Solution to Problem 244 Statically Indeterminate | Strength of Materials Review at MATHalino

Problem 244
A homogeneous bar with a cross sectional area of 500 mm² is attached to rigid supports. It carries the axial loads P₁ = 25 kN and P₂ = 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 P₁ and P₂ acting separately. Then use the principle of superposition to compute the reactions when both loads are applied.)

Solution 244

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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

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principle of superposition

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