Fig. 1 shows a bookshelf that has begun to sag in the middle. Explain the forces causing this and the design changes that would prevent it. [7]
Question 1 Report
Fig. 1 shows a bookshelf that has begun to sag in the middle. Explain the forces causing this and the design changes that would prevent it. [7]
Answer Details
The books act as a distributed downward load over the shelf span. This makes the shelf bend, with the greatest deflection at the middle.
- The shelf is in bending because the weight of the books acts downwards along its length. [1]
- In a sagging shelf, the upper surface is in compression and the lower surface is in tension; the sag is greatest at mid-span. [2]
- Deflection increases very rapidly as the span increases, so even a relatively small increase in shelf width can cause much more sag. [1]
- Reduce the span by adding a central support. This gives the shelf a shorter unsupported distance. [1]
- Increase the depth of the section, for example by adding a front lip or a batten beneath. Depth greatly increases stiffness, so this is often more effective than simply making the shelf slightly wider. [2]
- Use a stiffer material or add a supporting rail along the back edge. [1]
A strong judgement is that adding a central support and increasing section depth directly tackle the cause of sag by reducing span and increasing stiffness. [6–7]
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