Find the support reactions at A and C. (ANS: Ax = -8 kN, Ay = -4 kN, C=11.3 kN) M=0= 4.3 + Roco_45 RD=228N 1.5 m D 4 kN 1.5 m- -1.5 m- B
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- Beam AB has a pin support at A and a roller support at B Joint B is also restrained by a linearly elastic rotational spring with stiffness kR, which provides a resisting moment MBdue to rotation at B. Member AB has flexural rigidity EI. A moment M0acts counterclockwise at B. Use the method of superposition to solve for all reactions. Find an expression for joint rotation Ain terms of spring stiffness kR. What is Awhen kR 0? What is Awhen kR— ? What is Awhen kR= 6EI/L?A circular bar ACB of a diameter d having a cylindrical hole of length .r and diameter till from A to C is held between rigid supports at A and B. A load P acts at U2from ends A and B. Assume E is constant. (a) Obtain formulas for the reactions R, and RBat supports A and B. respectively, due to the load P (see figure part a). (b) Obtain a formula for the displacement S at the point of load application (see figure part a). (c) For what value of x is RB= (6/5)?,? (See figure part a.) (d) Repeat part (a) if the bar is now rotated to a vertical position, load P is removed, and the bar is hanging under its own weight (assume mass density = p). (See figure part b.) Assume that x = LI2.Repeat Problem 11.3-9. Use two C 150 × 12.2 steel shapes and assume that E = 205 GPa and L = 6 m.
- Find support reactions at 4 and Band then use the method of joints to find all member forces. Let b = 3 m and P = 80 kN.A lube structure is acted on by loads at B and D, as shown in the figure. The tubes are joined using two flange plates at C that are boiled together using six 0.5-in. diameter bolts. (a) Derive formulas for the reactions RAand REat the ends of the bar. (b) Determine the axial displacements S£. Sc, and SDat points B, C. and D. respectively. (c) Draw an axial-displacement diagram (ADD) in which the abscissa is the distance x From support A to any point on the bar and the ordinate is the horizontal displacement Sat that point. (d) Find the maximum value of the load variable P if allowable normal stress in the bolts is 14 ksi.An L-shaped reinforced concrete slab 12 Ft X 12 ft, with a 6 Ft X 6 ft cut-out and thickness t = 9.0 in, is lifted by three cables attached at O, B, and D, as shown in the figure. The cables are are combined at point Q, which is 7.0 Ft above the top of the slab and directly above the center of mass at C. Each cable has an effective cross-sectional area of Ae= 0.12 in2. (a) Find the tensile force Tr(i = 1, 2, 3) in each cable due to the weight W of the concrete slab (ignore weight of cables). (b) Find the average stress ov in each cable. (See Table I-1 in Appendix I for the weight density of reinforced concrete.) (c) Add cable AQ so that OQA is one continuous cable, with each segment having Force T, which is connected to cables BQ and DQ at point Q. Repeat parts (a) and (b). Hini: There are now three Forced equilibrium equations and one constrain equation, T1= T4.
- Repeat Problem 2.4-8, but assume that the bar is made of aluminum alloy and that BC is prismatic. Assume that P = 20 kim. L = 3 ft.t = 314 in., b1 2m.b 2.Sin.andElO.400ksi.-4-4 A cantilever beam is supported at B by cable BC. The beam carries a uniform load q = 200 N/M. If the length of the beam is L = 3 m, find the force in the cable and the reactions at A. Ignore the axial flexibility of the cable.Repeat Problem 6.4-14 but use the configuration of channel shapes and loading shown in the figure. Use P = 250 N.
- A 150-lb rigid bar AB. with friction less rollers al each end. is held in the position shown in the figure by a continuous cable CAD. The cable is pinned at C and D and runs over a pulley at A. (a) Find reactions at supports A and B. (b) Find the force in the cable.Find the reactions. Fill in the blanks and draw the final free body diagram correctly.1-For the figure below take M number of you and find the reactions? 2-ls the body balanced or not? 3 m 3 m + 3 m E 12 M= 59 13 50N D