The truss ABC shown in the figure supports a horize load P2 = 18 kN. Both bars have cross-sectional area A with E= 210 GPa. a) Determine the strain energy U₁ of the truss whe b) Determine the strain energy U₂ when the load F Determine the strain energy U when both loads c) T
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- A 4.75-in, outside diameter polyethylene pipe designed to carry chemical waste is placed in a trench and bent around a quarter-circular 90° bend (see figure). The bent section of the pipe is 52 ft long. Determine the maximum compressive strain If the normal strain cannot exceed 6.1 × 10-3 , what is the maximum diameter of the pipe? If d = 4.75 in., what is the minimum acceptable length of the bent section of the pipe?A prismatic bar AD of length L, cross-sectional area A. and modulus of elasticity E is subjected to loads 5P, 3P, and P acting at points B, C, and D, respectively (see figure). Segments AB, BC, and CD have lengths L/6, L/2, and L/3, respectively. (a) Obtain a formula for the strain energy U of the bar. (b) Calculate the strain energy if P = 6 kips, L = 52 in., A = 2.76 in2, and the material is aluminum with E = 10.4 × 106 psi.A slightly tapered bar AB of rectangular cross section and length L is acted upon by a force P (see figure). The width of the bar varies uniformly From b2at end A to b1at end B. The thickness t is constant. (a) Determine the strain energy U of the bar. (b) Determine the elongation ?? of the bar by equating the strain energy to the work done by the force P.
- 7.5-11 in. cube of concrete (E = 4.5 X 106 psi. v = 0.2) is compressed in biaxial stress by means of a framework that is loaded as shown in the figure. Assuming that each load F equals 25 kips. determine the change iv in the volume of the cube and the strain energy U stored in the cube.-7 The truss A BC Shawn in the figure supports a horizontal load P1= 300 lb and a vertical load P2= 9001b. Both bars have a cross-sectional area A = 2.4 in2 and are made of steel with E = 30 X 106 psi. (a) Determine the strain energy U1of the truss when the load P1acts alone (P2= 0). (b) Determine the strain energy U2when the load P2acts alone (P1= 0). (c) Determine the strain energy U3when both loads act simultaneously.The bar ABC shown in the figure is loaded by a force P acting at end C and by a force Q acting at the midpoint B. The bar has a constant axial rigidity EA. (a) Determine the strain energy U1of the bar when the Force P acts alone (Q = 0). (b) Determine the strain energy U2when the force Q acts alone (P = 0). (c) Determine the strain energy U3when the Forces P and Q act simultaneously upon the bar
- An aluminum bar subjected to tensile Forces P has a length L = 150 in. and cross-sectional area A = 2.0 in2 The stress-strain behavior of the aluminum may be represented approximately by the bilinear stress-strain diagram shown in the figure. Calculate the elongation S of the bar for each of the following axial loads: p = 8 kips, 16 kips. 24 kips, 32 kips, and 40 kips. From these results, plot a diagram of load P versus elongation S (load-displacement diagram).A prismatic bar in tension has a length L = 2.0 m and cross-sectional area A =249 mn2. The material of the bar has the stress-strain curve shown in the figure. Determi ne t he elongation 5 of the bar for each of the following axial loads: P = 10 kN, 20 kN, 30 kN, 40 kN. and 45 kN. From these results, plot a diagram of load P versus elongation 5 (load-displacement diagram).The truss ABC shown in the Figure is subjected to a horizontal load P at joint B. The two bars are identical with cross-sectional area A and modulus of elasticity E. (a) Determine the strain energy U of the truss if the angle ß = 60°. (b) Determine the horizontal displacement dBof joint B by equating the strain energy of the truss to the work done by the load.
- A flat brass bar has length L, constant thickness t, and a rectangular cross section whose width varies linearly between b2at the fixed support to b1at the free end (see figure). Assume that the taper of the bar is small. The bar has modulus of elasticity E. Calculate the displacements ??Band ??cif P = 200 kN, L = 2 m, t = 20 mm, b, = 100 mm, b, = 115 mm, and E = 96 GPa.Wires B and C are attached to a support at the left-hand end and to a pin-supported rigid bar at the right-hand end (see figure). Each wire has cross-sectional area A =0.03 in2 and modulus of elasticity E = 30 X 106 psi. When the bar is in a vertical position, the length of each wire is L = 80 in. However, before being attached to the bar, the length of wire B was 79.98 in. and wire C was 79.95 in. Find the tensile forces TBand Tc in the wires under the action of a force P = 700 lb acting at the upper end of the bar.A bungee cord that behaves linearly elastically has an unstressed length L0= 760 mm and a stiffness k = 140 N/m. The cord is attached to two pegs, distance/? = 380 mm apart, and is pulled at its midpoint by a Force P = 80 N (see figure). (a) How much strain energy U is stored in the cord? (b) What is the displacement Scof the point where the load is applied? (c) Compare the strain energy (with the quantity PSC12. Note: The elongation of the cord is not small compared lo its original length.