1. CTC 422 Design of Steel Structures
Beams
Shear and Deflection

2. 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

3. 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

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

5. 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 2.1a applies to I-shaped sections with h / tw ≤ a given limit
Section G 2.1b applies to other doubly symmetric shapes and channels
Nominal shear strength in this case is less than calculated by G 2.1a

6. Design for Shear Chapter G of AISC Code
Nominal shear strength, Vn, can be calculate by Section G 2.1a, or G 2.1b
Then check ΦvVn ≥ Vu
Or, shear strength ΦvVn 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

7. Seviceability Chapter L of AISC Code
Deflection – Section L3
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
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

8. 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 = 5wL4 / 384EI
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 ≥ wL3 / 43
For Δ ≤ span / 240, I ≥ wL3 / 64.5
For Δ ≤ span / 600, I ≥ wL3 / 25.8
In these equations, w is in kips / ft, L in feet, and I in in4
Approximate deflection in beams with non-uniform loads
Calculate the equivalent uniform load based on moment
E.U.L = 8 M / L2
Use this value for w in the equations above