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- Question : 1P - Two solid cylindrical rods AB and BC are welded together at B and loaded as shown. Knowing that the average normal stress must not exceed 175 MPa in rod AB and 150 MPa in rod BC, determine the smallest allowable values of d1 and d2.
- Question : 2P - Two solid cylindrical rods AB and BC are welded together at B and loaded as shown. Knowing that d1 5 50 mm and d2 5 30 mm, find the average normal stress at the midsection of (a) rod AB, (b) rod BC.
- Question : 3P - Two solid cylindrical rods AB and BC are welded together at B and loaded as shown. Determine the magnitude of the force P for which the tensile stress in rod AB has the same magnitude as the compressive stress in rod BC 2 in. 3 in. 30 kips 30 kips C A B 30 in. 40 in. P Fig. P1.3
- Question : 4P - In Prob. 1.3, knowing that P 5 40 kips, determine the average normal stress at the midsection of (a) rod AB, (b) rod BC.
- Question : 5P - Two steel plates are to be held together by means of 16-mm-diameter high-strength steel bolts fitting snugly inside cylindrical brass spacers. Knowing that the average normal stress must not exceed 200 MPa in the bolts and 130 MPa in the spacers, determine the outer diameter of the spacers that yields the most economical and safe design.
- Question : 6P - Two brass rods AB and BC, each of uniform diameter, will be brazed together at B to form a nonuniform rod of total length 100 m which will be suspended from a support at A as shown. Knowing that the density of brass is 8470 kg/m3, determine (a) the length of rod AB for which the maximum normal stress in ABC is minimum, (b) the corresponding value of the maximum normal stress.
- Question : 7P - Each of the four vertical links has an 8 3 36-mm uniform rectan- Problems 21 gular cross section and each of the four pins has a 16-mm diameter. Determine the maximum value of the average normal stress in the links connecting (a) points B and D, (b) points C and E
- Question : 8P - Knowing that link DE is 1 8 in. thick and 1 in. wide, determine the normal stress in the central portion of that link when (a) u 5 0, (b) u 5 908.
- Question : 9P - Link AC has a uniform rectangular cross section 16 1 in. thick and 14 in. wide. Determine the normal stress in the central portion of the link.
- Question : 10P - Three forces, each of magnitude P 5 4 kN, are applied to the mechanism shown. Determine the cross-sectional area of the uniform portion of rod BE for which the normal stress in that portion is 1100 MPa. 0.100 m 0.150 m 0.300 m 0.250 m
- Question : 11P - The frame shown consists of four wooden members, ABC, DEF, BE, and CF. Knowing that each member has a 2 3 4-in. rectangular cross section and that each pin has a 1 2-in. diameter, determine the maximum value of the average normal stress (a) in member BE, (b) in member CF. 40 in. 45 in. 15 in. 4 in. A B C D E F 4 in. 30 in. 30 in. 480 lb Fig. P1.11
- Question : 12P - For the Pratt bridge truss and loading shown, determine the average normal stress in member BE, knowing that the cross-sectional area of that member is 5.87 in2
- Question : 13P - An aircraft tow bar is positioned by means of a single hydraulic cylinder connected by a 25-mm-diameter steel rod to two identical arm-and-wheel units DEF. The mass of the entire tow bar is 200 kg, and its center of gravity is located at G. For the position shown, determine the normal stress in the rod.
- Question : 14P - A couple M of magnitude 1500 N ? m is applied to the crank of Problems 23 an engine. For the position shown, determine (a) the force P required to hold the engine system in equilibrium, (b) the average normal stress in the connecting rod BC, which has a 450-mm2 uniform cross section.
- Question : 15P - When the force P reached 8 kN, the wooden specimen shown failed in shear along the surface indicated by the dashed line. Determine the average shearing stress along that surface at the time of failure. 20
- Question : 16P - The wooden members A and B are to be joined by plywood splice Fig. P1.14 plates that will be fully glued on the surfaces in contact. As part of the design of the joint, and knowing that the clearance between the ends of the members is to be 1 4 in., determine the smallest allowable length L if the average shearing stress in the glue is not to exceed 120 psi
- Question : 17P - A load P is applied to a steel rod supported as shown by an aluminum plate into which a 0.6-in.-diameter hole has been drilled. Knowing that the shearing stress must not exceed 18 ksi in the steel rod and 10 ksi in the aluminum plate, determine the largest load P that can be applied to the rod
- Question : 18P - Two wooden planks, each 22 mm thick and 160 mm wide, are joined by the glued mortise joint shown. Knowing that the joint will fail when the average shearing stress in the glue reaches 820 kPa, determine the smallest allowable length d of the cuts if the joint is to withstand an axial load of magnitude P 5 7.6 kN.
