## Problem 725 | Propped beam with partially restrained wall and settling simple support

**Problem 725**

If the support under the propped beam in Problem 724 settles an amount $\delta$, show that the propped reaction decreases by $3EI\delta / L^3$.

**Problem 725**

If the support under the propped beam in Problem 724 settles an amount $\delta$, show that the propped reaction decreases by $3EI\delta / L^3$.

**Problem 724**

The beam shown in Fig. P-724 is only partially restrained at the wall so that, after the uniformly distributed load is applied, the slope at the wall is $w_oL^3 / 48EI$ upward to the right. If the supports remain at the same level, determine $R$.

Temperature changes cause the body to expand or contract. The amount δ_{T}, is given by

$\delta_T = \alpha L \, (T_f \, - \, T_i) = \alpha L \, \Delta T$

where α is the coefficient of thermal expansion in m/m°C, L is the length in meter, T_{i} and T_{f} are the initial and final temperatures, respectively in °C. For steel, α = 11.25 × 10^{-6} m/m°C.

If temperature deformation is permitted to occur freely, no load or stress will be induced in the structure. In some cases where temperature deformation is not permitted, an internal stress is created. The internal stress created is termed as thermal stress.

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