# Solution to Problem 244 Statically Indeterminate

**Problem 244**

A homogeneous bar with a cross sectional area of 500 mm^{2} is attached to rigid supports. It carries the axial loads P_{1} = 25 kN and P_{2} = 50 kN, applied as shown in Fig. P-244. Determine the stress in segment BC. (Hint: Use the results of Prob. 243, and compute the reactions caused by P_{1} and P_{2} acting separately. Then use the principle of superposition to compute the reactions when both loads are applied.)

**Solution 244**

**From the solution of Problem 243:**

$R_1 = 25(2.10)/2.70$

$R_1 = 19.44 \, \text{kN}$

$R_2 = 50(0.90)/2.70$

$R_2 = 16.67 \, \text{kN}$

$R_A = R_1 + R_2$

$R_A = 19.44 + 16.67$

$R_A = 36.11 \, \text{kN}$

**For segment BC**

$P_{BC} + 25 = R_A$

$P_{BC} + 25 = 36.11$

$P_{BC} = 11.11 \, \text{kN}$

$\sigma_{BC} = \dfrac{P_{BC}}{A} = \dfrac{11.11(1000)}{500}$

$\sigma_{BC} = 22.22 \, \text{ MPa}$ *answer*