Test 1.2. Plane truss subjected to mechanical, thermal and kinematic loads

Objective

To determine the stress–strain state of a plane truss under mechanical, thermal and kinematic loads.

Reference

M. Laredo, Résistance des matériaux, Paris, Dunod, 1970, P. 579.

Problem statement

Determine the axial force in the diagonal element at support BD and the vertical displacement v at point D.

Design model

The two-span truss is subjected to:

• two concentrated loads F_E and F_F applied at the nodes of the top chord,

• uniform heating of all cross-sections of the elements by ΔT,

• displacements of its supports by V_A, V_B and V_C.

Geometry

The inclination angle of the support zone at node C relative to the horizontal is θ = 30°.
Cross-sectional areas of the bars А₁ = 1,41 * 10^-3 m²; А₂ = 2,82 * 10^-3 m².

Material properties

Modulus of elasticity Е = 2,1 * 10¹¹ Pa.
Coefficient of thermal expansion α = 10^-5 C^-1.

Boundary conditions

In both linear and nonlinear analyses, no restraint is imposed in the direction of a prescribed displacement. Since all loads are applied within a single load case, the model is restrained only at node A against displacement along the global X-axis (X(uA) = 0).

Loads

Forced displacements: V_A = -0,02 m; V_В = -0,03 m; V_C = -0,015 m.
Vertical concentrated loads: F_E = 150 kN; F_F = 100 kN.
Thermal load: all bars are heated to a temperature of 150°C.

Output data

Comparison of calculation results