Question

A simply supported solid beam is subjected to a vertical point load of 10 N at the middle. The length of the beam is 4 m, and the cross-section is 0.5 m \(\times\) 0.5 m. The magnitude of maximum tensile stress in the beam is ________ N/m\(^2\) (answer in integer).

Hint:

For beams subjected to point loads at the center, use the formulas for bending moment and bending stress. The maximum tensile stress occurs at the outermost fibers of the beam.

Answer 1

Step 1: Calculate maximum bending moment.
For a simply supported beam with a central point load: \[ M_{{max}} = \frac{P \cdot L}{4} = \frac{10 \cdot 4}{4} = 10 \, {Nm} \] Step 2: Calculate moment of inertia of cross-section.
Given cross-section is rectangular with \( b = 0.5 \, {m}, \, h = 0.5 \, {m} \): \[ I = \frac{b h^3}{12} = \frac{0.5 \cdot (0.5)^3}{12} = \frac{0.5 \cdot 0.125}{12} = \frac{0.0625}{12} = 0.0052083 \, {m}^4 \] Step 3: Calculate maximum bending stress.
Use: \[ \sigma = \frac{M \cdot y}{I} \] Where \( y = \frac{h}{2} = 0.25 \, {m} \). Therefore: \[ \sigma = \frac{10 \cdot 0.25}{0.0052083} \approx \frac{2.5}{0.0052083} \approx 480 \, {N/m}^2 \]