- Question : 19P - The load P applied to a steel rod is distributed to a timber support by an annular washer. The diameter of the rod is 22 mm and the inner diameter of the washer is 25 mm, which is slightly larger than the diameter of the hole. Determine the smallest allowable outer diameter d of the washer, knowing that the axial normal stress in the steel rod is 35 MPa and that the average bearing stress between the washer and the timber must not exceed 5 MPa
- Question : 20P - The axial force in the column supporting the timber beam shown is P 5 20 kips. Determine the smallest allowable length L of the bearing plate if the bearing stress in the timber is not to exceed 400 psi.
- Question : 21P - An axial load P is supported by a short W8 3 40 column of crosssectional area A 5 11.7 in2 and is distributed to a concrete foundation by a square plate as shown. Knowing that the average normal stress in the column must not exceed 30 ksi and that the bearing stress on the concrete foundation must not exceed 3.0 ksi, determine the side a of the plate that will provide the most economical and safe design
- Question : 22P - A 40-kN axial load is applied to a short wooden post that is supported by a concrete footing resting on undisturbed soil. Determine (a) the maximum bearing stress on the concrete footing, (b) the size of the footing for which the average bearing stress in the soil is 145 kPa.
- Question : 23P - A 5 8-in.-diameter steel rod AB is fitted to a round hole near end C of the wooden member CD. For the loading shown, determine (a) the maximum average normal stress in the wood, (b) the distance b for which the average shearing stress is 100 psi on the surfaces indicated by the dashed lines, (c) the average bearing stress on the wood.
- Question : 24P - Knowing that u 5 408 and P 5 9 kN, determine (a) the smallest Problems 25 allowable diameter of the pin at B if the average shearing stress in the pin is not to exceed 120 MPa, (b) the corresponding average bearing stress in member AB at B, (c) the corresponding average bearing stress in each of the support brackets at B.
- Question : 25P - Determine the largest load P that can be applied at A when u 5 608, knowing that the average shearing stress in the 10-mm-diameter pin at B must not exceed 120 MPa and that the average bearing strein member AB and in the bracket at B must not exceed 90 MPa
- Question : 26P - Link AB, of width b 5 50 mm and thickness t 5 6 mm, is used to support the end of a horizontal beam. Knowing that the average normal stress in the link is 2140 MPa, and that the average shearing stress in each of the two pins is 80 MPa, determine (a) the diameter d of the pins, (b) the average bearing stress in the link.
- Question : 27P - For the assembly and loading of Prob. 1.7, determine (a) the average shearing stress in the pin at B, (b) the average bearing stress at B in member BD, (c) the average bearing stress at B in member ABC, knowing that this member has a 10 3 50-mm uniform rectangular cross section.
- Question : 28P - The hydraulic cylinder CF, which partially controls the position of rod DE, has been locked in the position shown. Member BD is 58 in. thick and is connected to the vertical rod by a 3 8-in.-diameter bolt. Determine (a) the average shearing stress in the bolt, (b) the bearing stress at C in member BD.
- Question : 29P - The 1.4-kip load P is supported by two wooden members of uniform cross section that are joined by the simple glued scarf splice shown. Determine the normal and shearing stresses in the glued splice
- Question : 30P - Two wooden members of uniform cross section are joined by the simple scarf splice shown. Knowing that the maximum allowable tensile stress in the glued splice is 75 psi, determine (a) the largest load P that can be safely supported, (b) the corresponding shearing stress in the splice.
- Question : 31P - Two wooden members of uniform rectangular cross section are joined by the simple glued scarf splice shown. Knowing that P 5 11 kN, determine the normal and shearing stresses in the glued splice
- Question : 32P - Two wooden members of uniform rectangular cross section are joined by the simple glued scarf splice shown. Knowing that the maximum allowable shearing stress in the glued splice is 620 kPa, determine (a) the largest load P that can be safely applied, (b) the corresponding tensile stress in the splice.
