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- Solve the preceding problem (W 250 × 44.8) if the resultant force P equals 110 kN and E = 200 GPa.An 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.?The 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.)
- A cylindrical brick chimney of height H weighs w = 825 lb/ft of height (see figure). The inner and outer diameters are d1= 3 ft and d2= 4 ft, respectively. The wind pressure against the side of the chimney is p = 10 lb/ft2 of projected area. Determine the maximum height H if there is to be no tension in the brickwork.The shear stresses t in a rectangular beam arc given by Eq. (5-43): in which Fis the shear force, / is the moment of inertia of the cross-sectional area, /lis the height of the beam, and i] is the distance from the neutral axis to the point where the shear stress is being determined (Fig. 5-32). By integrating over the cross-sectional area, show that the resultant of the shear stresses is equal to the shear force V..10 A built-up bourn supporting a condominium balcony is made up of a structural T (one half of a W 200 x 31.3) for the top flange and web and two angles (2 L 2 / b / 6.4. long legal back-lo-backl lot the bottom flange and web. as shown. The beam is subjected to a bending moment .1/ having its vector at an angle ft lo the z axis (see figure). Determine the or ion ta I ion of the neutral axis and calculate the maximum tensile stress ir, and maximum compressive stress tr. in ".he beam. .Assume that 9 = 30°andM = 15 kN · m. Use the numerical properties: c =4.111mm, c2 =4.169 mm, of = 134 mm, I, = 76 mm, A = 4144 mm 3 =3.88 X 106 mm 4, and = 34.18 X 10 mm 4.
- A sandwich beam having steel faces enclosing a plastic core is subjected to a bending moment M = 5 kN · m. The thickness of each steel face is 1 = 3 mm with modulus of elasticity E = 200 GPa, The height of the plastic core is hp= 140 mm, and its modulus of elasticity is Ep= 800 MPa. The overall dimensions of the beam are h = 146 mm and h = 175 mm. Using the transformed-section method, determine the maximum tensile and compressive stresses in the faces and the core.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.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?
- 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 flying but tress transmit s a load P = 25 kN, acting at an angle of 60º to the horizontal, to the top of a vertical buttress AB (see figure). The vertical buttress has height h = 5.0 m and rectangular cross section of thickness t = 1.5 m and width b = 1.0 m (perpendicular to the plane of the figure). The stone used in the construction weighs y = 26 kN/m3. What is the required weight W of the pedestal and statue above the vertical buttress (that is, above section A) to avoid any tensile stresses in the vertical buttress?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.