A steel beam with length 4 m is to be connected between two columns (Column A and Column B) as shown in Figure 1. This beam is found to be short by 2 mm. Determine the force needed to pull the beam so that it can be connected at the two columns. The cross-section of the beam is shown in Figure 2.
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- Solve the preceding problem (W 250 × 44.8) if the resultant force P equals 110 kN and E = 200 GPa.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?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.
- 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 steel bar has a square cross section of width b = 2.0 in. (sec figure). The bar has pinned supports at the ends and is 3.0 ft long. The axial forces acting at the end of the bar have a resultant P = 20 kips located at distance e = 0,75 in, from the center of the cross section. Also, the modulus of elasticity of the steel is 29,000 ksi. Determine the maximum compressive stress max, in the bar. If the allowable stress in the steel is 18,000 psi, what is the maximum permissible length Lmaxof the bar?The cross section of a bimetallic strip is shown in the figure. Assuming that the moduli of elasticity for metals A and B are EA=168 GPa and EB= 90 GPa, respectively, determine the smaller of the two section moduli for the beam. (Recall that section modulus is equal to bending moment divided by maximum bending stress.) In which material does the maximum stress occur?
- 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.?‘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.A cable CD of a length H is attached to the third point of a simple beam AB of a length L (see figure). The moment of inertia of the beam is I, and the effective cross-sectional area of the cable is A. The cable is initially taut but without any initial tension, (a) Obtain a formula for the tensile force S in the cable when the temperature drops uniformly by T degrees, assuming that the beam and cable are made of the same material (modulus of elasticity E and coefficient of thermal expansion . Use the method of superposition in the solution, (b) Repeat part (a), assuming a wood beam and steel cable.
- A wide-flange member (W200 × 22.5) is compressed by axial loads that have a resultant P acting at the point shown in the figure. The member has modulus of elasticity E = 200 GPa and pinned conditions at the ends. Lateral supports prevent any bending about the weak axis of the cross section. If the length of the member is 6.2 m and the deflection is limited to 6.5 mm. what is the maximum allowable load Pallow.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.A non prism elk- bar ABC made up of segments AB(length £,, cross-sectional area .Inland BC (length i-,, cross-sectional area A2) is fixed at end A and free al end C (see figure). The modulus of elasticity of the bar is E. A small gap of d intension s exists between the end of the bar and an elastic spring of length Lj and spring constant k3. If bar ABC only (not tin? spring} is subjected to temperature increase A3", determine the following. (a) Write an expression for reaction forces R^ and RDif the elongation of /I BC exceeds gap length s. (b) Find expressions for the displacements of points B and C if the elongation of ABC exceeds gap length s.