Finding Maximum Shear Stress in a Box Beam

What is the shear stress at point B and the maximum shear stress in a box beam?

In a box beam shown with dimensions in fig. 1, determine the maximum shear stress and the shear stress at point B, if the internal shear force at the given cross section is V = 100 kN.

Answer:

The correct answer is option (a): Shear stress at point B: 1.12 MPa, Maximum shear stress: 2.24 MPa.

In the given box beam, we can determine the shear stress at point B and the maximum shear stress using the formula for shear stress tau = VQ / Ib where: - tau is the shear stress - V is the internal shear force - Q is the statical moment of the area above or below the point in consideration - I is the moment of inertia of the cross-section - b is the width of the section. At point B, the shear stress tau_B is calculated using Q_B and b, and the maximum shear stress tau_max occurs at the section where Q is maximum. The statical moment Q at point B is determined by the formula Q_B = bd^2 / 2. For the given dimensions in Fig. 1, we can substitute the values into the formula to find Q_B. The maximum statical moment Q_max occurs at the center of the beam and is given by Q_max = bd^2 / 4. Substituting the values into the shear stress formula for both point B and the maximum shear stress, we get: - tau_B = 2Vbd - tau_max = Vbd^2 By substituting the shear force V = 100 kN and the dimensions into these equations, we find tau_B = 1.12 MPa and tau_max = 2.24 MPa. Therefore, the correct answer is option (a).