L16: Nonlinear Thermal Load

The three-span simply supported member in the figure below is subjected to a nonlinear thermal gradient. The member has a T-shaped cross-section (1.6m depth, 2.8 m width, 0.4 m web thickness, 0.2 m flange thickness). The material has a modulus of elasticity of 3x108 N/m2 and a coefficient of thermal expansion of 10x10-6 1/°C.

The spans are 21 m, 27 m, and 21 m.

The thermal load is uniform along the length of the member but it varies as a fifth-order parabola along the depth of the section, from a maximum of 25°C at the top fiber to 0°C at a depth of 1.2 m and below. The temperature change as a function of depth, measured from the top of the section, is given by the equation:

for y < 1.2 m, and ΔT = 0 in 1.2 m <= y <= 1.6 m.

The nonlinear gradient creates self-equilibriating stresses.

Calculate the total stress at a fiber.

The model, cross-section, and thermal gradient are depicted in the figure below: