1.An axial pull of 40000 N is acting on a bar consisting of three sections of length 30 cm,25 cm and 20 cm and of diameters 2 cm, 4 cm and 5 cm respectively as shown in figure 1. If the Young's modulus 2 x 10 N/mm2, Calculate: (i) stress in each section and (i) total extension of the bar. SECTION 3
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- A solid circular bar of steel (G = 78 GPa) transmits a torque T = 360 N - m. The allowable stresses in tension, compression, and shear arc 90 MPa, 70 MPa, and 40 MPa, respectively. Also, the allowable tensile strain is 220 x 10-6, Determine the minimum required diameter d of the bar, If the bar diameter d = 40 mm, what is Tmax?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?A cylindrical pressure vessel having a radius r = 14 in. and wall thickness t = 0,5 in, is subjected to internal pressure p = 375 psi, In addition, a torque T = 90 kip-ft acts at each end of the cylinder (see figure), (a) Determine the maximum tensile stress ctniXand the maximum in-plane shear stress Tmjv in the wall of the cylinder. (b) If the allowable in-plane shear stress is 4.5 ksi, what is the maximum allowable torque T\ (c) If 7 = 150 kip-ft and allowable in-plane shear and allowable normal stresses are 4.5 ksi and 11.5 ksi, respectively, what is the minimum required wall thickness
- -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 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 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 ^ Pr
- The flat bars shown in parts a and b of the figure are subjected to tensile forces P = 2.5 kN. Each bar has thickness t = 5.0 mm. (a) For the bar with a circular hole, determine the maximum stresses for hole diameters d = 12 mm and d = 20 mm il" the width h = 60 mm. (b) For the stepped bar with shoulder fillets, determine the maximum stresses Tor fillet radii R = 6 mm and R = 10 mm if the bar widths are h = 60 mm and c = 40 mm.A vertical pole of solid, circular cross section is twisted by horizontal forces P = 5kN acting at the ends of a rigid horizontal arm AB (see figure part a). The distance from the outside of the pole to the line of action of each force is c = 125 mm (sec figure part b) and the pole height L = 350 mm. (a) If the allowable shear stress in the pole is 30 MPa, what is the minimum required diameter dminof the pole? (b) What is the torsional stiffness of the pole (kN · m/rad)? Assume that G = 28 GPa. (c) If two translation al springs, each with stiffness k =2550 kN/m, are added at 2c/5 from A and B (see figure part c), repeat part (a) to find dmin. Hint: Consider the pole and pair of springs as "springs in parallel."A prismatic bar with a length L = 3 ft and cross-sectional area A = 8 in2 is compressed by an axial centroidal load P = 10 kips. Determine the complete state of stress acting on an inclined section pq that is cut through the bar at an angle W = 35", and show the stresses on a properly oriented stress element.
- A square steel tube of a length L = 20 ft and width b2= 10.0 in. is hoisted by a crane (see figure). The lube hangs from a pin of diameter d that is held by the cables at points A and B. The cross section is a hollow square with an inner dimension b1= 8.5 in. and outer dimension b2= 10,0 in. The allowable shear stress in the pin is 8,700 psi. and the allowable bearing stress between the pin and the tube is 13,000 psi. Determine the minimum diameter of the pin in order to support the weight of the tube. Note: Disregard the rounded corners of the tube when calculating its weight.A pressurized cylindrical tank with flat ends is loaded by torques T and tensile forces P (sec figure), The tank has a radius of r = 125 mm and wall thickness t = 6.5 mm. The internal pressure p = 7.25 MPa and the torque T = 850 N m. (a) What is the maximum permissible value of the forces P if the allowable tensile stress in the wall of the cylinder is 160 MPa? (b) If forces P = 400 kN, what is the maximum acceptable internal pressure in the tank?• - 3 A rectangular plate in biaxial stress (see figure) is subjected to normal stresses u = 67 MPa (tension) and s = -23 MPa (compression). The plate has dimensions 400 X 550 X 20 mm and is made of steel with E = 200 GPa and v = 0.30. (a) Determine the maximum in-plane shear strain ?max in the plate. (b) Determine the change ?t in the thickness of the plate. (c) Determine the change ?t in the volume of the plate.