How to Compute the Stress & Deflections in Steel Beams

Engineering steel-framed buildings requires many specific calculations.

An essential step in engineering steel framed structures is determining the stress which a beam will endure without suffering a catastrophic failure. Bridges and buildings are stressed when they encounter loads, or forces pressing against the steel frame. A semi-tractor trailer truck driving over a bridge creates a load on the bridge's steel framework. Gale force winds exert stress forces against the foundation and steel skeleton of a tall building. Engineers must design structures which endure the forces which man and nature exert on them.

Things You'll Need

• Calculator

Instructions

1. Fill in the variables for the beam according to the following equation. Make sure to match the units. Use all metric or all U.S. dimensions. Don't mix the systems. Maximum stress in a beam that experiences a uniform load, that is supported at each end is calculated with the following formula: σ = y *q * L2 / 8 * I. [σ = maximum stress, y = Perpendicular distance from to neutral axis X of the beam, q = uniform load, or beam unit weight, L = length of beam, I = moment of Inertia ( a function of the beam geometry, and construction geometry].

2. Collect and fill in the variables for the beam and construction configuration according to the following equation. Again, make sure you use consistent units of measure. Maximum deflection can be calculated by δ = 5 *q* L4 / E *I* 384. [δ = maximum deflection, E = modulus of elasticity, other variables defined above]

3. Collect and plug in the variables based on the beam and construction configuration based on the following equation. The maximum stress in a beam with uniform load in the center which is supported at both ends can be calculated as σ = y* F* L / 4* I. [σ = maximum stress, y = Perpendicular distance from to neutral axis, F = load on the beam, L = length of beam, I = moment of Inertia].

4. Collect the variables and plug them into the following equation to calculate the maximum deflection of a beam. Deflection is the amount the beam will bend, or deflect, when a load is placed on the beam. The maximum deflection is δ = F *L3 / E *I *48. [δ = maximum deflection, E = modulus of elasticity, other variables defined above].

References

• Engineering Toolbox: Stress and Deflection in Beams
• Efunda: Column Design: Structural Steel
• The Steel Institute: Beam Load Table

Resources

• StrucSoft: Beam Strength Calculations