Determine the downward displacement δ of the lower end of the copper bar with respect to the base support of the steel post at point A due to a load P = 150 kN. b)What is the maximum permissible load Pmax if the displacement δ is limited to 1.0 mm?
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a) Determine the downward displacement δ of the lower end of the copper bar with respect to the
base support of the steel post at point A due to a load P = 150 kN.
b)What is the maximum permissible load Pmax if the displacement δ is limited to 1.0 mm?
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- -21 Plastic bar AB of rectangular cross section (6 = 0.75 in. and h = 1.5 in.) and length L = 2 Ft is Fixed at A and has a spring support (Ar = 18 kips/in.) at C (see figure). Initially, the bar and spring have no stress. When the temperature of the bar is raised hy foot. the compressive stress on an inclined plane pq at Lq = 1.5 Ft becomes 950 psi. Assume the spring is massless and is unaffected by the temperature change. Let a = 55 × l0-6p and E = 400 ksi. (a) What is the shear stresst9 on plane pq? What is angle 07 =1 Draw a stress element oriented to plane pq, and show the stresses acting on all laces of this element. (c) If the allowable normal stress is ± 1000 psi and the allowable shear stress is ±560 psi, what is the maximum permissible value of spring constant k if the allowable stress values in the bar are not to be exceeded? (d) What is the maximum permissible length L of the bar if the allowable stress values in the bar are not be exceeded? (Assume £ = IB kips/in.) (e) What is the maximum permissible temperature increase (A7") in the bar if the allowable stress values in the bar are not to be exceeded? (Assume L = 2 ft and k = L& kips/inA trimetallic bar is uniformly compressed by an axial force P = 9 kips applied through a rigid end plate (see figure}. The bar consists of a circular steel core surrounded by brass and copper tubes. The steel core has a diameter of L.25 i n., the brass tube has an outer diameter of 1.75 in., and the copper tube has an outer diameter of 2.25 in. The corresponding modulus of elasticity are f, = 30, 000 ksi, Eb= 16,000 ksi, and E = 18,000 ksi Calculate the compressive stresses ers, ab, and cin the steel, brass, and copper, respectively, due to the force P.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 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?A hollow circular tube T of a length L = 15 in. is uniformly compressed by a force P acting through a rigid plate (see figure). The outside and inside diameters of the tube are 3.0 and 2.75 in., respectively. A concentric solid circular bar B of 1.5 in. diameter is mounted inside the lube. When no load is present, there is a clearance c = 0.0I0 in. between the bar B and the rigid plate. Both bar and tube are made of steel having an c[autoplastic stress-strain diagram with E = 29 X LO3 ksi and err= 36 ksi. (a) Determine the yield load Pt- and the corresponding shortening 3yof the lube. (b) Determine the plastic load Ppand the corresponding shortening Spof the tube. (c) Construct a load-displacement diagram showing the load Pas ordinate and the shortening 5 of the tube as abscissa. Hint: The load-displacement diagram is not a single straight line in the region 0 ^ P ^ PrA bar of solid circular cross section is loaded in tension by forces P (see figure). The bar has a length L = 16.0 in. and diameter d = 0.50 in. The material is a magnesium alloy having a modulus of elasticity E = 6.4 × 106 psi. The allowable stress in tension is ?? allow= 17,000 psi, and the elongation of the bar must not exceed 0.04 in. What is the allowable value of the forces F?
- A sliding collar of weight W = 150 lb falls From a height h = 2.0 in. onto a flange at the bottom of a slender vertical rod (see figure). The rod has a length L = 4.0 ft, cross-sectional area A = 0.75 in2, and modulus of elasticity E = 30 X 106 psi. Calculate the following quantities: (a) the maximum downward displacement of the flange, (b) the maximum tensile stress in the rod, and (c) the impact factor.A plastic bar of rectangular cross section (ft = 1.5 in. and h = 3 in.) fits snugly between rigid supporls at room temperature (68oF) but with no initial stress (see Figure). When the temperature of the bar is raised to 160oF, the compressive stress on an inclined plane pq at mid-span becomes 1700 psi. (a) What is the shear stress on plane pq? (Assume a = 60 × 10-6/*t and E = 450 × 103psi.) (b) Draw a stress element oriented to plane pq and show the stresses acting on all laces of this element. (c) If the allowable normal stress is 3400 psi and the allowable shear stress is 1650 psi. what is the maximum load P (in the positive x direction), which can be added at the quarter point (in addition to thermal effects given) without exceeding allowable stress values in the bar?A rigid bar AB is pinned al end A and is supported by a wine CD and loaded by a force P at end B (see figure). The wire is made of high-strength steel having a modulus of elasticity E = 210 GPa and yield stress ??Y= 820 MPa. The length of the wire is L = 1.0 m. and its diameter is d = 3 mm. The stress-strain diagram for the steel is defined by the riuniift-ed power taw. as
- Truss members supporting a roof are connected to a 26-mm-thick gusset plate by a 22-mm diameter pin, as shown in the figure and photo. The two end plates on the truss members are each 14 mm thick. (a) If the load P = 80 kN, what is the largest bearing stress acting on the pin? (b) If the ultimate shear stress for the pin is 190 MPa, what force Pult is required to cause the pin to fail in shear? Disregard friction between the plates.The length of the end segments of the bar (see figure) is 20 in. and the length of the prismatic middle segment is 50 in. Also, the diameters at cross sections A. B, C, and D are 0.5, 1.0, 1.0, and 0.5 in., respectively, and the modulus of elasticity is 18 ,000 ksi. (a) Calculate the elongation of a copper bar of solid circular cross section with tapered ends when it is stretched by axial loads of magnitude 3.0 kips (see figure). (b) If the total elongation of the bar cannot exceed 0.025 in., what are the required diameters at B and C? Assume that diameters at A and D remain at 0.5 in.A hollow, circular, cast-iron pipe (Ec =12,000 ksi) supports a brass rod (Ec= 14,000 ksi} and weight W — 2 kips, as shown. The outside diameter of the pipe is dc= 6 in. (a) If the allowable compressive stress in the pipe is S00O psi and the allowable shortening of the pipe is 0.02 in., what is the minimum required wall thickness trmm? (Include the weights of the rod and steel cap in your calculations.) (b) What is the elongation of the brass rod Srdue to both load Wand its own weight? (c) What is the minimum required clearance h?