Midspan deflection of a simply supported beam with a point load

Load and supports are symmetric. The deflection curve is therefore symmetric and has zero slope at midspan, where its extremum occurs. Asymmetric loads or support settlement can shift the maximum. Assume ideal simple supports, a central point load and linear Euler–Bernoulli behavior. Application: Check deflection of an idealized simply supported beam under a central load. The numerical example For F=1 kN, L=2 m, E=200 GPa and I=8·10⁻⁶ m⁴, δmax≈1.04 mm anchors the idea in a concrete measurement case. The corresponding units are δ and L in m; F in N; E in Pa; I in m⁴. For F=1 kN, L=2 m, E=200 GPa and I=8·10⁻⁶ m⁴, δmax≈1.04 mm. This checks that the reference quantities are compatible.

The factor comes from piecewise integration of the central-load moment diagram with support boundary conditions and midspan symmetry. A different load, such as uniform distributed loading, has another coefficient. Assume ideal simple supports, a central point load and linear Euler–Bernoulli behavior. The corresponding units are δ and L in m; F in N; E in Pa; I in m⁴. For F=1 kN, L=2 m, E=200 GPa and I=8·10⁻⁶ m⁴, δmax≈1.04 mm. This checks that the reference quantities are compatible. Scope: Assumes ideal pin and roller supports, a central point load, constant section and linear Euler–Bernoulli bending. Support settlement, shear deformation and self-weight are omitted. Other load and support cases have different coefficients; no code deflection limit is prescribed here. A practical application is Check deflection of an idealized simply supported beam under a central load.

For short or deep beams, shear deformation can matter relative to bending. Euler–Bernoulli omits it and can underpredict total deflection. A Timoshenko beam or suitable finite-element model may be more appropriate. Assume ideal simple supports, a central point load and linear Euler–Bernoulli behavior. Scope: Assumes ideal pin and roller supports, a central point load, constant section and linear Euler–Bernoulli bending. Support settlement, shear deformation and self-weight are omitted. Other load and support cases have different coefficients; no code deflection limit is prescribed here. A practical application is Check deflection of an idealized simply supported beam under a central load.

Write the quantity and unit from the variable list next to every value: δ and L in m; F in N; 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 F=1 kN, L=2 m, E=200 GPa and I=8·10⁻⁶ m⁴, δmax≈1.04 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 ideal simple supports, a central point load and linear Euler–Bernoulli behavior.

The background states this starting condition: Assumes ideal pin and roller supports, a central point load, constant section and linear Euler–Bernoulli bending. Support settlement,. 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 ideal simple supports, a central point load and linear Euler–Bernoulli behavior.