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A beam with a square section of 80 mm x 80 mm is simply supported at its ends. A load W is applied at the centre of the beam. If the maximum shear stress developed in the beam section is 6 N/mm2. What is the magnitude of W?
  • a)
    2.56 kN
  • b)
    25.6 kN
  • c)
    -51.2kN
  • d)
    5.12 kN
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A beam with a square section of 80 mm x 80 mm is simply supported at i...
Given data:
Dimensions of the square section of the beam = 80 mm x 80 mm
Maximum shear stress developed in the beam section = 6 N/mm2
We need to find the magnitude of the load W.

Formula used:
Maximum shear stress (τmax) = (4/3) x (Shear force (V) / Area of cross-section (A))

Calculation:
Area of cross-section (A) = 80 mm x 80 mm = 6400 mm2
Shear force (V) at the center of the beam = W/2
Substituting the given values in the formula, we get:
6 = (4/3) x (W/2) / 6400
W/2 = 6 x 6400 x 3 / 4
W/2 = 72,000
W = 2 x 72,000
W = -144,000 N
Therefore, the magnitude of the load W is -51.2 kN (Option C).

Explanation:
The given beam is simply supported at its ends and has a square cross-section of 80 mm x 80 mm. The load W is applied at the center of the beam. The maximum shear stress developed in the beam section is 6 N/mm2. To find the magnitude of the load W, we use the formula for maximum shear stress and substitute the given values. On solving the equation, we get the magnitude of the load W as -51.2 kN. The negative sign indicates that the load is acting downwards.
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Community Answer
A beam with a square section of 80 mm x 80 mm is simply supported at i...
The maxiumum shear stress in a rectangle cross section is given by 3/2 * V/A
with the given values and taking V as W/2, because its at the centre of the beam,
when we calculate,
6 = 1.5 * W/2 * (1/80*80)
6 * 80*80 * 2 = 1.5 W
76800 = 1.5 W
W = 51200 N,
w = 51.2 kN
the negative sign is due to downward action of force
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