Problem #2: Determine the resultant load of the given uniformly varying load (UVL) or trapezoidal load as shown in the figure below. Figure: W= 20 KN/m wj=6 KN/m A B length of the base = 5 m %3D
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- The main cables of a suspension bridge (see figure part a) follow a curve that is nearly parabolic because the primary load on the cables is the weight of the bridge deck, which is uniform in intensity along the horizontal. Therefore, represent the central region AOB of one of the main cables (see part b of the figure) as a parabolic cable supported at points A and B and carrying a uniform load of intensity q along the horizontal. The span of the cable is L, the sag is /i, the axial rigidity is EA\ and the origin of coordinates is at mid span. (a) Derive the following formula for the elongation of cable AOB shown in part b or the figure: (b) Calculate the elongation 5 of the central span of one of the main cables of the Golden Gate Bridge for which the dimensions and properties are L = 4200 ft,h = 470 ft, q = 12,700 lb/ft, and E = 23,300,000 psi The cable consists of 27,572 parallel wires of diameter 0.196 in. Hint: Determine the tensile force Tal any point in the cable from a free-body diagram of part of the cable; then determine the elongation of an element of the cable of length ds: finally, integrate along the curve of the cable to obtain an equation for the elongation £.Repeat Problem 2.3-29 if vertical load P at D is replaced by a horizontal load P at D (see figure).A large precast concrete panel for a warehouse is raised using two sets of cables at two lift lines, as shown in the figure part a. Cable 1 has a length L1 = 22 Ft, cable 2 has a length L2= 10 ft, and the distance along the panel between lift points Band D is d = 14 ft (see figure part b). The total weight of the panel is W = 85 kips. Assuming the cable lift Forces F at each lift line are about equal, use the simplified model of one half of the panel in figure part b to perform your analysis for the lift position shown. Find the required cross-sectional area AC of the cable if its breaking stress is 91 ksi and a factor of safety of 4 with respect to failure is desired.
- Repeat Problem 9,5-15 for the anti-symmetric loading shown in the figure.Repeat 1.3-9 but use the method of sections go find member forces in AC and BD.A space truss is restrained at joints A, B. and C, as shown in the figure. Load P acts in the +z direction at joint Band in the -z directions at joint C. Coordinates of all joints are given in terms of dimension variable L (see figure). Let P = 5 kN and L = 2 m. (a) Find the reaction force components Az and Bx. (b) Find the axial force in truss member AB.
- A T-frame structure is torn posed of a prismatic beam ABC and a nonprismatic column DBF. The beam and the column have a pin support at .A and D, respectively. Both members are connected with a pin at B. The lengths and properties of the members are shown in the figure. Find the vertical displacement of the column at points F and B. Plot axial force (AFD) and axial displacement (ADD) diagrams For column DBF.1.3-15 A space truss is restrained at joints A, B, and C, as shown in the figure. Load 2P is applied at in the -x direction at joint A, load 3P acts in the + - direction at joint B. and load P is applied in the + r direction al joint C. Coordinates of all joints are given in terms of dimension variable L (see figure). (a) Find reaction force components Ayand Azin terms of load variable P. (b) Find the axial force in truss member AB in terms of load variable P.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.
- A space truss is restrained at joints O, A. B. and C, as shown in the figure. Load P is applied at joint A and load IP acts downward at joint C. (a) Find reaction force components Ax, By, and B. in terms of load variable P. (b) Find the axial force in truss member AB in terms of load variable P.A thin metal strip of total weight W and length L is placed across the top of a flat table of width L2as shown in the figure. What is the clearance S between the strip and the middle of the table? (The strip of metal has flexural rigidity EI.)A long, slender bar in the shape of a right circular cone with length L and base diameter d hangs vertically under the action of its own weight (see figure). The weight of the cone is W and the modulus of elasticity of the material is E. Derive a formula for the increase S in the length of the bar due to its own weight. (Assume that the angle of taper of the cone is small.)