Determining Maximum Positive Bending Moment on AISI 1020 Hot-Rolled Steel Beam
- Maximum bending moment due to point load: \( M_{max} = \frac{P \cdot L}{4} \)
- Maximum bending moment due to distributed load: \( M_{max} = \frac{q_1 \cdot L^2}{8} \)
Calculation of Maximum Positive Bending Moment:
Firstly, we substitute the value of the point load \( P = 20 \, kN \) into the equation for the maximum bending moment due to the point load: \( M_{max} = \frac{P \cdot L}{4} = \frac{20 \cdot L}{4} = 5L \)
Similarly, for the distributed load ranging from 0 to 15 kN/m, we substitute the value of \( q_1 \) into the equation for the maximum bending moment due to the distributed load: \( M_{max} = \frac{q_1 \cdot L^2}{8} = \frac{(0-15) \cdot L^2}{8} = -\frac{15L^2}{8} \)
Therefore, the maximum positive bending moment for the AISI 1020 hot-rolled steel beam is a combination of the bending moments due to the point load and the distributed load, which are given by \( 5L - \frac{15L^2}{8} \).