Determine the orientation of the neutral axis

Reference no: EM132281194

Question 1. The asymmetric I-beam shown is made of A992 Gr. 50 steel (fy = 50 ksi).

a. Assuming Elastic-Perfectly Plastic behavior and the same properties in tension and compression, determine the fully plastic moment, Mp.

b. If the beam is curved and subjected to the uniform moment, M, shown below, determine the largest moment that can be applied if the circumferential stress (σ_θθ) cannot exceed 0.66 fy (33 ksi).

Question 2. The aluminum (E = 70 GPa) I-beam section shown is used as a simply-supported beam spanning 4 m and must support a load of 12 kN ( Φ = 110°) at the center of the beam. The maximum moment for this span configuration is therefore M = 12 kN-m and is directed along the plane shown on the cross-section.

a. Determine the orientation of the neutral axis, a and sketch its orientation on the cross-section.

b. Determine the maximum tensile stress and the maximum compressive stress in the beam and show on the cross-section where these stresses occur.

c. Determine the vertical, horizontal, and total displacement (v, u, δ) of the beam knowing that the vertical displacement for a simply-supported beam with a vertical load at the center is v = PL³/48El.

Question 3. A fabrication error resulted in an 1-beam with an off-center web causing the shear center to no longer be located at the centroid of the web. The cross-section of the I-beam is shown with centerline dimensions. The flanges are 3 mm thick, and the web is 1.5 mm thick. Because the I-beam still has one axis of symmetry, the x- and y-axes are principal axes. Therefore, when a vertical shear force, V, is applied, the x-axis is the neutral axis.

a. For a vertical shear force of V = 1 kN, determine the shear flow distribution in each segment of the beam. Also, determine the total shear
force in each segment of the beam clearly showing the direction of the resultant shear force in each section.

b. Determine the location of the shear center with respect to the centroid of the web, e, for the beam. You should use your results from part a to locate the shear center and verify this result by calculating the location of the shear center using the correct equation from Table 8.1 in the textbook (slides 12 and 13 in lecture 8b).

Reference no: EM132281194

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