- Question : 33P - A steel pipe of 12-in. outer diameter is fabricated from 1 4-in.-thick plate by welding along a helix that forms an angle of 258 with a plane perpendicular to the axis of the pipe. Knowing that the maximum allowable normal and shearing stresses in the directions respectively normal and tangential to the weld are s 5 12 ksi and t 5 7.2 ksi, determine the magnitude P of the largest axial force that can be applied to the pipe.
- Question : 34P - A steel pipe of 12-in. outer diameter is fabricated from 1 4-in.-thick plate by welding along a helix that forms an angle of 258 with a plane perpendicular to the axis of the pipe. Knowing that a 66 kip axial force P is applied to the pipe, determine the normal and shearing stresses in directions respectively normal and tangential to the weld.
- Question : 35P - A 1060-kN load P is applied to the granite block shown. Determine Problems the resulting maximum value of (a) the normal stress, (b) the shearing stress. Specify the orientation of that plane on which each of these maximum values occurs.
- Question : 36P - A centric load P is applied to the granite block shown. Knowing that the resulting maximum value of the shearing stress in the block is 18 MPa, determine (a) the magnitude of P, (b) the orientation of the surface on which the maximum shearing stress occurs, (c) the normal stress exerted on that surface, (d) the maximum value of the normal stress in the block.
- Question : 37P - Link BC is 6 mm thick, has a width w 5 25 mm, and is made of a steel with a 480-MPa ultimate strength in tension. What is the safety factor used if the structure shown was designed to support a 16-kN load P?
- Question : 38P - Link BC is 6 mm thick and is made of a steel with a 450-MPa ultimate strength in tension. What should be its width w if the structure shown is being designed to support a 20-kN load P with a factor of safety of 3?
- Question : 39P - Link BC is 6 mm thick and is made of a steel with a 450-MPa ultimate strength in tension. What should be its width w if the structure shown is being designed to support a 20-kN load P with a factor of safety of 3?
- Question : 40P - In the truss shown, members AC and AD consist of rods made of the same metal alloy. Knowing that AC is of 1-in. diameter and that the ultimate load for that rod is 75 kips, determine (a) the factor of safety for AC, (b) the required diameter of AD if it is desired that both rods have the same factor of safety
- Question : 41P - Link AB is to be made of a steel for which the ultimate normal stress is 450 MPa. Determine the cross-sectional area of AB for which the factor of safety will be 3.50. Assume that the link will be adequately reinforced around the pins at A and B.
- Question : 42P - A steel loop ABCD of length 1.2 m and of 10-mm diameter is placed as shown around a 24-mm-diameter aluminum rod AC. Cables BE and DF, each of 12-mm diameter, are used to apply the load Q. Knowing that the ultimate strength of the steel used for the loop and the cables is 480 MPa and that the ultimate strength of the aluminum used for the rod is 260 MPa, determine the largest load Q that can be applied if an overall factor of safety of 3 is desired.
- Question : 43P - wo wooden members shown, which support a 3.6-kip load, are joined by plywood splices fully glued on the surfaces in contact. The ultimate shearing stress in the glue is 360 psi and the clearance between the members is 1 4 in. Determine the required length L of each splice if a factor of safety of 2.75 is to be achieved. 240 mm 180 mm 24 mm C Q D
- Question : 44P - Two plates, each 1 8-in. thick, are used to splice a plastic strip as shown. Knowing that the ultimate shearing stress of the bonding between the surfaces is 130 psi, determine the factor of safety with respect to shear when P 5 325 lb.
- Question : 45P - load P is supported as shown by a steel pin that has been inserted in a short wooden member hanging from the ceiling. The ultimate strength of the wood used is 60 MPa in tension and 7.5 MPa in shear, while the ultimate strength of the steel is 145 MPa in shear. Knowing that b 5 40 mm, c 5 55 mm, and d 5 12 mm, determine the load P if an overall factor of safety of 3.2 is desired.
- Question : 46P - For the support of Prob. 1.45, knowing that the diameter of the pin is d 5 16 mm and that the magnitude of the load is P 5 20 kN, determine (a) the factor of safety for the pin, (b) the required values of b and c if the factor of safety for the wooden member is the same as that found in part a for the pin.
- Question : 47P - Three steel bolts are to be used to attach the steel plate shown to a wooden beam. Knowing that the plate will support a 110-kN load, that the ultimate shearing stress for the steel used is 360 MPa, and that a factor of safety of 3.35 is desired, determine the required diameter of the bolts.
