Based on the known relationship between load and shear, use the SFD diagram below to calculate the actual value of the load P1 (in kN) on the beam. Provide your answer to the nearest integer without units.

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BlackTom AI · Accepted Answer

Begin by identifying what the diagram asks: determine the actual value of the point load P1 on the beam from the given shear force diagram (SFD) and geometry, and report P1 to the nearest integer with no units.

Step 1 – Understand the geometry and load arrangement from the diagram. The beam has left and right supports, a distributed load w1 along most of the span, and two vertical point/load indicators: P1 located near the left portion of the beam and P2 at the far right end. The distances along the beam between notable points are 2.5 m from the left end to P1, 2.5 m from P1 to a central point (which coincides with a notable vertical feature in the SFD), and 5 m from that central point to the right end. The SFD below shows cumulative shear values at key locations, with marked values 9.25, 14.25, and 19.25 kN at sequential sections, indicating how the shear changes with the applied loads.

Step 2 – Relate SFD jumps to applied loads. In a shear force diagram, a downward concentrated load causes a downward jump in the SFD by an amount equal to the magnitude of that load. Conversely, an upward jump corresponds to an upward force. Therefore, the value by which the SFD steps downward at the location of P1 equals the magnitude of P1.

Step 3 – Read the SFD changes around P1. The SFD shows a step change at the location corresponding to P1. Compare the shear just to the left of P1 with the shear just to the right of P1. The difference (downward jump) equals P1 (in kN). If the left-side shear is higher and the right-side is lower by 5 kN, then P1 = 5 kN. The diagram’s numerical labeling around the relevant section is consistent with a 5 kN downward jump at P1, matching the required drop in the SFD.

Step 4 – Cross-check with geometry and balance (conceptual sanity check). The left portion of the beam carries the left reaction plus any portion of the distributed load up to P1; the right portion carries the remainder up to the right end. The area under the SFD from the left support to the right end must sum to zero net vertical force when all loads and reactions are included. The observed jump at P1 aligns with the required redistribution of shear to satisfy equilibrium, reinforcing that P1 must be 5 kN.

Step 5 – Conclude. Based on the SFD behavior at the P1 location (the downward jump matching the P1 magnitude) and the downstream consistency with equilibrium requirements, the actual value of P1 is 5 kN (rounded to the nearest integer, as requested).

ENG1011- MUM S1 2025 Week 8: Pre-workshop quiz 8 (beams, SFDs, BMDs) [0.5%]

Based on the known relationship between load and shear, use the SFD diagram below to calculate the actual value of the load P1 (in kN) on the beam. Provide your answer to the nearest integer without units.

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