A horizontal, rigid bar of negligible weight is fixed against a vertical wall at one end and supported by a vertical string at the other end. The bar has a length of 50.0 cm and is used to support a hanging block of weight 400.0 N from a point 30.0 cm from the wall as shown in Figure P14.81. The string is made from a material with a tensile strength of 1.2 108 N/m2. Determine the largest diameter of the string for which it would still break. FIGURE P14.81

The lintel of prestressed reinforced concrete in Figure P12.27 is 1.50 m long. The concrete encloses one steel reinforcing rod with cross-sectional area 1.50 cm2. The rod joins two strong end plates. The cross-sectional area of the concrete perpendicular to the rod is 50.0 cm2. Youngs modulus for the concrete is 30.0 109 N/m2. After the concrete cures and the original tension T1 in the rod is released, the concrete is to be under compressive stress 8.00 106 N/m2. (a) By what distance will the rod compress the concrete when the original tension in the rod is released? (b) What is the new tension T2 in the rod? (c) The rod will then be how much longer than its unstressed length? (d) When the concrete was poured, the rod should have been stretched by what extension distance from its unstressed length? (e) Find the required original tension T1 in the rod. Figure P12.27

What Is Static Equilibrium? Problems 13 are grouped. 1. C A ball is attached to a strong, lightweight rod (Fig. P14.1). The rod is supported by a horizontal pin near the top. The ball is at rest. Is the ball in static equilibrium? If not, why not? If so, which type of equilibrium is itstable, unstable, or neutral? Hint: What would happen if you displaced the ball slightly? FIGURE P14.1

Steel beams are used for load bearing supports in a building. Each beam is 4.0 m long with a cross-sectional area of 9.3 x 10-3 m2 and supports a load of 7.5 x 104 N. Young's modulus for steel is 210 x 109 N/m2. (a) How much compression does each beam undergo along its length? mm (b) Determine the maximum load one of these beams can support without any structural failure if the compressive strength of steel is 1.50 x 10° N/m2. N

A control rod made of yellow brass must not stretch more than 3 mm when the tension in the wire is 4 kN. Knowing that E 105 GPa and that the maximum allowable normal stress is 180 MPa, determine (a) the smallest diameter rod that should be used, (b) the corresponding maximum length of the rod.

The radius of a copper bar is 4 mm. What force is required to stretch the rod by 20% of its length assuming that the elastic limit is not exceeded? Y = 12 × 1010 N/m².

The bell crank is in equilibrium for the forces acting in rods (1) and (2). The bell crank is supported by a pin with a diameter of 12 mm at B that acts in single shear. The thickness of the bell crank is 6 mm. Assume a = 50 mm, b = 150 mm, F₁ = 1260 N, and 0 = 52° Determine the following: (a) the average shear stress in pin B (b) the average bearing stress in the bell crank at B a (1) 0 Bell crank e C B (2) b F2

The truss is made of three A-36 steel members, each having a cross-sectional area of 400 mm2. Determine the magnitude P required to displace the roller to the right 0.2 mm.