We have the plane truss shown in Figure 1. The truss carries three forces, as shown in the same figure. Point 1 has a pin support, while point 4 has a horizontal roller support. a) Calculate the support reactions b) Obtain the axial forces of the truss members c) Find the change in length for member 3-4, if the cross-sectional area of that member is 5in? and the elastic modulus for the material is 20,000 ksi 5 kip 10 ft 4 5 kip TAm 10 kip 10 ft 10 ft Figure 1
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- 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.A two-span, continuous wood girder (E = 1700 ksi) supports a roof patio structure (figure part a). A uniform load of intensity q acts on the girder, and each span is of length 8 ft. The girder is made up using two 2×8 wood members (see figure part b). Ignore the weight of the beam. Use the nominal dimensions of the beam in your calculations. Find the reactions at A, B, and C. Use the method of superposition to calculate the displacement of the beam at the mid-sapn of segment AB. Hind: See Figs. 10-14c and 10-14d in Example 10-3.An aluminum bar AD (see figure) has a cross-sectional area of 0.40 in- and is loaded by Forces Pi= 1700 lb, Pz- 1200 lb, and P3 = 1300 lb. The lengths of the segments of the bar are ti = 60 in., b = 24 in.T and c = 36 in. (a) Assuming that the modulus of elasticity is E = 10.4 × 10o psi. calculate the change in length of the bar. Does the bar elongate or shorten? (b) By what amount ^should the load Pibe increased so that the bar does not change in length when the three loads are applied? (c) IF Pzremains at 1300 lb, what revised cross-sectional area For segment AB will result in no change of length when all three loads are applied?
- A rigid triangular frame is pivoted at C and held by two identical horizontal wires at points A and B (see figure). Each wire has an axial rigidity EA = 120 kips and coefficient of thermal expansion a = 12.5 X 10-6/°F. (a) If a vertical load P = 500 lb acts at point D, what are the tensile forces TAand TBin the wires at A and B, respectively? (b) If both wires have their temperatures raised by 180°F while the load P is acting, what are the forces TAand TB (c) What further increase in temperature will cause the wire at B to become slack?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.Two pipe columns (AB, FC) are pin-connected to a rigid beam (BCD), as shown in the figure. Each pipe column has a modulus of E, but heights (L1or L2) and outer diameters (d1or different for each column. Assume the inner diameter of each column is 3/4 of outer diameter. Uniformly distributed downward load q = 2PIL is applied over a distance of 3L/4 along BC, and concentrated load PIA is applied downward at D. (a) Derive a formula for the displacement
- Segments A B and BCD of beam A BCD are pin connected at x = 4 m. The beam is supported by a sliding support at A and roller supports at C and D (see figure). A triangularly distributed load with peak intensity of SO N/m acts on EC. A concentrated moment is applied at joint D. (a) Find reactions at supports A, C, and D. (b) Find internal stress resultants N, Y, and Mat x = 5m. (c) Repeat parts (a) and (b) for die case of the roller support at C replaced by a linear spring of stiffness kr™ 200 kN/m (see figure).A vertical bar is loaded with axial loads at points B, C, and D. as shown in the figure. The bar is made of steel with a modulus of elasticity E = 29,000 ksi., The bar has a cross-sectional area of 8.24 in2. Calculate the displacements at points B, C, and D. Ignore the weight of the barA plane Frame is restrained at joints A and D, as shown in the figure. Members AB and BCD are pin connected at B. A triangularly distributed lateral load with peak intensity of SO N/m acts on CD. An inclined concentrated force of 200 N acts at the mid-span of BC. (a) Find reactions at supports A and D. (b) Find resultant forces in the pins at B and C.