Which option best depicts the shape of the SFD (Shear Force Diagram) of the following beam?

Question

BlackTom AI · Accepted Answer

To determine the SFD shape, I first identify the loading on the beam and the support conditions. The beam is simply supported with a point load P applied somewhere between the supports and a uniformly distributed load (UDL) across the right portion of the beam. In a shear-force diagram:

- Start at the left support with the reaction force R_A as the initial shear value (positive on the diagram). This creates a constant positive value up to the location of any jump caused by the point load.
- At the location of the point load P, the shear diagram experiences a vertical downward jump equal to P (the shear is reduced by the magnitude of the applied downward load).
- After the point load, the UDL causes the shear to vary linearly with the slope equal to the negative of the distributed load intensity w (since the UDL removes shear as we move along the beam). This results in a straight line with a downward slope until the right support.
- At the right support, the shear value ends at the reaction at the right support, which closes the diagram to zero if the reactions are balanced for equilibrium.

Option-by-option reasoning:

- Option a.: If this option shows an initial positive shear with a downward jump at the location of P but then a nonlinear or incorrect continuation after the jump, it would misrepresent the constant slope due to the uniform distributed load or misplace the jump magnitude. This would misalign with how a UDL affects shear (a constant slope) and how a point load changes shear (a discrete vertical drop).

- Option b.: This option is consistent with the expected sequence: positive shear before P, a downward jump of magnitude P at the point load, followed by a linear (constant-slope) decrease due to the UDL, ending at the right support. The line after the jump should be straight with a slope corresponding to the negative w, which matches static beam theory.

- Option c.: If this option depicts either an incorrect order of features (e.g., a jump where none should occur, or a slope direction opposite to the load configuration) or shows a non-linear post-P segment, it would violate the linear relationship between shear and x for a uniform load portion and/or misplace the jump at P.

- Option d.: A wrong placement or size of the jump, or an inappropriate slope after the jump (for instance, a positive slope where the UDL should create a negative slope), would contradict the effects of the UDL and point load on the shear diagram. Such a depiction would not satisfy equilibrium of shear along the beam.

In summary, the correct SFD must start with the left-reaction value, exhibit a downward jump equal to P at the location of the point load, and then proceed with a straight line of constant negative slope corresponding to the UDL, finishing at the right support. Among the provided options, the one that matches this sequence and geometry best is option b.

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

Which option best depicts the shape of the SFD (Shear Force Diagram) of the following beam?

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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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