 = 96/2 V = 48 k

Bending moment M = 48(3) M = 144 k’

Since the beam would fail in bending, a composite beam is used.

Since the shear force remains unchanged, the web shear stress is still ok.

Shear flow q in welded plate connection

Since there are two welds, each resists half the total shear flow

Note: in this steel beam, bending is stress is more critical than shear stress; this is typical for steel beams, except very short ones.

1 Beam of L= 6 ft (1.83 m) span with P = 96 k point load

2 Composite wide-flange beam W10x49 with 8x½ inch stiffener plates

Shear force V = P/2 = 96/2 V = 48 k

Bending moment M = 48(3) M = 144 k’

**Wide-flange beam**Since the beam would fail in bending, a composite beam is used.

**Composite beam**Since the shear force remains unchanged, the web shear stress is still ok.

Shear flow q in welded plate connection

Since there are two welds, each resists half the total shear flow

Note: in this steel beam, bending is stress is more critical than shear stress; this is typical for steel beams, except very short ones.