**DEFLECTION TEST – VERIFICATION OF MAXWELL’S**

**RECIPROCAL THEOREM**

**Aim:**

To verify Maxwell’s reciprocal theorem by conducting deflection test for the given specimen.

Maxwell’s reciprocal theorem:

In any beam, the deflection at a point ‘A’ due to the load at a point ‘B’ is equal to the deflection at the point ‘B’ due to the same load at the point ‘A’ and vice versa.

Apparatus and Specimen required:

1. Bending table or Bench type apparatus

2. Beam specimen

3. Dial gauge with stand

4. Set of weights with load hanger

5. Vernier caliper and scale.

Procedure:

1. Measure the length (L), breadth (b) and depth (d) of the given beam specimen.

2. Place the beam specimen over two knife edge supports in the bending table apparatus and measure centre to centre distance between the supports. The distance is known as span of the beam (l).

3. Mark two points ‘A’ and ‘B’ in the beam at a distance of l/3 and 2l/3, respectively from left support.

4. For first case (case I), place the load hanger at a point ‘A’ and dial gauge at point ‘B’. Now adjust the dial gauge reading at zero.

5. Apply ½ kg load on the load hanger and note down the dial gauge reading. Increase the load at the rate of ½ kg and note down the corresponding dial gauge reading. After the maximum loading, remove the load at the rate pf ½ kg and note down the corresponding dial gauge readings.

6. For the next case (case II), change the dial gauge to point ‘A’ and the load hanger to point ‘B’ and adjust the dial gauge reading to zero. Repeat the same procedure in step.4.

7. Find the average value of loading and unloading dial gauge readings for both the cases.

8. Find the actual deflection by multiplying the average value with least count of the dial gauge.

Discussion:

When a load of -----------N applied at point ‘A’ gives a deflection of ---------------mm at ‘B’. When the same load applied ‘B’ gives a deflection of ----------------mm t ‘A’. Both these deflections are --------------------.

**Result:**

Since the deflection are ------ for bith the cases, which proves Maxwell’s reciprocal theorem.

**Observation:**

1. Material of specimen =

2. Length of the specimen, (L) = mm

3. Span of the specimen, l = mm

4. Breadth of the specimen, b = mm

5. Depth of the specimen. D = mm

6. Least count (LC) of the dial gauge = mm

Sl.No. | Case I | Case II | |||||||||

Load at A in | Deflection at B | Deflection at A | |||||||||

kg | N | Dial gauge reading in division | Actual deflection in mm (L.C x Avg.) | Dial gauge reading in division | Actual deflection in mm (L.C x Avg.) | ||||||

Loading | Unloading | Average | Loading | Unloading | Average | ||||||

| | | | | | | | | | | |

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