Calculate the reactions at RL and RR - NSC Mechanical Technology Welding and Metalwork - Question 6 - 2021 - Paper 1

The bending moment at any point can be calculated using the internal moment equation.

• At point B: The moment due to the load before point B is:

$M_B = R_1 \times 3 m$

• At point C: The moment will sum the contributions from both R1 and the 80 N load:

$M_C = R_1 \times 5 m - 80 N \times 2 m$

• At point D: The contributions will include R1, the 80 N, and 60 N load:

$M_D = R_1 \times 7 m - 80 N \times 4 m - 60 N \times 2 m$

To construct the bending moment diagram:

1. Calculate the points B, C, and D moments using the values derived above.
2. Translate these calculated moments into the diagram using the provided scaling factor (1 m = 1 cm and 10 N m = 1 cm).
3. Plot the bending moments accordingly on the X-axis and connect these points to visualize the diagram.

Using the tensile stress formula:

$\sigma = \frac{F}{A}$

Where

• $\,\sigma = 20 MPa$
• $F = 40 kN$

The area A can be expressed as:

$A = \frac{F}{\sigma}$

Solving for A gives us the cross-sectional area. The diameter can be found using:

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

Strain ($\epsilon$) is defined as the change in length ($\Delta L$) over the original length (L):

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

We can express the change in length with Young's modulus:

$\epsilon = \frac{\sigma}{E}$

Substituting in the values for stress and Young's modulus:

$\epsilon = \frac{20 MPa}{90 GPa}$.

To find the change in length ($\Delta L$), we use the formula derived for strain:

$\Delta L = \epsilon \times L$

Substituting in our strain calculation and the original length of 2 m to find the change in length in mm.