2.99 See Answer

Question: A steel bar with a uniform cross

A steel bar with a uniform cross section is fixed at both ends. A load P = 2.5 kips is applied at point C. The bar has a cross-sectional area of 8 in2. Calculate the reactions at joints A and B and the displacement at joint C. Assume that the modulus of elasticity E = 29,000 ksi.
A steel bar with a uniform cross section is fixed at both ends. A load P = 2.5 kips is applied at point C. The bar has a cross-sectional area of 8 in2. Calculate the reactions at joints A and B and the displacement at joint C. Assume that the modulus of elasticity E = 29,000 ksi.





Transcribed Image Text:

3 ft Pc=2.5 kips 6 ft B


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> Find expressions for all support reaction forces in the plane frame with load 3P applied at C as shown in the figure. Joints A and D are pin supported, and there is a roller support at joint F. The lengths and the properties of the members are shown in t

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> Find expressions for all support reaction forces in the plane frame with load 2P applied at C, as shown in the figure. Joint A is a sliding support, joint D is pinned, and joint F is a roller support. Assume that member AC is a flat prismatic bar of leng

> A rigid bar AB of a length L = 66 in is hinged to a support at A and supported by two vertical wires attached at points C and D (see figure). Both wires have the same cross-sectional area (A = 0 .0272 in2 ) and are made of the same material (modulus E =

> A rigid bar ABCD is pinned at point B and supported by springs at A and D (see figure). The springs at A and D have stiffnesses k1 = 10 kN/m and k2 = 25 kN/m, respectively, and the dimensions a, b, and c are 250 mm, 500 mm, and 200 mm, respectively. A lo

> A bar AB supports a load P acting at the centroid of the end cross section (see figure). In the middle region of the bar the cross-sectional area is reduced by removing one-half of the bar. (a) If the end cross sections of the bar are square with sides o

> A horizontal rigid bar of weight W = 7200 lb is supported by three slender circular rods that are equally spaced (see figure). The two outer rods are made of aluminum (E1 = 10 × 106 psi)with diameter d1 = 0.4 in and length L1 = 40 in. The in

> Three-bar truss ABC (see figure) is constructed of steel pipes having a cross-sectional area A = 3500 mm2 and a modulus of elasticity E = 210 GPa. Member BC is of length L = 2.5 m, and the angle between members AC and AB is known to be 60°. Me

> A bimetallic bar (or composite bar) of square cross section with dimensions 2b × 2b is constructed of two different metals having moduli of elasticity E1 and E2 (see figure). The two parts of the bar have the same cross-sectional dimensions.

> A rigid bar of weight W = 800 N hangs from three equally spaced vertical wires (length L = 150 mm, spacing a = 50 mm): two of steel and one of aluminum. The wires also support a load P acting on the bar. The diameter of the steel wires is ds = 2 mm, and

> The aluminum and steel pipes shown in the figure are fastened to rigid supports at ends A and B and to a rigid plate C at their junction. The aluminum pipe is twice as long as the steel pipe. Two equal and symmetrically placed loads P act on the plate at

> A hollow circular pipe (see figure) supports a load P that is uniformly distributed around a cap plate at the top of the lower pipe. The inner and outer diameters of the upper and lower parts of the pipe are d1 = 50 mm, d2 = 60 mm, d3 = 57 mm, and d4 = 6

> A bungee cord that behaves linearly elastically has an unstressed length Lo = 760 mm and a stiffness k = 140 N/m. The cord is attached to two pegs, distance b = 380 mm apart, and is pulled at its midpoint by a force P = 80 N (see figure). (a) How much st

> A block B is pushed against three springs by a force P (see figure). The middle spring has a stiffness k1, and the outer springs each have stiffness k2. Initially, the springs are unstressed, and the middle spring is longer than the outer springs (the di

> 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 fol

> 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 b2 at end A to b1 at end B. The thickness t is constant. (a) Determine the strain energy U of the bar.

> Two cables, each carrying a tensile force P = 1200 lb, are bolted to a block of steel (see figure). The block has thickness t = 1 in and width b = 3 in. (a) If the diameter d of the cable is 0.25 in., what are the maximum tensile and compressive stresses

> The statically indeterminate structure shown in the figure consists of a horizontal rigid bar AB supported by five equally spaced springs. Springs 1, 2, and 3 have stiffnesses 3k, 1.5k, and k, respectively. When unstressed, the lower ends of all five spr

> The truss ABC shown in the figure supports a horizontal load P1 = 300 lb and a vertical load P2 = 900 lb. Both bars have a cross-sectional area A = 2.4 in2 and are made of steel with E = 30 × 106 psi. (a) Determine the strain energy U1 of th

> 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 β = 60Â&de

> Determine the strain energy per unit volume (units of psi) and the strain energy per unit weight (units of in.) that can be stored in each of the materials listed in the accompanying table, assuming that the material is stressed to the proportional limit

> 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 U1 of the bar when the force P acts alone (Q = 0). (b) Determine t

> A three-story steel column in a building supports roof and floor loads as shown in the figure. The story height H is 10.5 ft, the cross-sectional area A of the column is 15.5 in2, and the modulus of elasticity E of the steel is 30 × 106 psi.

