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- 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.The compound beam ABC shown in the figure has a sliding support at A and a fixed support at C. The beam consists of two members joined by a pin connection (i.e., moment release) at B. Find the deflectionAn S6 × 12.5 steel cantilever beam AB is supported by a steel tic rod at B as shown. The tie rod is just taut when a roller support is added at Cat a distance s to the left of £, then the distributed load q is applied to beam segment AC, Assume E = 30 × 106 psi and neglect the self-weight of the beam and tie rod. Sec Table F-2(a) in Appendix F for the properties of the S-shape beam. (a) What value of uniform load q will, if exceeded, result in buckling of the tie rod if L1, =6 ft, s = 2 ft, H = 3 ft, and d = 0.25 in.? (b) What minimum beam moment of inertia ibis required to prevent buckling of the tie rod if q = 200 lb/ft, L1, = 6 ft, H = 3 ft, d = 0.25 in., and s = 2 ft? (c) For what distance s will the tic rod be just on the verge of buckling if q = 200 lb/ft, L1= 6 ft, M = 3 ft, and d = 0.25 in.?
- ‘11.5-2 A steel bar having a square cross section (50 mm × 50 mm)and length L = 2.0 in is compressed by axial loads that have a resultant P = 60 kN acting at the midpoint of one side of the cross section (sec figure). Assuming that the modulus of elasticity £is equal to 210 GPa and that the ends of the bar are pinned, calculate the maximum deflection S and the maximum bending moment Mmax.The T-beam shown in the figure has cross-sectional dimensions: b = 210 mm, t = 16 mm, h = 300 mm, and A, = 280 mm. The beam is subjected to a shear force V = 68 kN. Determine the maximum shear stress tntijlin the web of the beam.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 beam supporting a uniform load of intensity q throughout its length rests on pistons at points A, C and B (sec figure). The cylinders are filled with oil and are connected by a tube so that the oil pressure on each piston is the same. The pistons at A and B have diameter d1and the piston at C has diameter D2. (a) Determine the ratio of d2to d1so that the largest bending moment in the beam is as small as possible. Under these optimum conditions, what is the largest bending moment Mmaxin the beam? What is the difference in elevation between point C and the end supports?An aluminum bar having a rectangular cross section (2.0 in. × 1.0 in.) and length L = 30 in. is compressed by axial loads that have a resultant P = 2800 lb acting at the midpoint of the long side of the cross section (sec figure). Assuming that the modulus of elasticity E is equal to 10 × 106 psi and that the ends of the bar are pinned, calculate the maximum deflection and the maximum bending moment Mmax.Determine the angle of rotation 0Band deflection
- The cantilever beam ACE shown in the figure has FlexuraI rigidity EI = 2,1 x 106kip-in". Calculate the downward deflections Scand 8Sat points C and B, respectively, due to the simultaneous action of the moment of 35 kip-in. applied at point C and the concentrated load of 2,5 kips applied at the free end B.The tapered cantilever beam AB shown in the figure has a solid circular cross section. The diameters at the ends A and B are dAand dB= 2dA, respectively. Thus, the diameter d and moment of inertia / at distance v from the free end are, respectively, in which IAis the moment of inertia at end A of the beam. Determine the equation of the deflection curve and the deflection SAat the free end of the beam due to the load P.The deflection curve for a simple beam AB (sec figure) is given by v=q0L44EIsinxL Describe the load acting on the beam. Deter mine the reactions RAand RBat the supports, Determine the maximum bending moment Mmax.