Bending in Beam

TITLE: Bending in beam

OBJECTIVE: To determine the elastic modulus (E) of beam specimen by method of

deflection.

APPARATUS:

1.vernier caliper

2. brass specimen

3. aluminium specimen

4. mild steel specimen

5. gauge

6. blast of various weight

7. screw driver

THEORY: Pure bending

· The radius of curvature for this arc is defined as the distance R, which is measured from the center of curvature, 0 to dx.

· The strain in arc ds, located at position y from the position neutral axis is

є = (ds’– ds)/ds. However, ds= dx= R dӨ and є = [ (p-y) dӨ - R dӨ]/ R dӨ or 1/R = - є/y

· Based on Hooke’s Law: є = σ/E and

Flexture formula applied: σ = - My/I

E/R = M/I

Thus,

· Is known that,

R² = (R- y)² + (L/2)²

R² = R²- 2Ry + y² +L²/4

Therefore, 2Ry = L²/4

R = L²/8y

We know, M = W(x)

I = bh³/12

·

8Ey/L2 = W(x)/I

Thus,

EXPERIMENTAL PROCEDURE:

The apparatus was setup as been shown in figure1.The length, height and width of the specimen was measured and been recorded. The center of each specimen was marked on each specimen; brass, aluminium and mild steel. The distance x was measured from point A and point B and been marked. The specimen of mild steel was been setup on the apparatus as shown in figure 1. Make sure the center of specimen was attached or touch the gauge. The dial gage was setup to 0.Blast was located at the distance x = 15cm from point A and B. The maximum displacement (y) was taken. For the next reading, the weight of blast was added and continued until 8 readings. The procedure was repeated for other specimens. For aluminium, the, maximum blast is 20N.Then, the graph of weight (W) against deflection (y) was plotted. The elastic modulus (E) of beam specimen was determined from the graph.

DATA AND RESULTS

Mild Steel: b = 20.48mm

h = 4.2mm

Aluminium: b = 20.4mm

h = 6.6mm

CALCULATION:

Mild Steel:

L = 0.50 m

x = 0.15 m

Slope of graph

Moment of inertia, I

Slope

Aluminium:

L = 0.50 m

x = 0.15 m

Slope of graph

Moment of inertia, I

Slope

DISCUSSION.

Compare the value (E) obtained from this method with their theoretical value.

From the calculation, we get 389.9 GPa for Modulus Young (E) of Mild Steel, 147.399 GPa for Modulus Young (E) of Aluminum. Obviously, the theoretical values of Modulus Young (E) for those three beams are

210 GPa and 70 GPa. Comparing our experiment results to theoretical value, the differences for those three beams in percentage are 49.7% for mild steel and 71.7% for aluminium

There are some errors occur when do this experiment. One of them is parallax error. It occur when our eyes is not same level with the reading points. In this experiment, parallax error occurs when we take the deflection reading at bending gage. Beside that, it also occur when measure the length of beam. So, to avoid from this experiment, make sure our eyes is at same level with reading points. Beside parallax error, system error also occurs in this experiment. This error occurs due to the instruments that have been already damage. Beside that, zero scale of instrument is not at their actual place. So from this error, it will influence the readings that have taken. So to avoid this error, we should change with new instrument with more precise. It will give a readings that more accurate.

CONCLUSION:

From the experiment we can conclude that, different material has a different elastic curve or Modulus young (E) and the behaviors of each material. By regarding to the test result, we know that aluminium has the lowest value of Modulus Young (E) and this shows that the aluminium is softer than mild steel.