Question

A rectangular beam 200 mm deep and 300 mm wide is simply supported over a span of 8 m. What uniformly distributed load per metre the beam may carry, if the bending stress is not to exceed 120N/mm2.

Answer 1

The uniformly distributed load per meter the beam may carry will be 1.275 × 10 ⁶ N/mm.

What is bending stress?

When an object is subjected to a heavy load at a specific spot, it often experiences bending stress, which causes the object to bend and tire.

The given data in the problem is;  

Bending stress, σ = 120 N/mm2  

Moment of inertia, I = 8.5 × 106 mm⁴

Depth of beam, y = d/2 = 200/2 = 100 mm  

Length of beam, L = 8 m = 8000 mm  

Width of beam, W = 300 mm

The maximum bending moment of the beam with UDL;

$\rm W = \frac{wL^2}{8}$

From the bending equation;

$\rm M = \frac{\sigma I}{y_{max}} \\\\ M = \frac{120 \ N / mm^2 \times 8.5 \times 10^6 }{100 \ mm } \\\\ M = 10.2 \times 10^6 \ N - mm$

The maximum bending moment of the beam with UDL;

$\rm M = \frac{wL^2}{8} \\\\ 10.2 \times 10^6 = \frac{w \times 8^2}{8} \\\\ w = 1.275 \times 10^6 \ N/mm$

Hence the uniformly distributed load per meter the beam may carry will be 1.275 × 10 ⁶ N/mm.

To learn more about the bending stress, refer;

brainly.com/question/24227487

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