- Question : 48P - Three 18-mm-diameter steel bolts are to be used to attach the steel plate shown to a wooden beam. Knowing that the plate will support a 110-kN load and that the ultimate shearing stress for the steel used is 360 MPa, determine the factor of safety for this design.
- Question : 49P - A steel plate 16 5 in. thick is embedded in a horizontal concrete slab and is used to anchor a high-strength vertical cable as shown. The diameter of the hole in the plate is 3 4 in., the ultimate strength of the steel used is 36 ksi, and the ultimate bonding stress between plate and concrete is 300 psi. Knowing that a factor of safety of 3.60 is desired when P 5 2.5 kips, determine (a) the required width a of the plate, (b) the minimum depth b to which a plate of that width should be embedded in the concrete slab. (Neglect the normal stresses between the concrete and the bottom edge of the plate.)
- Question : 50P - Determine the factor of safety for the cable anchor in Prob. 1.49 when P 5 3 kips, knowing that a 5 2 in. and b 5 7.5 in.
- Question : 51P - In the steel structure shown, a 6-mm-diameter pin is used at C and 10-mm-diameter pins are used at B and D. The ultimate shearing stress is 150 MPa at all connections, and the ultimate normal stress is 400 MPa in link BD. Knowing that a factor of safety of 3.0 is desired, determine the largest load P that can be applied at A. Note that link BD is not reinforced around the pin holes.
- Question : 52P - Solve Prob. 1.51, assuming that the structure has been redesigned to use 12-mm-diameter pins at B and D and no other change has been made.
- Question : 53P - Each of the two vertical links CF connecting the two horizontal members AD and EG has a uniform rectangular cross section 1 4 in. thick and 1 in. wide, and is made of a steel with an ultimate strength in tension of 60 ksi. The pins at C and F each have a 1 2-in. diameter and are made of a steel with an ultimate strength in shear of 25 ksi. Determine the overall factor of safety for the links CF and the pins connecting them to the horizontal members.
- Question : 54P - Solve Prob. 1.53, assuming that the pins at C and F have been replaced by pins with a 3 4-in. diameter.
- Question : 55P - In the structure shown, an 8-mm-diameter pin is used at A, and 12-mm-diameter pins are used at B and D. Knowing that the ultimate shearing stress is 100 MPa at all connections and that the ultimate normal stress is 250 MPa in each of the two links joining B and D, determine the allowable load P if an overall factor of safety of 3.0 is desired. 200 mm 180 mm Top view Side view Front view 8 mm 20 mm 8 mm 8 mm 12 mm 1
- Question : 56P - In an alternative design for the structure of Prob. 1.55, a pin of 10-mm diameter is to be used at A. Assuming that all other specifications remain unchanged, determine the allowable load P if an overall factor of safety of 3.0 is desired.In an alternative design for the structure of Prob. 1.55, a pin of 10-mm diameter is to be used at A. Assuming that all other specifications remain unchanged, determine the allowable load P if an overall factor of safety of 3.0 is desired.
- Question : 57P - The Load and Resistance Factor Design method is to be used to select the two cables that will raise and lower a platform supporting two window washers. The platform weighs 160 lb and each of the window washers is assumed to weigh 195 lb with equipment. Since these workers are free to move on the platform, 75% of their total weight and the weight of their equipment will be used as the design live load of each cable. (a) Assuming a resistance factor f 5 0.85 and load factors gD 5 1.2 and gL 5 1.5, determine the required minimum ultimate load of one cable. (b) What is the conventional factor of safety for the selected cables
- Question : 58P - A 40-kg platform is attached to the end B of a 50-kg wooden beam AB, which is supported as shown by a pin at A and by a slender steel rod BC with a 12-kN ultimate load. (a) Using the Load and Resistance Factor Design method with a resistance factor f 5 0.90 and load factors gD 5 1.25 and gL 5 1.6, determine the largest load that can be safely placed on the platform. (b) What is the corresponding conventional factor of safety for rod BC?