> A bar with a circular cross section having two different diameters d and 2d is shown in the figure. The length of each segment of the bar is L/2, and the modulus of elasticity of the material is E. (a) Obtain a formula for the strain energy U of the bar

> 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) Ob

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> Bar ABC is fixed at both ends (see figure) and has load P applied at B. Find reactions at A and C and displacement δB if P = 200 kN, L = 2 m, t = 20 mm, b1 = 100 mm, b2 = 115 mm, and E = 96 GPa. b2 3L/5 2L/5 B P A C

> Three prismatic bars, two of material A and one of material B, transmit a tensile load P (see figure). The two outer bars (material A) are identical. The cross-sectional area of the middle bar (material B) is 50% larger than the cross-sectional area of o

> A solid circular steel cylinder S is encased in a hollow circular aluminum tube A. The cylinder and tube are compressed between the rigid plates of a testing machine which applies forces P. Calculate the allowable value of the compressive force if the yi

> A horizontal rigid bar ABC is pinned at end A and supported by two cables at points B and C. A vertical load P = 10 kN acts at end C of the bar. The two cables are made of steel with a modulus elasticity E = 200 GPa and have the same cross- sectional are

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> A plain concrete wall (i.e., a wall with no steel reinforcement) rests on a secure foundation and serves as a small dam on a creek (see figure). The height of the wall is h = 6.0 ft and the thickness of the wall is t = 1.0 ft. (a) Determine the maximum t

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> A T-frame structure is composed of prismatic beam ABC and non prismatic column DBF that are joined at B by a frictionless pin connection. The beam has a sliding support at A and the column is pin supported at F (see figure). Beam ABC and column segment D

> A T-frame structure is composed of a prismatic beam ABC and a non prismatic 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 i

> A vertical steel bar ABC is pin-supported at its upper end and loaded by a force P1 at its lower end. A horizontal beam BDE is pinned to the vertical bar at joint B and supported at point D. Load P2 and moment M are applied at end E. Calculate the vertic

> A uniformly tapered tube AB of circular cross section and length L is shown in the figure. The average diameters at the ends are dA and dB = 2dA. Assume E is constant. Find the elongation δ of the tube when it is subjected to loads P acting

> A 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 1.5 b × 1.5 b at the base. Derive a formu

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> A weight W rests on top of a wall and is attached to one end of a very flexible cord having cross-sectional area A and modulus of elasticity E (see figure). The other end of the cord is attached securely to the wall. The weight is then pushed off the wal

> A bungee jumper having a mass of 55 kg leaps from a bridge, braking her fall with a long elastic shock cord having axial rigidity EA = 2.3 kN (see figure). If the jump off point is 60 m above the water, and if it is desired to maintain a clearance of 10

> A bumper for a mine car is constructed with a spring of stiffness k = 1120 lb/in. (see figure). If a car weighing 3450 lb is traveling at velocity v = 7 mph when it strikes the spring, what is the maximum shortening of the spring?

> A bumping post at the end of a track in a railway yard has a spring constant k = 8.0 MN/m (see figure). The maximum possible displacement δ of the end of the striking plate is 450 mm. What is the maximum velocity vmax that a railway car of w

> Solve the preceding problem if the slider has W = 100 lb, h = 45 in., A= 0.080 in2, E = 21 × 106 psi, and the allowable stress is 70 ksi. Data from Problem 8: A cable with a restrainer at the bottom hangs vertically from its upper end (se

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> A weight W = 4500 lb falls from a height h onto a vertical wood pole having length L = 15 ft, diameter d = 12 in., and modulus of elasticity E = 1.6 × 106 psi (see figure). If the allowable stress in the wood under an impact load is 2500 psi

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> A cylindrical brick chimney of height H weighs w = 825 lb/ft of height (see figure). The inner and outer diameters are d1 = 3 ft and d2 = 4 ft, respectively. The wind pressure against the side of the chimney is p = 10 lb/ft2 of projected area. Determine

> Solve Problem 1 if the collar has weight W = 50 lb, the height h = 2.0 in., the length L = 3.0 ft, the cross-sectional area A = 0.25 in2, and the modulus of elasticity E = 30,000 ksi. Data from Problem 1: A sliding collar of weight W = 150 lb falls fr

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> A steel bracket of solid circular cross section is subjected to two loads, each of which is P = 4.5 kN at D (see figure). Let the dimension variable be b = 240 mm. (a) Find the minimum permissible diameter dmin of the bracket if the allowable normal stre

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2.99

See Answer