What is Measured?

During the compression test, the following quantities are measured:

• Applied compressive load, $P$
• Original specimen diameter, $d$
• Original specimen length, $L$
• Change in length, $\Delta L$

These measurements are used to determine the compressive properties of the material.

Why are the Calculations Required?

The measured quantities alone do not fully describe the behaviour of a material under compression.

The calculations help determine:

• Compressive stress
• Compressive strain
• Young's Modulus
• Yield strength
• Compressive strength

These properties are required for engineering analysis and design.

Observation Table

Assume a cylindrical specimen having:

• Diameter = 20 mm
• Original length = 40 mm

Load (kN)	Reduction in Length (mm)
0	0.000
20	0.020
40	0.040
60	0.065
80	0.095
100	0.140
120	0.220
140	0.350
160	0.550

Sequential Calculations

1. Cross-Sectional Area

$$A=\frac{\pi d^2}{4}$$

For a specimen diameter of 20 mm,

$$A=\frac{\pi(20)^2}{4}$$

$$A=314.16\ mm^2$$

2. Compressive Stress

$$\sigma_c=\frac{P}{A}$$

3. Compressive Strain

$$\epsilon_c=\frac{\Delta L}{L}$$

4. Young's Modulus

$$E=\frac{\sigma_c}{\epsilon_c}$$

5. Compressive Strength

Compressive strength is the maximum compressive stress sustained by the specimen.

$$\sigma_{comp}=\frac{P_{max}}{A}$$

where:

• $P_{max}$ = Maximum load carried by the specimen

Solved Numerical Example

Given:

• Diameter = 20 mm
• Original length = 40 mm
• Applied load = 80 kN
• Reduction in length = 0.095 mm

Step 1: Area

$$A=\frac{\pi(20)^2}{4}$$

$$A=314.16\ mm^2$$

Step 2: Compressive Stress

$$\sigma_c=\frac{80000}{314.16}$$

$$\sigma_c=254.6\ N/mm^2$$

Step 3: Compressive Strain

$$\epsilon_c=\frac{0.095}{40}$$

$$\epsilon_c=0.002375$$

Step 4: Young's Modulus

$$E=\frac{254.6}{0.002375}$$

$$E=107200\ N/mm^2$$

$$E=107.2\ GPa$$

Interpretation of Results

• A linear stress-strain relationship indicates elastic behaviour.
• Increasing compressive stress causes shortening of the specimen.
• Ductile materials exhibit significant deformation before failure.
• Brittle materials fail by cracking or crushing.
• Higher compressive strength indicates greater resistance to crushing.

Result

The compression test was performed successfully, and the compressive properties of the material were determined from the load-deformation behaviour.