Question

Suppose the beam is carrying a known shear load of RD = 28 kN . In this particular situation, the resistance factor is ϕ=0.9 for the shear load, and the nominal shear stress is 204 MPa . What is the magnitude of the maximum live load (in addition to RD) that can be supported in shear by this beam? Express your answer to three significant figures with the appropriate units.

Answer 1

49.5 kN

Step-by-step explanation:

From the information given:

`R_D = 28 \ kN`
`\delta _D = 1.4; \ \ \ \delta _L = 1.6`

`\sigma_n = 204 \ MPa; \ \ \ A_w = 6.45 \ cm^2 = 645 \ mm^2`

Thus ;
`P_n = (\sigma_n)/((1)/(A)) \\ \\ = \ {\sigma_n}*{A} \\ \\ = 645 *204 \\ \\ = 131.58 \ kN`

From the given inequality; maximum live load (in addition to RD) that can be supported in shear by this beam is calculated by using the relation;

`\phi P_n \geq \sum \delta_i R_i \\ \\ \geq \delta_DR_D + \delta_L R_L \\ \\ 0.9*131.58 \geqq [1.4*28+1.6*R_L ] \\ \\ 118.4 \geq 39.2+ 16 R_L \\ \\ 118.4 - 39.2 \geq 16R_L \\ \\ 79.2 \geq 16R_L\\ \\ R_L \leq 49.5 \ kN`