Equilibrium of a Beam

To verify the use of the conditions of equilibrium in calculating the reactions of a simply supported beam or a cantilever.

Apparatus

The apparatus basically provides a channel section aluminum alloy beam 1.04m long which rest of knife edge supports that replace the scale pans of two weighing machines. The base plates of the weighing machines can be clamped in any position along the bottom member of HST1 test frame to permit the span of the beam to be varied. Three load hangers are available for loading the beam at different points along its length.

An alternative arrangement can be constructed by using only one weighing machine near the middle of the beam. To the right of this support loading is applied using the load hangers, while to the left a downward load is applied at the end of the beam using the tie rod on a spring balance anchored to the bottom member of the frame.

Procedure

Part 1, Beam reactions

  1. In the test frame fixed the reaction balances with the knife edges 1m apart.
  2. Rest the channel section beam over the knife edge supports with zero of the scale lined up with the left hand support.
  3. Added a stirrup and load hanger at mid span.
  4. To bring the pointer to zero on the balances we used the zero adjustment.
  5. This is an artificial way of nullifying the self weight of the beam, stirrup and load hanger so that the balances will read only the reaction for any added load.
  6. We recorded the two reaction values for each case when add the secession of the weight up to 60 N to the mid span load hanger.
  7. The reaction should be equal each half of the load must satisfy vertical equilibrium because of the symmetry.
  8. The results are recorded in Table 1.
  9. 40 N load are used, the reactions are recorded when more the stirrup and load hanger to the quarter span position
  10. Used the three stirrups and load hanger at pre-selected positions.
  11. Added a set of three loads, one at a time, to these hangers, recording the reactions as each load is applied.

Part 2, Cantilever beam reactions

  1. Attached the spring balance assembly mid way between the reactions balances.
  2. Moved the channel section beam to the right so that the threaded tie rod of the spring balance passes through the hole in the top of the beam by the zero on the beam scale.
  3. Through the right hand side of the test frame the beam will then extend and been levels by adjusts the tie rod.
  4. The beam cantilever to the right of the upward reaction balance, while the spring balance provides a downward reaction.
  5. Any initial readings will be those due to the self weight of the cantilever.
  6. On the end of the cantilever position a stirrup and load hanger 500 mm from the reaction balance and adjust the zero of the reaction balance.
  7. Add a succession of 5 N loads of hanger. For each loading adjust the length of the spring balance tie rod to re-level the cantilever.
  8. The reading are recorded in Table 2
  9. Changed the position of the spring balance by moving it closer (say 200 mm) to the reaction balance.
  10. Reposition the stirrup and load hanger so that it is the same distance of 500 mm from the reaction balance as above. Zero the balance.
  11. Add a succession of 10 N loads on the hanger.
  12.  Re-level the cantilever and recorded the balance readings for each load.
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