- Question : 59RP - A strain gage located at C on the surface of bone AB indicates that the average normal stress in the bone is 3.80 MPa when the bone is subjected to two 1200-N forces as shown. Assuming the cross section of the bone at C to be annular and knowing that its outer diameter is 25 mm, determine the inner diameter of the bone
- Question : 60RP - Two horizontal 5-kip forces are applied to pin B of the assembly shown. Knowing that a pin of 0.8-in. diameter is used at each connection, determine the maximum value of the average normal stress (a) in link AB, (b) in link BC B A C 0.5 in. 1.8 in. 1.8 in. 45 60 5 kips 5 kips
- Question : 61RP - For the assembly and loading of Prob. 1.60, determine (a) the average shearing stress in the pin at C, (b) the average bearing stress at C in member BC, (c) the average bearing stress at B in member BC.
- Question : 62RP - n the marine crane shown, link CD is known to have a uniform cross section of 50 3 150 mm. For the loading shown, determine the normal stress in the central portion of that link. A
- Question : 63RP - Two wooden planks, each 1 2 in. thick and 9 in. wide, are joined by the dry mortise joint shown. Knowing that the wood used shears off along its grain when the average shearing stress reaches 1.20 ksi, determine the magnitude P of the axial load that will cause the joint to fail. P' 2 in. 1 in. P' 2 in. 1 in. 9 in. P 5 in. 8 5 in. 8 Fig. P1.63
- Question : 64RP - Two wooden members of uniform rectangular cross section of sides a 5 100 mm and b 5 60 mm are joined by a simple glued joint as shown. Knowing that the ultimate stresses for the joint are sU 5 1.26 MPa in tension and tU 5 1.50 MPa in shear and that P 5 6 kN, determine the factor of safety for the joint when (a) a 5 208, (b) a 5 358, (c) a 5 458. For each of these values of a, also determine whether the joint will fail in tension or in shear if P is increased until rupture occurs.
- Question : 65RP - Member ABC, which is supported by a pin and bracket at C and Review Problems 47 a cable BD, was designed to support the 16-kN load P as shown. Knowing that the ultimate load for cable BD is 100 kN, determine the factor of safety with respect to cable failure. A D B C 0.4 m 30 40 0.8 m 0.6 m P
- Question : 66RP - The 2000-lb load may be moved along the beam BD to any position between stops at E and F. Knowing that sall 5 6 ksi for the steel used in rods AB and CD, determine where the stops should be placed if the permitted motion of the load is to be as large as possible. diameter diameter x B E F D A C xE xF 5 -in. 1 2 -in. 8
- Question : 67RP - Knowing that a force P of magnitude 750 N is applied to the pedal shown, determine (a) the diameter of the pin at C for which the average shearing stress in the pin is 40 MPa, (b) the corresponding bearing stress in the pedal at C, (c) the corresponding bearing stress in each support bracket at C
- Question : 68RP - A force P is applied as shown to a steel reinforcing bar that has been embedded in a block of concrete. Determine the smallest length L for which the full allowable normal stress in the bar can be developed. Express the result in terms of the diameter d of the bar, the allowable normal stress sall in the steel, and the average allowable bond stress tall between the concrete and the cylindrical surface of the bar. (Neglect the normal stresses between the concrete and the end of the bar.)
- Question : 69RP - The two portions of member AB are glued together along a plane forming an angle u with the horizontal. Knowing that the ultimate stress for the glued joint is 2.5 ksi in tension and 1.3 ksi in shear, determine the range of values of u for which the factor of safety of the members is at least 3.0.
- Question : 70RP - The two portions of member AB are glued together along a plane forming an angle u with the horizontal. Knowing that the ultimate stress for the glued joint is 2.5 ksi in tension and 1.3 ksi in shear, determine (a) the value of u for which the factor of safety of the member is maximum, (b) the corresponding value of the factor of safety. (Hint: Equate the expressions obtained for the factors of safety with respect to normal stress and shear.)
- Question : 1CP - A solid steel rod consisting of n cylindrical elements welded together is subjected to the loading shown. The diameter of element i is denoted by di and the load applied to its lower end by Pi, with the magnitude Pi of this load being assumed positive if Pi is directed downward as shown and negative otherwise. (a) Write a computer program that can used with either SI or U.S. customary units to determine the average stress in each element of the rod. (b) Use this program to solve Probs. 1.2 and 1.4
- Question : 2CP - A 20-kN load is applied as shown to the horizontal member ABC. Member ABC has a 10 3 50-mm uniform rectangular cross section and is supported by four vertical links, each of 8 3 36-mm uniform rectangular cross section. Each of the four pins at A, B, C, and D has the same diameter d and is in double shear. (a) Write a computer program to calculate for values of d from 10 to 30 mm, using 1-mm increments, (1) the maximum value of the average normal stress in the links connecting pins B and D, (2) the average normal stress in the links connecting pins C and E, (3) the average shearing stress in pin B, (4) the average shearing stress in pin C, (5) the average bearing stress at B in member ABC, (6) the average bearing stress at C in member ABC. (b) Check your program by comparing the values obtained for d 5 16 mm with the answers given for Probs. 1.7 and 1.27. (c) Use this program to find the permissible values of the diameter d of the pins, knowing that the allowable values of the normal, shearing, and bearing stresses for the steel used are, respectively, 150 MPa, 90 MPa, and 230 MPa. (d) Solve part c, assuming that the thickness of member ABC has been reduced from 10 to 8 mm.
