Consider the free-body diagram of the beam shown in

Which of the following correctly represents the

Use the sign convention for forces and moments shown in the figure.

Figure P3. Beam free-body diagram

Two workers are assembling the centre pole of a large tent. They use separate tensioned ropes to stabilise the pole, as shown in Figure P2. The workers each apply a force along their ropes, F₁ and F₂, respectively, acting at the angles shown in the figure. Assume that the pole is vertical and that both forces act at the same point (A). 

For F₁ = 500 N and F₂ = 600 N, determine the magnitude of the resultant force F_R acting on the pole due to the two ropes. 

Select the correct answer.

Figure P2. Stabilising rope connection

Consider the truss shown in Figure P1

. Using the dimensions provided in the figure for AD and AC,

determine the length of member BD

. Express your answer in metres to at least 2 decimal places. 

Figure P1. Truss

To receive marks for this question, you must submit a hard copy of your FBD at the end of your test.  Do not write in the text box.

Consider the frame that is loaded as shown in Figure P17.

The frame consists of multiple beams welded together. The frame is supported at three locations, by a guided roller, pin and a fixed support as indicated in the figure. 

Draw the complete free-body diagram (FBD) of the frame using the parameters given in the figure.

Instructions

• Show all external loads acting on the frame.
• Include relevant dimensions shown in the figure.
• Label all reaction forces and moments clearly.
• Include a clearly defined coordinate system  (x and y axes, and moments).
• Ensure you use the correct numerical values and units where they are provided.
• Do not calculate reactions. 
• Present distributed loads as correctly labelled distributed loads, i.e., do not present or calculate the equivalent point load.

Use the following sign convention:

• Positive
  Image failed to load: x
  x is to the right.
• Positive
  Image failed to load: y
  y is upward.
• Anti-clockwise moments are taken as positive.

Determine the number of

Select the correct number.

Determine the

Select the correct statement.

Consider the beam systems shown below.  Each support is either a fixed, roller or pin support. 

Select which beam is unstable based on its support configuration.

Ensure you consider both translation (in the x and y directions) and rotation.

Now consider the diagram of a different simply supported beam shown in Figure P11. The dimensions of the beam may be different to the previous questions.

A triangular distributed load (w₃) is applied between point B and point C

,

varying

linearly from zero at B to a maximum at C, as shown. The beam span between A and D is as shown on the diagram. 

Which of the following correctly identifies the value of x (in m) where x  is the point of application (distance from A

)

of the equivalent resultant force

Assume the load acts vertically downward and varies linearly as shown in the figure.

Figure P11b. The point of application of the equivalent resultant force F_EQ due to the triangular distributed load, x (in m), measured from point A

A triangular distributed load is applied to the beam, increasing from

Determine the

Select the correct value of F

Figure P10. Simply supported beam with a triangular distributed load.

Determine the

Select the correct value of F