College

A rectangular beam, 100 mm wide and 380 mm deep, is subjected to a shear force of 180 kN. Calculate the shear stress in the beam:

1. At mid-depth

Answer :

Final answer:

The shear stress in the beam at mid-depth is approximately 4736.84 kPa.

Explanation:

To calculate the shear stress at mid-depth of the rectangular beam, we need to determine the cross-sectional area at that point. The cross-sectional area of a rectangular beam can be calculated by multiplying its width by its depth.

Given:

  • Width of the beam (b) = 100 mm
  • Depth of the beam (d) = 380 mm
  • Shear force (F) = 180 kN

First, we need to convert the dimensions to meters:

  • Width of the beam (b) = 100 mm = 0.1 m
  • Depth of the beam (d) = 380 mm = 0.38 m

Next, we can calculate the cross-sectional area (A) of the beam:

A = b * d = 0.1 m * 0.38 m = 0.038 m²

Finally, we can calculate the shear stress (τ) at mid-depth:

τ = F / A = 180 kN / 0.038 m² = 4736.84 kPa

Learn more about calculating shear stress in a rectangular beam here:

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