Deflection of a simply supported beam under uniform load

It follows from integrating the moment function for a uniformly loaded simply supported span with support boundary conditions. A central point load uses 1/48, so the load cases are not interchangeable. Assume simple supports, uniform load across the span and constant elastic bending stiffness. Application: Estimate an idealized simply supported beam’s response to distributed load. The numerical example For q=1 kN/m, L=4 m, E=200 GPa and I=8·10⁻⁶ m⁴, δmax≈5.21 mm anchors the idea in a concrete measurement case. The corresponding units are δ,L in m; q in N/m; E in Pa; I in m⁴. For q=1 kN/m, L=4 m, E=200 GPa and I=8·10⁻⁶ m⁴, δmax≈5.21 mm. This checks that the reference quantities are compatible.

For uniform self-weight, q is mass per length times gravitational acceleration, plus other permanent line loads. Units must be N/m. Variable section or additional loads can make q(x) nonuniform, invalidating this closed form. Assume simple supports, uniform load across the span and constant elastic bending stiffness. The corresponding units are δ,L in m; q in N/m; E in Pa; I in m⁴. For q=1 kN/m, L=4 m, E=200 GPa and I=8·10⁻⁶ m⁴, δmax≈5.21 mm. This checks that the reference quantities are compatible.

Yes. At fixed q, E and I, maximum deflection scales as L⁴; doubling span gives a factor of sixteen. Real self-weight and section requirements also change, so this is a comparison model, not a full structural design. Assume simple supports, uniform load across the span and constant elastic bending stiffness. Scope: Assumes pin and roller supports, a uniform load, constant EI and linear Euler–Bernoulli bending. Continuous spans, fixed ends or varying sections require other coefficients or an integration model. A practical application is Estimate an idealized simply supported beam’s response to distributed load.

Write the quantity and unit from the variable list next to every value: δ,L in m; q in N/m; E in Pa; I in m⁴. Substitute only after converting to a consistent unit system, and state sign or reference direction explicitly. The example For q=1 kN/m, L=4 m, E=200 GPa and I=8·10⁻⁶ m⁴, δmax≈5.21 mm. is a calculation check: result, unit and order of magnitude must fit the described situation. Round after intermediate calculations so small contributions are not lost prematurely. Assume simple supports, uniform load across the span and constant elastic bending stiffness.

The background states this starting condition: Assumes pin and roller supports, a uniform load, constant EI and linear Euler–Bernoulli bending. Continuous spans, fixed ends. That limits when the result is a valid model prediction. Compare the problem’s boundary conditions with this assumption before substituting values; real components, material properties or loads can introduce additional effects. The cited reference supports the relation used here but does not remove the need to check whether the specific case fits the model. Assume simple supports, uniform load across the span and constant elastic bending stiffness.