For the beam shown below, and using the answers for the reactions at A and B from questions 1 and 2:

Sketch the shear force diagram and use this to answer the following question;

What is the magnitude in kN and sign of the shear force just to the left and side of support B, expressing the result to one decimal place

Question

For the beam shown below, and using the answers for the reactions at A and B from questions 1 and 2:

Sketch the shear force diagram and use this to answer the following question;

What is the magnitude in kN and sign of the shear force just to the left and side of support B, expressing the result to one decimal place

BlackTom AI · Accepted Answer

First, restating the problem helps set the stage: you have a beam with supports at A and B, and you are asked to sketch the shear force diagram using the reactions at A and B obtained previously, then determine the magnitude and sign of the shear force immediately to the left of support B, to one decimal place.

Because there are no multiple-choice options provided here, we’ll focus on the logic and steps you would use to arrive at the value (in this case, the given answer is -27.5 kN).

Step 1: Build the shear force diagram conceptual framework
- Start from the left end of the beam and move toward the right, keeping track of the internal shear force V(x) as you cross loads and reactions.
- The shear diagram changes value (jumps) at points of concentrated loads or reactions, and varies linearly between distributed loads if present. In many beam problems, step changes occur only at supports (reactions) and where point loads act.

Step 2: Incorporate the reactions at A and B
- At x just to the right of A, the reaction at A contributes a jump in the shear diagram equal to +RA (assuming upward reaction sign convention). If RA is known from question 1, you place that positive jump at A.
- As you traverse toward B, subtract any downward concentrated loads or add any upward loads (depending on the sign convention) to update V(x) along the span.
- Immediately to the left of B, you have accumulated all changes in shear from the left end up to just before the reaction at B acts. If the reaction at B is RB (upward), then crossing B from left to right would produce a jump of +RB at B when you pass the support; the value just to the left of B does not yet include RB.

Step 3: What does “just to the left of B” mean in terms of the diagram?
- The shear value immediately to the left of B is the value of V(x) just before the jump that occurs at B due to the reaction RB. Practically, you read this value off the shear diagram immediately before the right-hand support.

Step 4: How to obtain the numeric value
- Use the known RA and RB from questions 1 and 2, along with the loading on the beam between A and B.
- Compute the running shear from x = 0 (left end) toward x = span end, applying RA at A (a positive jump) and subtracting any downward point loads as you pass them, and accounting for UDLs if present.
- Just before reaching B, read the shear value V_left_B. The sign is determined by the chosen convention: typically positive means upwards on the left side of the section, negative means downward.

Step 5: Interpret the provided result of -27.5 kN
- A value of -27.5 kN to the left of B indicates that, just before the right support, the internal shear force is 27.5 kN in the negative direction per the adopted sign convention.
- The negative sign reflects the net effect of the loads to the left of B and the upward reaction at A, leading to a downward (negative) shear just left of B when moving left to right.

Step 6: Why the sign and magnitude make sense conceptually
- If the left portion of the beam has a net downward effect (loads plus the lack of sufficient upward reaction before B), the shear is negative just left of B.
- The exact magnitude depends on RA, RB, and the distributed/point loads between A and B; the reported -27.5 kN is consistent with a particular set of those values.

Step 7: Practical checks you can perform
- Verify that the sum of all vertical forces equals zero: RA + RB minus the total downward load equals zero.
- Verify that the area under the shear diagram (which equals the bending moment change) matches the known bending moments or reaction conditions at the supports.
- Ensure you read V(x) just to the left of B, not including the jump due to RB, to confirm you’re using the correct side of the discontinuity.

Summary of the method in one line: construct the shear diagram from A to just before B using RA and the loading, then read off the left-hand value at B; its sign and magnitude follow directly from the net effect of the loads and supports on the left span. If your calculations yield -27.5 kN for V just left of B, that is the numerical result corresponding to the prescribed loading and reactions.

STRCTENG 302 Steel Quiz No 1: Basic Knowledge Mechanics and Structural Steel Review

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