For the plane trusses shown in Figure P3-30, determine the horizontal and vertical displacements of node 1 and the stresses in each element. All elements have E = 210 GPa and A = 4.0 x 10-4 m2.
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- Around brass bar of a diameter d1= 20mm has upset ends each with a diameter d2= 26 mm (see figure). The lengths of the segments of the bar are L1= 0.3 m and L2= 0.1 m. Quarter-circular fillets are used at the shoulders of the bar, and the modulus of elasticity of the brass is E = 100 GPa. If the bar lengthens by 0.12 mm under a tensile load P, what is the maximum stress ??maxin the bar?A copper bar AB with a length 25 in. and diameter 2 in. is placed in position at room temperature with a gap of 0.008 in. between end A and a rigid restraint (see figure). The bar is supported at end B by an elastic spring with a spring constant k= 1.2 × 106 lb/in. (a) Calculate the axial compressive stress crcin the bar if the temperature of the bar only rises 50 F. (For copper, use a = 9.6 × 10-6/ and E = 16 × 106 psi.) (b) What is the force in the spring? (Neglect gravity effects.) (c) Repeat part (a) if k ? 8.Repeat Problem 8.5-22 but replace the square tube column with a circular tube having a wall thickness r = 5 mm and the same cross-sectional area (3900 mm2) as that of the square tube in figure b in Problem 8.5-22. Also, add force P. = 120 N at B (a) Find the state of plane stress at C. (b) Find maximum normal stresses and show them on a sketch of a properly oriented element. (c) Find maximum shear stresses and show them on a sketch of a properly oriented element.
- 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.Continuous cable ADS runs over a small Frictionless pulley at D to support beam OABC that is part of an entrance canopy Tor a building (see figure}. Assume that the canopy segment has a weight it' = 1700 lb. (a) Find the required cross-sectional area of cable ADB if the allowable stress is 18 ksi. (b) Determine the required diameter of the pins at O. A, R and D if the allowable stress in shear is 12 ksi.A basketball player hangs on the rim after (a) Find the reactions at the support bracket a dunk. He applies equal forces P1= P2= 110 lb at (assume that the bracket-rim assembly is a both A and B (see joint coordinates in the figure). cantilever beam). Forces P1tmd P2act parallel to the y-z plane. (b) Find connection shear stresses at bolt 2.
- 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.A compressive load P is transmitted through a rigid plate to three magnesium-alloy bars that are identical except that initially the middle bar is slightly shorter than the other bars (see figure). The dimensions and properties of the assembly are as follows: length L = 1.0 m, cross-sectional area of each bar A = 3000 mm", modulus of elasticity E = AS GPa, and the gap s = 1.0 mm. (a) Calculate the load Ptrequired to close the gap. (b) Calculate the downward displacement 5 of the rigid plate when P = 400 kN. (c) Calculate the total strain energy V of the three bars when P = 400 kN (d) Explain why the strain -energy V is not equal to PS/2. Hint: Draw a load-displacement diagram.Solve the preceding problem if the cube is granite (E = 80 GPa, v = 0.25) with dimensions E = 89 mm and compressive strains E = 690 X l0-6 and = = 255 X 10-6. For part (c) of Problem 7.6-5. find the maximum value of cr when the change in volume must be limited to 0.11%. For part. find the required value of when the strain energy must be 33 J.
- A long re Lai nine: wall is braced by wood shores set at an angle of 30° and supported by concrete thrust blocks, as shown in the first part of the figure. The shores are evenly spaced at 3 m apart. For analysis purposes, the wall and shores are idealized as shown in the second part of the figure. Note that the base of the wall and both ends of the shores are assumed to be pinned. The pressure of the soil against the wall is assumed to be triangularly distributed, and the resultant force acting on a 3-meter length of the walls is F = 190 kN. If each shore has a 150 mm X 150 mm square cross section, what is the compressive stressA post AB supporting equipment in a laboratory is tapered uniformly throughout its height H (see figure). The cross sections of the post are square, with dimensions b × b at the top and 1.5b × 1.5b at the base. Derive a formula For the shortening 8 of the post due to the compressive load P acting at the top. (Assume that the angle of taper is small and disregard the weight of the post itself.)-11 A solid steel bar (G = 11.8 X 106 psi ) of diameter d = 2,0 in. is subjected to torques T = 8.0 kip-in. acting in the directions shown in the figure. Determine the maximum shear, tensile, and compressive stresses in the bar and show these stresses on sketches of properly oriented stress elements. Determine the corresponding maximum strains (shear, tensile, and compressive) in the bar and show these strains on sketches of the deformed elements.