A horizontal bar, fixed at one end (x = 0), has a length of 1 m. and cross-sectional area of 100 mm2 Its elastic modulus varies along its length as given by E(x) = 100e-x GPa, where is the length coordinate (in m) along the axis of the bar. An axia
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A horizontal bar, fixed at one end (x = 0), has a length of 1 m. and cross-sectional area of 100 mm2 Its elastic modulus varies along its length as given by E(x) = 100e-x GPa, where is the length coordinate (in m) along the axis of the bar. An axial tensile load of 10 KN is applied at the free end (x = 1). The axial displacement of the free end is..... mm
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- A wine of length L = 4 ft and diameter d = 0.125 in. is stretched by tensile forces P = 600 lb. The wire is made of a copper alloy having a stress-strain relationship that may be described mathematically by =18,0001+30000.03(=ksi) in which is nondimensional and has units of kips per square inch (ksi). (a) Construct a stress-strain diagram for the material. (bj Determine the elongation, of the wire due to the Forces P. (c) IF the forces are removed, what is the permanent set of the bar? (d) If the forces are applied again, what is the proportional limit?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.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 joint between iwo concrete slabs A and B is filled, with a flexible epoxy lhal bonds securely lo the concrete (see figure). The height of the joint is h = 4.0 in., its length is L = 40 in., and its thickness is t = 0.5 in. Under the action of shear forces K the slabs displace vertically through the distance d = 0.002 in. relative lo each other. (a) What is the average shear strain in the epoxy? (b) What is the magnitude of the forces V if the shear modulus of elasticity G for the epoxy is 140 ksi?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 bar ABC of length L consists of two parts of equal lengths but different diameters. Segment AB has a diameter d 1 = 100 mm and segment BC has a diameter d 2 = 60 mm. Both segments have a length L / 2 = 0.6 m. A longitudinal hole of diameter d is drilled through segment AB in the middle of its length (distance L / 4 = 0.3 m). The bar is made of plastic with a modulus of elasticity. E = 4.0 GPa. Compressive loads P = 110 kN act at the ends of the bar. (a) If the shortening of the bar is limited to 8.0 mm, what is the maximum allowable diameter d max of the hole? (See figure part a.) (b) Now, if d max is set to d 2/2, at what distance b from the end C must the load P be applied to limit the shortening of the bar to 8.0 mm? (See Figure part b.) (C) Finally, if the loads P are applied at the ends and d max = d 2/2, what is the allowable length x of the hole if shortening is limited to 8.0 mm? (See figure part c.)
- A bar ABC of length L consists of two parts of equal lengths but different diameters. Segment AB has diameter d1= 100 mm while segment BC has diameter dz = 60 mm. Both segments have length L/2 = 0.6 m. A longitudinal hole of diameter d is drilled through segment AB for one-half of its length (distance L/4= 0.3 m). The bar is made of plastic having modulus of elasticity E = 4.0 GPa. Compressive loads P= 110 kN act at the ends of the bar. If the shortening of the bar is limited to 8.0 mm, what is the maximum allowable diameter dmax (mm) of the hole? dmax d2 4. 2 (a)For a cylindrical rod subjected to an uniaxial tensile load P as shown, given P = 800 (N), the original length of the rod L = 60 (mm), and the diameter of the circular cross-section of the rod D = 8 (mm). 1. What is the tensile stress developed on the cross-section? 2. If the Young's Modulus of the material made the rod is E-80 (GPa), what is the strain & the rod experience? 3. What is the rod's elongation ? a. Rod b. Uniaxially Loaded Rod P L P LA bar ABC length L consists of two parts of equal lengths but different diameters.Segment AB has diameter dt=100 mm,and segment BC has diameter d2 = 60 mm.Both segments have a length B2=0.6 m.A longitudinal hole of diameter d is drilled through segment AB for one half of its length (distance L/4 = 0.3 m).The bar is made plastic having a module of elasticity E=4.0 GPa.Comprssive loads P = 110 KN act at the ends of the bar. (a) If the shortening of the bar is limited to 8.0 mm.What is the maximum allowable diameter dma of the hole? (see the figure part a.) (b) Now if daxx is instead set at p1/2 . at what distanc h from end c should load P be applied to limit the bar shortening to 8.0 mm?(see the figure part b) (c) Finally if loads t are applied at the ends and "mm is the permissible length.v of the hole if shortening is to be limited to 8.0 mm?(see the figure part c)