Determining Maximum Positive Bending Moment on AISI 1020 Hot-Rolled Steel Beam

What are the equations used to calculate the maximum positive bending moment on an AISI 1020 hot-rolled steel beam under specific loads? The equations for calculating the maximum positive bending moment on an AISI 1020 hot-rolled steel beam under specific loads are as follows:
  • Maximum bending moment due to point load: \( M_{max} = \frac{P \cdot L}{4} \)
  • Maximum bending moment due to distributed load: \( M_{max} = \frac{q_1 \cdot L^2}{8} \)
The location at which the maximum positive bending moment occurs for both the point load and the distributed load is found by dividing the length of the beam by 2.

Calculation of Maximum Positive Bending Moment:

When analyzing an AISI 1020 hot-rolled steel beam supported by a point load of 20 kN and a variable distributed load ranging from 0 to 15 kN/m, we can determine the maximum positive bending moment using the provided equations.

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 \( 5L - \frac{15L^2}{8} \).

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