Answer :
i) The shear stress at mid-depth of the beam is 5 MPa.
ii) The shear stress 80 mm below the top of the beam is 6.33 MPa.
i) To calculate the shear stress at the mid-depth of the beam, we need to determine the cross-sectional area of the beam and divide the shear force by that area.
Cross-sectional area of the beam: A = width × depth
A = 100 mm × 380 mm = 38,000 mm² = 0.038 m²
Shear stress at mid-depth: τ = Shear force / Cross-sectional area
τ = 190 kN / 0.038 m² = 5,000 kPa or 5 MPa
ii) To calculate the shear stress 80 mm below the top of the beam, we need to consider the reduced effective depth of the section.
Effective depth = Total depth - Distance from the top
Effective depth = 380 mm - 80 mm = 300 mm
Cross-sectional area at 80 mm below the top: A' = width × effective depth
A' = 100 mm × 300 mm = 30,000 mm² = 0.03 m²
Shear stress at 80 mm below the top: τ' = Shear force / Cross-sectional area
τ' = 190 kN / 0.03 m² = 6,333.33 kPa or 6.33 MPa
Therefore, the shear stress at the mid-depth is 5 MPa, and at 80 mm below the top, it is 6.33 MPa.
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