Worked Example
A 10 ft simply supported beam carries a 2,000 lb load at midspan. M_max = 2,000 × 10 / 4 = 5,000 lb·ft (60,000 lb·in), each reaction is 1,000 lb, and at an allowable stress of 24,000 psi the required section modulus is 60,000 / 24,000 = 2.5 in³.
Frequently Asked Questions
How do I calculate the maximum bending moment of a simply supported beam?
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It depends on the load. For a central point load P over a span L, the maximum moment at midspan is M = PL/4. For a uniformly distributed load of w per unit length, the maximum moment is M = wL²/8. Both occur at midspan for these symmetric cases. The maximum moment is what governs the beam's bending stress and therefore the size of the beam you must select.
What is section modulus and how do I use it?
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Section modulus (S) is a geometric property of a beam's cross-section that relates bending moment to bending stress: stress = M/S. The required section modulus is S = M/F_b, where F_b is the allowable bending stress. Once you compute the required S, you pick any beam whose section modulus (from a steel W-shape or lumber table) meets or exceeds it, ensuring the bending stress stays within the allowable value.
What are the reactions on a simply supported beam?
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For a symmetric load, each of the two supports carries half the total load. A central point load P gives reactions of P/2 at each end; a uniform load w over span L gives reactions of wL/2 (half the total load wL) at each end. The reactions equal the maximum shear in the beam and are used to design the supports, connections and bearing.
What allowable bending stress should I use?
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For structural steel, the allowable bending stress in allowable-stress design is roughly 0.66 times the yield strength — about 24,000 psi for A36 (Fy = 36 ksi) and around 30,000 psi for A992/Grade 50 (Fy = 50 ksi). Wood allowable stresses are far lower and species-dependent (hundreds to ~1,500 psi). Modern steel design often uses LRFD instead; this calculator uses an allowable-stress approach for a quick required-section-modulus estimate.
Does this calculator check deflection?
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No — it computes strength (bending moment, shear and required section modulus), not deflection. Deflection depends on the beam's moment of inertia and the material's modulus of elasticity (δ = PL³/48EI for a central point load, 5wL⁴/384EI for a uniform load), which require a specific section to evaluate. Many beams are governed by deflection limits (like L/360) rather than strength, so always check deflection after selecting a section.
What is the difference between a point load and a uniform load?
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A point load is a concentrated force applied at one location (like a column bearing on a beam), while a uniform load is spread evenly along the beam (like the weight of a floor or a wall). For the same total load on the same span, a central point load produces twice the maximum moment of a uniform load (PL/4 versus wL²/8 with wL = P), so the load distribution significantly affects the beam size required.
Is this beam calculator accurate for design?
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It applies the exact statics formulas for a simply supported beam under symmetric point or uniform loading, so the moment, shear and required section modulus are correct for those cases. It does not cover multiple or unsymmetrical loads, continuous or cantilever beams, combined loading, lateral-torsional buckling, or deflection and code load factors. Use it for preliminary sizing, and have final structural designs prepared and stamped by a licensed structural engineer.
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