What are Beams and Loads?
A beam is a structural member that resists loads mainly through bending, carrying forces from slabs and walls down to columns and foundations. Understanding beams and loads means understanding shear, bending moment and bending stress.
A beam bends under transverse loads, developing internal shear force and bending moment; the resulting bending stress is σ = Mc/I, where M is the moment, c the distance to the extreme fiber, and I the moment of inertia.
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Step-by-step worked examples
A beam has M=8000 N·m, distance to extreme fiber c=150 mm, and I=4.5×10⁷ mm⁴. Find the bending stress (convert M to N·mm).
M = 8000 N·m = 8,000,000 N·mm σ = Mc/I = 8,000,000×150 / 45,000,000 σ = 1,200,000,000/45,000,000 = 26.67 MPa
A simply supported beam of span 8 m carries a uniform load w=10 kN/m. Find the maximum bending moment (at midspan).
M_max = w·L²/8 = 10×8²/8 = 10×64/8 M_max = 80 kN·m
A cantilever beam of length 3 m carries a 5 kN point load at the free end. Find the maximum shear force and moment at the fixed support.
Max shear V = P = 5 kN (constant along the beam) Max moment M = P×L = 5×3 = 15 kN·m (at the fixed end)
Flashcards
Quick quiz
Q1.The bending stress formula is…
Q2.Max moment for a simply supported beam under UDL w over span L is…
Q3.For a cantilever with end load P and length L, the maximum moment occurs…
Q4.Increasing I (moment of inertia) for the same M and c…
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Common mistakes
Using overall beam height instead of distance to extreme fiber (c). — Correct: c is measured from the neutral axis to the outermost fiber, not the total depth.
Mixing units — moment in kN·m with I in mm⁴. — Correct: Convert everything to consistent units (usually N·mm and mm⁴) before dividing.
Assuming max moment is always at midspan. — Correct: It depends on load and support type — cantilevers peak at the fixed support.
Ignoring shear force and only checking bending stress. — Correct: Beams must be checked for both bending stress AND shear stress.
FAQ
What are beams and loads?
A beam is a member that carries transverse loads by bending; loads are the forces (dead, live, point, distributed) it must resist.
What is the beams and loads bending stress formula?
σ = Mc/I, where M is bending moment, c is distance to the extreme fiber, and I is the moment of inertia.
How do you calculate the bending moment in a beam?
For a simply supported beam under uniform load w and span L, the maximum moment is M=wL²/8 at midspan.
What are examples of beams and loads problems?
Finding reactions, drawing shear/moment diagrams, and checking bending stress against a beam's allowable stress.