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Midterm2 - Problem 2(15 points The 36-ft long wide-flange...

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MAE 131A/SE110A – FALL 2009 Mid term #2 Tuesday Nov. 17, 2009 Time: 3:35 to 4:55 Problem 1 (10 points) Consider the cantilever beam AB, fix at A into a rigid support, and carrying a uniform load of 1kN/m as well as a concentrated load of 2kN at its free end. The beam is fabricated from a steel plate of 10mm uniform thickness, welded to form a T-section, as shown on the right. a. (0.5 point): Find the area of the cross section and the first moment of the area with respect to the bottom of the web (dashed line). b. (1 point): Find the location of the neutral axis. c. (1 point): Identify and calculate the reactions at the rigid support. d. (2 points): Draw the shear and bending moment diagrams. e. (1.5 points): Find the maximum tensile and the maximum compressive stresses in the beam. f. (1 point): Find the shear stress at the weld. g. (3 points): Find the slope, dy/dx and the deflection, y, as functions of x, and evaluate them at x = 0.6m. The elastic modulus is 200GPa.
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Unformatted text preview: Problem 2 (15 points) The 36-ft long wide-flange beam shown below supports a uniformly distributed load of 4 k/ft. The beam cross-sectional dimensions are shown in the lower figure. (a) (3 points): Find the reactions and draw the shear and bending moment diagrams. (b) (2 points): Find the section modulus. (c) (1 point): Find the maximum flexural normal stress in the beam. (d) (1 point): Find the maximum transverse shear stress in the beam. (e) (2 points): Determine the shear force and bending moment at section a-a located 6 feet to the left of support B. (f) (3 points) At section a-a, 6 ft from the right support, determine the flexural normal stress and the transverse shear stress at point H located 5 inches above the shape's centroidal axis. (g) (3 points): Determine the principal stresses at point H and show them on a properly oriented stress element. 1.0kN/m 2kN 0.6m 100mm 50mm A B...
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