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 of the shear force in kN just to the left hand side of support A, taking the sign as positive and 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 of the shear force in kN just to the left hand side of support A, taking the sign as positive and expressing the result to one decimal place

BlackTom AI · Accepted Answer

To determine the shear force just to the left of support A, we must analyze the left-hand segment of the beam up to A and use the shear-force diagram (SFD) built from the reactions and loads.

- Step 1: Identify the left segment up to A. The shear just to the left of A is the net transverse force that the beam carries immediately before reaching A. This is found by summing vertical forces on the left-hand portion of the beam (up to but not including A).

- Step 2: Include the known reaction at A. Since we are considering the region just to the left of A, the reaction at A itself does not act on that left-hand segment; instead, RA acts at A to the right-hand side. However, when drawing the SFD, the shear value immediately to the left of A equals the sum of all vertical forces on the left side, which typically includes any loads to the left of A but excludes RA (as RA acts at the boundary between left and right segments).

- Step 3: Account for loads on the left segment. If there are downward loads on the left portion of the beam, they reduce the shear value as you move from left to right toward A. Conversely, upward loads would increase the shear value. The exact value is obtained by subtracting the total downward load on the left segment from any upward reactions that lie on that same segment (if present).

- Step 4: Use sign convention. The problem states to take the sign as positive for the shear force on the left-hand side of A. In typical beam conventions, upward reactions are positive contributions to shear on the left segment, while downward loads are negative. Ensure you consistently apply this convention when summing forces.

- Step 5: Express the magnitude to one decimal place. After performing the summation, you will obtain a value with units of kN. The magnitude is the absolute value of that shear, and you report it to one decimal place as required.

- Step 6: Verify with the SFD. Cross-check by sketching the left portion of the SFD: start at the far left end with the appropriate boundary condition, plot jumps at loads (upward or downward) according to their magnitudes, and ensure continuity up to the point just left of A. The value at that point is the shear you’re asked to report.

- Additional considerations: If the left segment includes an overhang or an internal support to the left of A, repeat the force-summing process for that specific geometry. If the question provided the numerical reaction values at A and B from earlier parts, those values feed directly into the SFD construction; the key is to sum all forces on the left side of A to obtain the shear just left of A.

In short, the required quantity is the net vertical force carried by the left-hand portion of the beam immediately before A, computed by summing all vertical forces on that portion (with the chosen sign convention), independent of the reaction at A itself.

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

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类似问题

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

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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