Each member in the pin-jointed planar truss in Fig. P1.4-2 is 6 ft long. The truss is attached to a firm base by a frictionless pin at B, and it rests on a roller support at A. (F₁ = 3 kips and F₂ = 12 kips)

Figure P1.4-2.

For the loading shown, determine the following:
(a) the reactions at A and B

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1 (vertical reaction at A)

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2 (vertical reaction at B)

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3 (horizontal reaction at B)
(b) the force in each of the three members, labeled (1) through (3)

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4 (member 1)

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5 (member 2)

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6 (member 3)

In this truss equilibrium problem, adopt the sign convention for axial force that a tensile force is positive. That is, on your free-body diagrams, show all unknown forces F_i as tensile forces. Then, a force that is compressive will be negative.

A 550 kN capacity hydraulic punch press is used to punch circular holes in a 10 mm thick aluminum plate, as illustrated in Fig. P2.7-1. If the average punching shear resistance of this plate is 270 MPa, what is the maximum diameter of hole that can be punched?

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1 mm

Figure P2.7-1.

The tapered solid stone pier in Fig. P3.4-11 is 20 ft high, and it has a square cross section with side dimension that varies linearly from 36 in. at the top to 48 in. at the bottom. Assume that the stone is linearly elastic with modulus of elasticity E = 4.0 x 10³ ksi. Determine the shortening of the pier under a compressive load of P = 150 kips. (Neglect the weight of the stone.)

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1 in.

Figure P3.4-11.

While rotating at 1050 rpm, the rear drive shaft of a four-wheel-drive sport utility vehicle (Fig. P4.8-9) delivers 180 hp to the rear differential gear box. The allowable shear stress in the drive shaft is 6 ksi, and its outer diameter is d_o = 3.00 in. To the nearest 0.01 in. what is the maximum permissible inner diameter?

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1 in.

Figure P4.8-9.

Two transverse forces and a couple are applied as external loads to the cantilever beam AC in Fig. P5.2-5. (P₁ = 17 kips and P₂ = 4 kips) Determine the transverse shear force V_A and the bending moment M_A at the fixed end A.
V_A =

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1 kips
M_A =

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2 kip · ft

Figure P5.2-5.

For this problem, you are to determine the internal resultants (transverse shear force V and bending moment M) at specific cross sections of a beam. Use the sign conventions for V and M given in Fig. 5.6, p. 303, and always draw complete and correct free-body diagrams. The minus-sign superscript signifies "just to the left of" the referenced point; the plus-sign superscript means "just to the right of" the referenced point.

Figure 5.6.