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- Determine the angle of rotation 0Band deflectionThe cantilever beam A CB shown in the hgure is subjected to a uniform load of intensity q acting between points A and C. Determine the angle of rotation ÔAat the free end A>(Obtain the solution by using the modified form of Castigliano's theorem.)The wing of a small plane is represented by a simplified prismatic cantilever beam model acted on by the distributed loads shown in the figure. Assume constant El = 1200kN-m~, Find the tip deflection and rotation at B.
- A simple beam ABC DE supports a uniform load of intensity iy (see figure). The moment of inertia in the central part of the beam (BCD) is twice the moment of inertia in the end parts (AB and DE). Find the deflection Scat the midpoint C of the beam. (Obtain the solution by using the modified form of Castigliano's theorem.)A cantilever beam of a length L = 2.5 ft has a rectangular cross section {b = 4in,, h = Sin,) and modulus E = 10,000 ksi. The beam is subjected to a linearly varying distributed load with a peak intensity qQ= 900 lb/ft. Use the method of superposition and Cases 1 and 9 in Table H-l to calculate the deflection and rotation at B.A square wood column with side dimensions b (see figure) is constructed of a structural grade of southern pine for which Fc= 10,5 MPa and E = 12 GPa. An axial force P = 200 kN acts on the column. If the dimension b = 150 mm, what is the maximum allowable lensth Lmax, of the column? If the length L = 4.0 m, what is the minimum required dimension bmin?
- The simple beam shown in the figure supports a concentrated load P acting at distance a from the left-hand support and distance h from the right-hand support. Determine the deflection SDat point D where the load is applied. (Obtain the solution by determining the strain energy of the beam and then using Castigliano's theorem.)A temporary wood flume serving as a channel for irrigation water is shown in the figure. The vertical boards forming the sides of the flume are sunk in the ground, which provides a fixed support. The top of the flume is held by tic rods that are tightened so that there is no deflection of the boards at that point. Thus, the vertical boards may be modeled as a beam AB, supported and loaded as shown in the last part of the figure. Assuming that the thickness t of the boards is 1,5 in., the depth d of the water is 40 in., and the height h to the tie rods is 50 in., what is the maximum bending stress in the boards? Hint: The numerically largest bending moment occurs at the fixed support.Determine the plastic modulus Z and shape factor/for a W 12 x 14 wide-flange beam. Obtain the cross-sectional dimensions and section modulus of the beam from Table F-l(a) in Appendix F.
- A C 200 x 17.1 channel section has an angle with equal legs attached as shown; the angle serves as a lintel beam. The combined steel section is subjected to a bending moment M having its vector directed along the z axis, as shown in the figure. The cent roi d C of the combined section is located at distances xtand ycfrom the centroid (C1) of the channel alone. Principal axes yl and yvare also shown in the figure and properties Ix1,Iy1and 0pare given. Find the orientation of the neutral axis and calculate the maximum tensile stress exand maximum compressive stress if the angle is an L 76 x 76 x 6.4 section and M = 3.5 kN - m. Use the following properties for principal axes for the combined section:/^, = 18.49 X 106 nrai4,/;| = 1.602 X 106 mm4, ep= 7.448*(CW),_r£ = 10.70 mm,andvf= 24.07 mm.A gold-alloy microbeam attached to a silicon wafer behaves like a cantilever beam subjected to a uniform load (see figure). The beam has a length L = 27.5 m and rectangular cross section of a width b = 4.0 m and thickness t = 0.88 m. The total load on the beam is 17.2 N. If the deflection at the end of the beam is 2.46 m is what is the modulus of elasticity Egof the gold alloy? (Use the formulas of Example 9-2.)A propped cantilever beam, fixed at the left-hand end A and simply supported at the right-hand end B, is subjected to a temperature differentia] with temperature T1on its upper surface and T2on its lower surface (see figure).