In this page we consider a one-dimensional beam fixed at both ends subjected to an uniform temperature rise T.

If you want, you can build the FE model with the data shown in the following table.

Youngâ€™s modulus

E

69637000

kPa

Section

A

1,00

\(m^2\)

Length

L

10,00

m

Coefficient of thermal expansion

\(\alpha\)

0,0000234

1/K

Temperature increase

T

293,00

K

On the other hand, you can find it through our tutorials, so you just have to start the calculation.

First you have to determine the analytical solution: in order to do it, consider the axial direction. [1] The strain on the beam due to uniform temperature change is:

\(\epsilon_T=\alpha \cdot T\)

The stress/strain law is linear, therefore the nodal forces must be

\(F=A \cdot \sigma=A \cdot E \cdot \epsilon = A \cdot E \cdot \alpha \cdot T\)

Therefore you can compare the analytical solution with WeStatiX’s results, as shown in the following table.

Description

Parameter

UM

Analytical solution

WSX

Error

Force

\(F\)

kN

477445

477445

0,00%

In the pictures you can see the diagram of the normal force.

WeStatiX catches the solution perfectly.

[1] DARYL L. LOGAN, A First Course in the Finite Element Method, 4th edition, Thomson