Answer :
The shear stress in the rectangular beam is 0.474 MPa at mid-depth and 0.948 MPa at 80 mm below the top.
Shear stress is a measure of the force per unit area that acts parallel to the face of a material. To calculate shear stress, we use the formula: Shear Stress (τ) = Shear Force (F) / Area (A). Given the dimensions of the rectangular beam (width = 100 mm, depth = 380 mm) and the shear force (180 KN), we can calculate the area for each case.
Mid-Depth:
The mid-depth of the beam is half of the depth, which is 380 mm / 2 = 190 mm. The area at mid-depth is A = width × depth = 100 mm × 190 mm = 19000 mm² = 0.019 m². Substituting the shear force (180 KN = 180,000 N) and the area into the formula: τ = 180,000 N / 0.019 m² ≈ 9474.21 N/m² = 0.474 MPa.
80 mm below the top:
The distance below the top is 80 mm. The area at this section remains the same: A = 100 mm × 380 mm = 38000 mm² = 0.038 m². Applying the formula: τ = 180,000 N / 0.038 m² ≈ 4736.84 N/m² = 0.948 MPa.
These calculations demonstrate that shear stress is greater at the higher location within the beam due to the smaller cross-sectional area. Shear stress is a critical factor in designing beams and structures to ensure they can withstand external forces without failure.
Shear stress is an important consideration in structural engineering and materials science. It plays a significant role in determining the stability and safety of various structures, such as bridges, buildings, and mechanical components.
Understanding how shear stress distributes within different sections of a beam is essential for designing reliable and resilient structures. Engineers carefully analyze shear stress along with other factors like bending moments, material properties, and load distributions to ensure structures can endure the forces they encounter.
Learn more about shear stress
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