- Question : 3CP - Two horizontal 5-kip forces are applied to pin B of the assembly shown. Each of the three pins at A, B, and C has the same diameter d and is in double shear. (a) Write a computer program to calculate for values of d from 0.50 to 1.50 in., using 0.05-in. increments, (1) the maximum value of the average normal stress in member AB, (2) the average normal stress in member BC, (3) the average shearing stress in pin A, (4) the average shearing stress in pin C, (5) the average bearing stress at A in member AB, (6) the average bearing stress at C in member BC, (7) the average bearing stress at B in member BC. (b) Check your program by comparing the values obtained for d 5 0.8 in. with the answers given for Probs. 1.60 and 1.61. (c) Use this program to find the permissible values of the diameter d of the pins, knowing that the allowable values of the normal, shearing, and bearing stresses for the steel used are, respectively, 22 ksi, 13 ksi, and 36 ksi. (d) Solve part c, assuming that a new design is being investigated in which the thickness and width of the two members are changed, respectively, from 0.5 to 0.3 in. and from 1.8 to 2.4 in.
- Question : 4CP - A 4-kip force P forming an angle a with the vertical is applied as shown to member ABC, which is supported by a pin and bracket at C and by a cable BD forming an angle b with the horizontal. (a) Knowing that the ultimate load of the cable is 25 kips, write a computer program to construct a table of the values of the factor of safety of the cable for values of a and b from 0 to 458, using increments in a and b corresponding to 0.1 increments in tan a and tan b. (b) Check that for any given value of a, the maximum value of the factor of safety is obtained for b 5 38.668 and explain why. (c) Determine the smallest possible value of the factor of safety for b 5 38.668, as well as the corresponding value of a, and explain the result obtained.
- Question : 5CP - A load P is supported as shown by two wooden members of uniform rectangular cross section that are joined by a simple glued scarf splice. (a) Denoting by sU and tU, respectively, the ultimate strength of the joint in tension and in shear, write a computer program which, for given values of a, b, P, sU and tU, expressed in either SI or U.S. customary units, and for values of a from 5 to 858 at 58 intervals, can calculate (1) the normal stress in the joint, (2) the shearing stress in the joint, (3) the factor of safety relative to failure in tension, (4) the factor of safety relative to failure in shear, (5) the overall factor of safety for the glued joint. (b) Apply this program, using the dimensions and loading of the members of Probs. 1.29 and 1.31, knowing that sU 5 150 psi and tU 5 214 psi for the glue used in Prob. 1.29, and that sU 5 1.26 MPa and tU 5 1.50 MPa for the glue used in Prob. 1.31. (c) Verify in each of these two cases that the shearing stress is maximum for a 5 458.
- Question : 6CP - Member ABC is supported by a pin and bracket at A, and by two Computer Problems 51 links that are pin-connected to the member at B and to a fixed support at D. (a) Write a computer program to calculate the allowable load Pall for any given values of (1) the diameter d1 of the pin at A, (2) the common diameter d2 of the pins at B and D, (3) the ultimate normal stress sU in each of the two links, (4) the ultimate shearing stress tU in each of the three pins, (5) the desired overall factor of safety F.S. Your program should also indicate which of the following three stresses is critical: the normal stress in the links, the shearing stress in the pin at A, or the shearing stress in the pins at B and D (b and c). Check your program by using the data of Probs. 1.55 and 1.56, respectively, and comparing the answers obtained for Pall with those given in the text. (d) Use your program to determine the allowable load Pall, as well as which of the stresses is critical, when d1 5 d2 5 15 mm, sU 5 110 MPa for aluminum links, tU 5 100 MPa for steel pins, and F.S. 5 3.2.

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