What is Measured?

During the shear test, the following quantities are measured:

• Diameter of the specimen, (d)
• Failure load, (P)
• Number of shear planes

These measurements are used to determine the double shear strength of the material.

Why are the Calculations Required?

The measured failure load alone cannot be used to compare different materials or specimens.

The calculations help determine:

• Cross-sectional area
• Double shear strength
• Average double shear strength

These properties are important for the design of bolts, rivets, pins, and structural connections subjected to shear loading.

Observation Table

Assume three specimens are tested under double shear.

Diameter (mm)	Failure Load (kg)
5.91	1300
5.95	1450
6.00	1500

Sequential Calculations

1. Cross-Sectional Area

The cross-sectional area of a circular specimen is:

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

where:

• $A$ = Cross-sectional area (mm$^2$)
• $d$ = Diameter of specimen (mm)

2. Double Shear Strength

For a specimen under double shear,

$$\tau=\frac{P\times9.81}{2A}$$

where:

• $\tau$ = Double shear strength (N/mm$^2$)
• $P$ = Failure load (kg)
• $A$ = Cross-sectional area (mm$^2$)

Solved Numerical Example

For Trial 3:

Given:

• Diameter, (d = 6.00) mm
• Failure Load, (P = 1500) kg

Step 1: Calculate Cross-Sectional Area

$$A=\frac{\pi(6)^2}{4}$$

$$A=28.27\ \text{mm}^2$$

Step 2: Calculate Double Shear Strength

$$\tau=\frac{1500\times9.81}{2\times28.27}$$

$$\tau=260.35\ \text{N/mm}^2$$

Average Double Shear Strength

Using the values obtained from the three trials:

Trial	Double Shear Strength (N/mm(^2))
1	232.55
2	255.93
3	260.35

Average Double Shear Strength:

$$\tau_{avg} = \frac{232.55+255.93+260.35}{3}$$

$$\tau_{avg} = 249.61\ \text{N/mm}^2$$

Interpretation of Results

• Higher failure load indicates greater resistance to shear failure.
• Double shear loading provides two resisting shear planes, increasing the load-carrying capacity of the specimen.
• The calculated double shear strength represents the maximum shear stress that the material can withstand before failure.
• The average value obtained from multiple trials provides a more reliable estimate of the material's shear strength.

Result

The double shear test was performed successfully, and the average double shear strength of the material was determined as:

$$249.61\ \text{N/mm}^2$$