Problem 919 | Additional Axial Compression Load for the Section to Carry No Tensile Stress | Strength of Materials Review at MATHalino

Problem 919
From the data in Prob. 918, what additional load applied at the centroid is necessary so that no tensile stress will exist anywhere on the cross-section?

Solution 919

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Relevant data extracted from Solution 918

$\text{Area} = 60 ~ \text{in.}^2$

The largest tensile stress is at corner B
$\sigma_B = 320 ~ \text{psi}$

Additional compression force P₂ for zero stress at corner B

$\sigma_B = 320 - \dfrac{P_2}{60} = 0$

$P_2 = 19,200 ~ \text{lbs}$ ← answer

Stress at each corner from Solution 918

$\sigma_A = -480 ~ \text{psi}$

$\sigma_B = 320 ~ \text{psi}$

$\sigma_C = 80 ~ \text{psi}$

$\sigma_D = -720 ~ \text{psi}$

Stress at each corner due to additional stress σ₂ = -320 psi.

$\sigma_A = -480 - 320 = -800 ~ \text{psi}$

$\sigma_B = 320 - 320 = 0$

$\sigma_C = 80 - 320 = -240 ~ \text{psi}$

$\sigma_D = -720 - 320 = -1040 ~ \text{psi}$

See figure above.

Problem 919 | Additional Axial Compression Load for the Section to Carry No Tensile Stress

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