A concrete beam is reinforced by three steel rods placed as shown. The modulus of elasticity is 3 × 106 psi for the concrete and 29 × 106 psi for the steel. Using an allowable stress of 1342 psi for the concrete and 20 ksi for the steel, determine the largest allowable positive bending moment in the beam. 16 in. -in. diameter 8 in. 2 in. The largest allowable positive bending moment in the beam is kip-ft.

The reinforced concrete beam shown is subjected to a positive bending moment of 178 kN-m. Knowing that the modulus of elasticity is 25 GPa for the concrete and 200 GPa for the steel, determine the stress in the steel and the maximum stress in the concrete. 540 mm -350 mm The stress in the steel is The stress in the concrete is 25-mm diameter 60 mm ↑ MPa. MPa.

The reinforced concrete beam shown is subjected to a positive bending moment of 173 kN-m. Knowing that the modulus of elasticity is 25 GPa for the concrete and 200 GPa for the steel, determine the stress in the steel and the maximum stress in the concrete. 540 mm -350 mm- 25-mm diameter 60 mm 1 The stress in the steel is 209.7 MPa. The stress in the concrete is -15.417 MPa.

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A circular aluminum alloy [E = 70 GPa; a = 22.5 x 10-6/°C; v = 0.33] pipe has an outside diameter of 220 mm, a wall thickness of 15 mm, and a length of 4.0 m. The pipe supports a compressive load of 650 kN. After the temperature of the pipe drops 41°C, determine: (a) the axial deformation of the pipe. (b) the change in diameter of the pipe. Answer: (a) ō = i mm AD = i mm

Problem 317 A hollow bronze shaft of 3 in. outer diameter and 2 in. inner diameter is slipped over a solid steel shaft 2 in. in diameter and of the same length as the hollow shaft. The two shafts are then fastened rigidly together at their ends. For bronze, G = 6 x 10° psi, and for steel, G = 12 x 10° psi. What torque can be applied to the composite shaft without exceeding a shearing stress of 8000 psi in the bronze or 12 ksi in the steel? T 2 13" Hollow Bronze D = 3 in, d = 2 in Steel Core D= 2 in

1. A steel section of length L sits on an 8" x 8" bearing plate. The bearing plate is perfectly rigid and sits on a 15 in x 15 in x 4 foot high concrete block which is fixed at the base. The system supports an axial load of P. A. Determine the normal stress in the steel. B. Determine the normal stress in the concrete. C. How much did the entire system shorten (Hint: the plate is perfectly rigid so it does not deform-just pretend it isn't there.) 15 in. Concrete 4 ft. 15 in. 8 in. Top View 8 in. Given: P = 250 kips L = 12 ft. d₁= 1 in. d₂ = 4 in. Esteel = 30,000 ksi Econcrete = 4,000 ksi

The column shown is made by filling a steel pipe with concrete. The concrete has an Elastic Modulus of Ec = 3,800 ksi and a cross-sectional area of A = 80 in² the steel pipe has an Elastic Modulus of Est = 29,000 ksi and a cross-sectional area of Ast = 11 in?. If the column has a length of L = 10 ft and is subjected to a load of P = 350 kip, what is the stress in the concrete? Express your answer in psi, to %D the nearest 10 psi. P L

Q2. Three 160 mm by 80 mm planks are glued together to form a wooden beam. This beam is simply supported at both ends as shown in figure below. Determine the maximum shear stress in a. The glue b. The wood 8 kN/m Glue 80 mm B 80 mm - NA 6 m 80 mm 160 mm

3 Given a concrete beam (width b= 10 in., depth h = 25 in.) with flexural reinforcement at the bottom, the transformed moment of inertia is In=14,740 in“, and the location of the neutral axis from top of the beam is y = 13.2 in, assuming all material is elastic, calculate the maximum tensile stress of the concrete when a positive bending moment M= 40 kip-ft is applied to the beam. Is the section cracked under the given moment if concrete is normal weight and the compressive strength fe' is 3000 psi?