CTC 422 Design of Steel Structures Beams Shear

CTC 422 Design of Steel Structures Beams Shear and Deflection

Beam Design • Student Objectives • • Analyze a beam to calculate load, shear, moment and deflection and to determine if a given beam is adequate Design (select) a beam to safely to support a load considering moment, shear and deflection

Design for Shear - LRFD • Steel beams Shear seldom governs • Exceptions: • • Very short spans Very heavy loads • Normal procedure: • • Select beam for moment (bending) Then check for shear

Load and Resistance Factor Design - LRFD • Design strength ≥ Required strength • ΦRn ≥ Ru • For shear • • Φv Vn ≥ V u Where: • Vn = Nominal shear strength • Φv = Strength reduction factor for shear • Vu = Required shear strength based on factored loads

Design for Shear Chapter G of AISC Code • Nominal shear strength, Vn, depends on the failure mechanism of the beam • Beam can fail by: • • Shear yielding Shear buckling • Can be inelastic or elastic buckling • Failure mechanism is related to the width to thickness ratio of the beam’s web, h / tw • Section G 2. 1 applies to doubly symmetric sections (W, M, S and HP shapes) and channel shapes (C and MC) • • Section G 2. 1 a applies to I-shaped sections with h / tw ≤ a given limit Section G 2. 1 b applies to other doubly symmetric shapes and channels • Nominal shear strength in this case is less than calculated by G 2. 1 a

Design for Shear Chapter G of AISC Code • Nominal shear strength, Vn, can be calculate by Section G 2. 1 a, or G 2. 1 b • Then check Φv. Vn ≥ Vu • Or, shear strength Φv. Vn tabulated in design aids can be used • Shear strength is listed in the following tables: • W-Shapes – Table 3 -2 • Also listed in Table 3 -6 • • S-Shapes – Table 3 -7 Channel Shapes (C and MC) – Tables 3 -7 and 3 -8

Seviceability Chapter L of AISC Code • Deflection – Section L 3 • Deflections under service load combinations shall not impair the serviceability of the structure • Limits on deflections are specified in building codes • NYS Building Code Section 1604. 3 • Floor members • Live load deflection ≤ span / 360 • Dead load plus live load deflection ≤ span / 360 • ACI Masonry Code • Beams supporting masonry • Total deflection ≤ span / 600 ≤ 0. 3 inches • Very stringent criteria

Deflections • Beam deflections for various load conditions shown in table 3 -23 • For a simply supported beam with a uniform load on its full span • • Δ = 5 w. L 4 / 384 EI Use consistent units, usually kips and inches • If load, w, and span, L, are known this equation can be solved for the moment of inertia, I, that would produce a given deflection • • For Δ ≤ span / 360, I ≥ w. L 3 / 43 For Δ ≤ span / 240, I ≥ w. L 3 / 64. 5 For Δ ≤ span / 600, I ≥ w. L 3 / 25. 8 In these equations, w is in kips / ft, L in feet, and I in in 4 • Approximate deflection in beams with non-uniform loads • Calculate the equivalent uniform load based on moment • E. U. L = 8 M / L 2 • Use this value for w in the equations above