Problem 1.56 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 specifi¬cations remain unchanged, determine the allowable load P if an over¬all factor of safety of 3.0 is desired. Problem 1.55 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.
Problem 1.35 A steel pipe of 400-mm outer diameter is fabricated from 10-mm-thick plate by welding along a helix that forms an angle of 20° with a plane perpendicular to the axis of the pipe. Knowing that a 300-kN axial force P is applied to the pipe, determine the normal and shearing stresses in directions respectively normal and tangential to the weld.
Problem 1.52 Solve Prob. 1.51, assuming that the structure has been redesigned to use 5/16-in.-diameter pins at A and C as well as at B and that no other changes have been made. Problem 1.51 Link AC is made of a steel with a 65-ksi ultimate normal stress and has a 14× 12-in. uniform rectangular cross section. It is con¬nected to a support at A and to member BCD at C by 38-in.-diameter pins, while member BCD is connected to its support at B by a 5 16-in.-diameter pin. All of the pins are made of a steel with a 25-ksi ultimate shearing stress and are in single shear. Knowing that a factor of safety of 3.25 is desired, determine the largest load P that can be applied at D. Note that link AC is not reinforced around the pin holes.
Problem 1.54 Solve Prob. 1.53, assuming that the structure has been redesigned to use 12-mm-diameter pins at B and D and no other change has been made. Problem 1.53 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.
Problem 1.53 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.
Problem 1.55 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.
Problem 1.51 Link AC is made of a steel with a 65-ksi ultimate normal stress and has a 14× 12-in. uniform rectangular cross section. It is con¬nected to a support at A and to member BCD at C by 38-in.-diameter pins, while member BCD is connected to its support at B by a 5 16-in.-diameter pin. All of the pins are made of a steel with a 25-ksi ultimate shearing stress and are in single shear. Knowing that a factor of safety of 3.25 is desired, determine the largest load P that can be applied at D. Note that link AC is not reinforced around the pin holes.
Problem 1.50 Determine the factor of safety for the cable anchor in Prob. 1.49 when P = 2.5 kips, knowing that a = 2 in. and b = 6 in. Problem 1.49 A steel plate 14 in. thick is embedded in a concrete wall to anchor a high-strength cable as shown. The diameter of the hole in the plate is 34 in., the ultimate strength of the steel used is 36 ksi and the ultimate bonding stress between plate and concrete is 300 psi. Know¬ing that a factor of safety of 3.60 is desired when P = 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 end of the plate.)
Problem 1.48 For the support of Prob. 1.47, knowing that the diameter of the pin is d = 16 mm and that the magnitude of the load is P = 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. Problem 1.47 A 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 = 40 mm, c = 55 mm, and d = 12 mm, determine the load P if an overall factor of safety of 3.2 is desired.
Problem 1.49 A steel plate 14 in. thick is embedded in a concrete wall to anchor a high-strength cable as shown. The diameter of the hole in the plate is 34 in., the ultimate strength of the steel used is 36 ksi and the ultimate bonding stress between plate and concrete is 300 psi. Know¬ing that a factor of safety of 3.60 is desired when P = 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 end of the plate.)
Problem 1.42 Link AB is to be made of a steel for which the ultimate normal stress is 65 ksi. Determine the cross-sectional area of AB for which the factor of safety will be 3.20. Assume that the link will be adequately reinforced around the pins at A and B.
Problem 1.46 Three steel bolts are to be used to attach the steel plate shown to a wooden beam. Knowing that the plate will support a load P = 28 kips, that the ultimate shearing stress for the steel used is 52 ksi, and that a factor of safety of 3.25 is desired, determine the required diameter of the bolts.
Problem 1.45 Two plates, each 18 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 = 325 lb.
Problem 1.36 A steel pipe of 400-mm outer diameter is fabricated from 10-mm-thick plate by welding along a helix that forms an angle of 20° with a plane perpendicular to the axis of the pipe. Knowing that the maximum allow¬able normal and shearing stresses in the directions respectively normal and tangential to the weld are σ = 60 MPa and τ = 36 MPa, determine the magnitude P of the largest axial force that can be applied to the pipe.
Problem 1.39 Knowing that the ultimate load for cable BD is 100 kN and that a factor of safety of 3.2 with respect to cable failure is required, deter¬mine the magnitude of the largest force P that can be safely applied as shown to member ABC.
Problem 1.32 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.