The concrete beam is reinforced with three 20-mmdiameter

Chapter 6, Problem 6-131

(choose chapter or problem)

The concrete beam is reinforced with three 20-mm-diameter steel rods. Assume that the concrete cannot support tensile stress. If the allowable compressive stress for concrete is \(\left(\sigma_{\text {allow }}\right)_{\mathrm{con}}=12.5 \ \mathrm{MPa}\) and the allowable tensile stress for steel is \(\left(\sigma_{\text {allow }}\right)_{\mathrm{st}}=220 \ \mathrm{MPa}\), determine the required dimension d so that both the concrete and steel achieve their allowable stress simultaneously. This condition is said to be ‘balanced’. Also, compute the corresponding maximum allowable internal moment M that can be applied to the beam. The moduli of elasticity for concrete and steel are \(E_{\text {con }}=25 \ \mathrm{GPa}\) and \(E_{\mathrm{st}}=200 \ \mathrm{GPa}\), respectively.