Test 1.28. Beam fixed at both ends subjected to uniformly distributed load, concentrated axial and transverse forces, and a bending moment

Objective

To determine the stress–strain state of a beam fixed at both ends under the uniformly distributed load, concentrated axial and transverse forces, and a bending moment.

Reference

S. Timoshenko, Resistance des materiaux, t.1, Paris, Eyrolles, 1976, p. 26. M. Courtand et P. Lebelle, Formulaire du beton arme, t.2, Paris, Eyrolles, 1976, p. 219.

Problem statement

To determine the vertical displacement Z, the axial force N, and the bending moment M at mid-span of the beam (point G), as well as the horizontal reaction H at the left end (point A).

Design model

A beam fixed at both ends is subjected to:
– a uniformly distributed load P acting over the entire span length l;
– co-directional concentrated axial forces F₁ and F₂, located at a distance of 0.3l from the left and right ends, respectively;
– a concentrated transverse force F, located at a distance of 0.3l from the right end;
– a concentrated bending moment C, located at a distance of 0.3l from the left end.

Geometry

Beam length L = 1 m
Moment of inertia J = 1,7 * 10^-8 m⁴

Material properties

Modulus of elasticity Å = 2,0 * 10¹¹ Pa
Poisson's ratio ν = 0,2

Loads

Uniformly distributed load Ð = 24 kN/m;
Concentrated force F₁ = 30 kN;
Concentrated force F₂ = 10 kN;
Concentrated force F = 20 kN;
Concentrated bending moment C = 3 kN.

Output data

Comparison of calculation results