For the beam loaded as shown, derive the equation of the following: a. elastic curve b. slope c. deflection 250 kN В 6 m -3 m- -3 m- El = constant E = 200 GPa = 462 (106) mm4 I

A beam is subjected to equal bending moments of Mz = 3100 N·m. The cross-sectional dimensions are b = 180 mm, c = 35 mm, d = 70 mm, and t = 7 mm. Determine: (a) the centroid location (measured with respect to the bottom of the cross-section), the moment of inertia about the z axis, and the controlling section modulus about the z axis. (b) the bending stress at point H. Tensile stress is positive, while compressive stress is negative. (c) the bending stress at point K. Tensile stress is positive, while compressive stress is negative. (d) the maximum bending stress produced in the cross section. Tensile stress is positive, while compressive stress is negative.

34 3 Example 1: i moment My, the plastic c or nominal petermine the yield moment Mp (Mn), and the plastic modulus Z for the simply supported beam having the cross section shown in the figure. Also calculate the shape factor, and nominal load Practing transversely through the mid span of the beam. Assume that F, = 50 ksi. 12 ft Pr -- 12 ft 1 in 15 in. 8 in. 15 in. 17 in. in.

A simply supported I-beam is loaded with a distributed load, as shown. The deflection, y, of the center line of the beam as a function of the .position, x, is given by the equation: where L-4 m is the length, E=5 GPa is the elastic modulus, I=60 x 10^(-6) m^4 is the moment of inertia, and wo=20 kN/m. Find the position x where the deflection of the beam is maximum in meters. Express your answer in meters with six decimal digits after decimal point. Wox y = 360LEIL*- 10L2x² + 3x+)