3-5.7. A beam supports a load varying uniformly from an intensity w lb/ft at the left end to p lb/ft at the right end. Find the values of and p to cause the reactions shown in Fig. P-3-5.7. w= 1250-lb/ft; p = 1750 lb/ft Ans.
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- The fixed-end bar ABCD consists of three prismatic segments, as shown in the figure. The end segments have a cross-sectional area A1= 840 mm2and length Lt= 200 mm. The middle segment has a cross-sectional area A2= 1260 mm2 and length L2= 250 mm. Loads PBand Pcare equal to 25.5 kN and 17.0 kN, respectively. (a) Determine the reactions RAand RDat the fixed supports. (b) Determine the compressive axial force FBCin the middle segment of the bar.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.Two separate cables AC and BC support a sign structure of weight W = 1575 lb attached to a building. The sign is also supported by a pin support at O and a lateral restraint in the '-direction at D. (a) Find the tension in each cable. Neglect the mass of the cables. (b) Find the average stress in each cable if the area of each cable is Ae= 0.471 in2.
- Solve the preceding problem (W 250 × 44.8) if the resultant force P equals 110 kN and E = 200 GPa.A plane frame with a pin support at A and roller supports at C and £ has a cable attached at E. which runs over Frictionless pulleys al D and B (see figure). The cable force is known to be 400 N. There is a pin connection just Lo the left of joint C. (a) Find reactions at supports^, C, and E. (b) Find internal stress, resultants N, V, and M just to the right of joint C. (c) Find resultant force in the pin near C.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.
- 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 L-shaped arm ABCD shown in the figure lies in a vertical plane and pivots about a horizontal pin at A. The arm has a constant cross-sectional area and total weight W. A vertical spring of stiffness k supports the arm at point B. (a) Obtain a formula for the elongation of the spring due to the weight of the arm. (b) Repeat part (a) if the pin support at A is moved to D.A plane Frame with pin supports at A and E has a cable attached at C, which runs over a friction-less pulley at F(see figure). The cable Force is known to be 500 lb. (a) Find reactions at supports A and E. (b) Find internal stress resultants N, V, and M at point H.
- 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.A hollow circular pipe (see figure} support s a load P that is uniformly distributed around a cap plate at the top of the lower pipe. The inner and outer diameters of the upper and lower parts of the pipe are d1= 50 mm, d2= 60 mm, rf3 = 57 mm, and d1= 64 mm, respectively. Pipe lengths are Lt= 2 m and L, = 3 m. Neglect the self-weight of the pipes. Assume that cap plate thickness is small compared to I, and E,. Let E = 110 MPa. (a) If the tensile stress in the upper part is d = 10.5 MPa. what is load PI Also, what are reactions ft, at the upper support and R-, at the lower support? What is the stress ar(MPa) in the lower part? (b) Find displacement S(mm) at the cap plate. Plot the axial force diagram (AFD) [Ar(.f)] and axial displacement diagram (ADD)[5(.t)]. (c) Add the uniformly distributed load q along the censorial axis of pipe segment 2. Find q (kN/m) so that It, = 0. Assume that load P from part (a) is also applied.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?