Bending Deflection Due to Temperature Variation - Civil Engineering (CE) PDF Download

 Bending Deflection due to Temperature Variation 

Consider a beam member (refer Figure 4.29) subjected to temperature gradient ΔT over the depth of beam such that

ΔT=T_t - T_{b              (4.22)}

where T_t = temperature at the top of the beam; and T_b = temperature at the bottom of the beam.

The deflection of the beam due to temperature variation is shown in Figure 4.29(b). It is assumed that temperature varies linearly through the depth, d and ∝ is the coefficient of thermal expansion of the material.

Consider a small element of length dx . The strain at top and bottom of the small elements are

         (4.23a)

     (4.23b)

The curvature of the beam is given by

    (4.24)

The equation (4.24) can be used for finding out the bending deflection in beams due to temperature variation. If the beam is restrained from rotation, the moment induced in the beam will be given by

  (4.25)

The equation (4.25) is obtained by equating the right hand side of equation (4.24) to M_T/EI from the simple bending theory.

Temperature deflections of a cantilever beam:

Consider a cantilever beam as shown in Figure 4.30 subjected to temperature gradient ΔT=T_t - T_b over the depth. Integrating the equation (4.24)

                  (4.26)

          (4.27)

Boundary conditions: At x=0,dv/dx =0 and and v = 0 will give the values of arbitrary constants as C₁ = C₂ = 0.

The slope and deflection of the free end of the cantilever beam are

                 (4.28a)

               (4.28a)