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A plumber's valve wrench is used to replace valves in plumbing fixtures. A simplified model of the wrench (see figure part a) consists of pipe AB (length L. outer diameter D inner diameter dy), which is fixed at A and has holes of a diameter dhon either side of the pipe at B. A solid, cylindrical bar CBD (lengths, diameter^) is inserted into the holes at B and only one force F = 55 lb is applied in the -Z direction at C to loosen the fixture valve at A (see figure part c). Let G = 11,800 ksi, v = 0.30, L = 4 in., a = 4.5 in., d2= 1.25 in., dx= 1 in., and dh= 0.25 in. Find the state of plane stress on the top of the pipe near A (at coordinates A" = 0,Y = Q,Z = d->12), and show all stresses on a plane stress element (see figure part b). Compute the principal stresses and maximum shear stress, and show them on properly rotated stress elements
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Mechanics of Materials (MindTap Course List)
- 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.arrow_forwardA vertical pole of solid, circular cross section is twisted by horizontal forces P = 1100 lb 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 = 5.0 in. (see figure part b) and the pole height is L = 14in. (a) If the allowable shear stress in the pole is 4500 psi, what is the minimum required diameter dminof the pole? Find the torsional stiffness of the pole (kip-in./rad). Assume that G = 10,800 ksi. If two translational springs, each with stiffness k = 33 kips/in., are added at 2(75 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."arrow_forwardA steel riser pipe hangs from a drill rig located offshore in deep water (see figure). Separate segments are joined using bolted flange plages (see figure part b and photo). Assume that there are six bolts at each pipe segment connection. Assume that the total length of the riser pipe is L = 5000 ft: outer and inner diameters are d2= l6in.and d1= 15 in.; flange plate thickness t1= 1.75 in.; and bolt and washer diameters are db= 1.125 in..and dW. = 1.875 in., respectively. (a) If the entire length of the riser pipe is suspended in air. find the average normal stress a in each bolt, the average bearing stress abbeneath each washer, and the average shear stress t through the flange plate at each bolt location for the topmost bolted connection. (b) If the same riser pipe hangs from a drill rig at sea. what are the normal, bearing, and shear stresses in the connection? Obtain the weight densities of steel and sea water from Table I-1. Appendix I. Neglect the effect of buoyant foam casings on the riser pipearrow_forward
- The upper deck ala foothill stadium is supported by braces, each of which transfer a load P = 160 kips to the base of a column (see figure part a). A cap plate at the bottom of the brace distributes the load P to four flange pates (:1 = I in)t hrough a pin(d, = 2 in.) to two gusset plates t8 = l.5 in.) (see figure parts b and c). Determine the following quantities. (a) The average shear stress i in the pin. (b) The average bearing stress between the flange plates and the pin and also between the gusset plates and the pin Disregard friction between the plates. Determine the following quantities. (a) The average shear stress i in the pin. (b) The average bearing stress between the flange plates and the pin and also between the gusset plates and the pin (7j )L Disregard friction between the plates.arrow_forwardA round bar ABC of length 2L (see figure) rotates about an axis through the midpoint C with constant angular speed w (radians per second). The material of the bar has weight density y. (a) Derive a formula for the tensile stress a’ in the bar as a function of the distance x from the midpoint C. (b) What is the maximum tensile stress a max?arrow_forward-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/inarrow_forward
- 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 ^ Prarrow_forwardA 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?arrow_forward-22 Two tubes (AB, BC) of the same material arc connected by three pins (pin diameter = d ) just left of B as shown in the figure. Properties and dimensions for each tube are given in the figure. Torque 2ris applied at x = 2L/5 and uniformly distributed torque intensity tQ= 37/L is applied on tube BC. (a) Find the maximum value of load variable T(N m) based on allowable shear (tx) and bearing(cha ) stresses in the three pins which connect the two tubes at B. Use the following numerical properties: L = 1.5m, E = 74GPa, v = 0.33, dp= 18mm, ta=45MPa, =90 MPa, di=85 mm, di = T$ mm, and d3— 60 mm. (b) What is the maximum shear stress in the tubes for the applied torque in part (a)?arrow_forward
- Two pipe columns (AB, FC) are pin-connected to a rigid beam (BCD), as shown in the figure. Each pipe column has a modulus of E, but heights (L1or L2) and outer diameters (d1or different for each column. Assume the inner diameter of each column is 3/4 of outer diameter. Uniformly distributed downward load q = 2PIL is applied over a distance of 3L/4 along BC, and concentrated load PIA is applied downward at D. (a) Derive a formula for the displacementarrow_forwardA hollow circular pipe (see figure} support s 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, rf3 = 57 mm, and d1= 64 mm, respectively. Pipe lengths are Lt= 2 m and L, = 3 m. Neglect the self-weight of the pipes. Assume that cap plate thickness is small compared to I, and E,. Let E = 110 MPa. (a) If the tensile stress in the upper part is d = 10.5 MPa. what is load PI Also, what are reactions ft, at the upper support and R-, at the lower support? What is the stress ar(MPa) in the lower part? (b) Find displacement S(mm) at the cap plate. Plot the axial force diagram (AFD) [Ar(.f)] and axial displacement diagram (ADD)[5(.t)]. (c) Add the uniformly distributed load q along the censorial axis of pipe segment 2. Find q (kN/m) so that It, = 0. Assume that load P from part (a) is also applied.arrow_forwardA simple beam of span length 3.2 m carries a uniform load of intensity 48 kN/m, The cross section of the beam is a hollow box with wood flanges and steel side plates, as shown in the figure. The wood flanges are 75 mm x 100 mm in cross section, and the steel plates are 300 mm deep. What is the required thickness t of the steel plates if the allowable stresses are 120 M Pa for the steel and 6,5 M Pa for the wood? (Assume that the moduli of elasticity for the steel and wood are 210 GPa and 10 GPa, respectively, and disregard the weight of the beam.)arrow_forward
- Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning