The figure below shows a portal frame being acted on by a downwards acting vertical load. The supports at A and E are fixed and the connections at B, C and D are rigid.

Sketch the reactions, shear force diagram and bending moment diagram generated on this portal frame by the loading and use it to answer the following question:

Which of the following best describes the magnitude and distribution of shear force along member BCD

Question

The figure below shows a portal frame being acted on by a downwards acting vertical load. The supports at A and E are fixed and the connections at B, C and D are rigid.

Sketch the reactions, shear force diagram and bending moment diagram generated on this portal frame by the loading and use it to answer the following question:

Which of the following best describes the magnitude and distribution of shear force along member BCD

BlackTom AI · Accepted Answer

The question asks us to assess the magnitude and distribution of shear force along member BCD in a portal frame with fixed supports at A and E and rigid connections at B, C, and D, under a vertical downward load.

Option under analysis: "Maximum positive value at B, zero at C, Maximum negative value at D."

- Start by considering the overall loading and reactions: A downward external load on the top of the frame will be carried by the frame through the rigid joints, producing vertical reactions at the fixed supports A and E and internal shear transfers along the members B–C–D. Because the joints B, C, and D are rigid, the frame behaves as a continuous system rather than as three independent simply-supported members. The internal shear in member BCD is not constrained to be zero at any interior pin, since there is no pin at C (the joint is rigid), and the vertical load path and frame geometry determine a smooth distribution of shear along the member.

- Evaluate the possibility of a zero shear exactly at C: In a rigidly connected continuous frame, a flat (zero) shear at an internal joint would require a specific symmetry or a particular loading that creates a net no-shear transfer across that location. With a single downward load and non-symmetric supports (A and E are at the two ends), it is not generally expected that the shear becomes exactly zero at the interior joint C. Therefore, claiming zero shear at C across B–C–D is typically unlikely unless the loading and geometry produce a symmetric condition about C, which is not indicated here.

- Consider the idea of a maximum positive shear at B followed by a maximum negative shear at D: A downward point or distributed load tends to induce shear that may decrease in magnitude along the member from the left to right, with sign changes depending on how the reaction forces are distributed and how the frame transfers bending and shear through the rigid joints. However, asserting that the left end B carries the maximum positive shear, and the right end D carries the maximum negative shear, implies a specific linear-like variation and a zero at C. In a rigid, continuous frame with three rigid joints and fixed supports, the shear distribution is generally not guaranteed to have zero at an interior joint unless the analysis shows such a condition after solving the shear Diagram.

- Key misconception to watch for: Assuming a simple piecewise-linear shear with a zero at an interior joint (C) is a common trap. The actual shear distribution depends on the exact frame stiffness, the relative stiffness of the joints, and the reaction distribution. Without performing the full shear force diagram or providing the reaction magnitudes, it is risky to assert a zero at C and the sign change exactly at C.

- Conclusion about the option: While the statement describes a neat pattern (positive at B, zero at C, negative at D), such a pattern requires specific symmetry or loading that is not necessarily implied by the given description of a portal frame with fixed supports and rigid joints under a downward load. Therefore, this option makes a strong claim about the zero point at C and the extremal values at B and D that may not hold without explicit calculation.

In summary, the proposed description of the shear distribution (maximum positive at B, zero at C, maximum negative at D) rests on an assumption of zero shear at C and a linear-like variation, which is not guaranteed for a rigid, continuous portal frame under a single vertical load. A correct analysis would require constructing the full shear force diagram for member BCD by solving for the support reactions at A and E and then computing the internal shear along B–C–D, accounting for the rigid connections. The claim should be validated against that computed diagram rather than accepted as a given."

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