Which of the following correctly identifies the point of application (distance from A

)

of the equivalent resultant force

Determine the number of

Select the correct number.

Determine the

Select the correct statement.

Figure P12 shows an L-shaped beam with eight different support arrangements, labelled A–H.

Each case uses a combination of supports that may or may not adequately restrain the structure. The supports are either guided rollers (providing a reaction force normal to the surface, in either direction) or pins.

Which of the following cases are unstable? 

In your assessment, consider whether the structure is sufficiently restrained against both translation and rotation.

Assume all supports are ideal and that the beam behaves as a rigid body in a 2D plane.

Select all that apply.

Figure P12. Different L-shaped beam systems.

Determine the

Select the correct value of F

Figure P8 shows a spring-mass system consisting of multiple linear springs arranged in a combination of series and parallel connections. 

The top three springs with stiffness k, 2k, and 3k are connected in parallel to a rigid bar. This bar is then connected to the mass M through two identical springs (each of stiffness k) arranged in series.

Which of the following correctly represents the

Assume all springs are linear, massless, and deform only in the vertical direction.

Select the correct answer.

Figure P8. Spring and mass system.

Figure P7 shows a mass M suspended from a fixed ceiling by two identical verticals springs arranged in parallel. When the mass is attached, the systems comes to rest after undergoing a vertical deflection Δy.

Given:

• If

  M = 300 kg 
• Deflection Δy = 0.5 m
• Acceleration due to gravity g = 9.8 m/s²   

Assuming the system is in static equilibrium, determine the stiffness

Select the correct answer.

Consider the pulley system shown in

An input force T = 800 N is applied to the rope as shown.

Assuming the system is in equilibrium, and that the pulleys and cables are massless and frictionless, determine the mass m that can be supported. 

Take gravitational acceleration g = 9.8 m/s².

Select the correct answer.

Now consider the cantilever beam shown in Figure P5. The beam is fixed at support A. 

A force F₃ is applied at point B and acts in the direction shown. An applied moment M₁ acts at point C as shown, in the direction shown.

If

Select the correct answer (All answers are in kN·m)

Figure P5. Cantilever beam with applied moment and force.

To receive marks for this question, you must submit a hard copy of your FBD at the end of your test.  

Consider the frame shown in Figure P16.

The frame consists of multiple beams welded together. The frame is supported at four locations shown in the figure:

• Support A is a pin support.
• Support B is a fixed support.
• Support C and D are guided roller supports.

Draw the complete free-body diagram (FBD) of the beam using the following parameters:

• x_1 = 20\,\text{m}, x_2 = 12\,\text{m}, x_3 = 10\,\text{m}
• y_1 = 6\,\text{m}, y_2 = 10\,\text{m}, y_3 = 3\,\text{m}
• F_1 = 20\,\text{kN}
• F_2 = 40\,\text{kN}
• F_3 = 15\,\text{kN}
• w_1 = 3\,\text{kN/m}
• M_1 = 10\,\text{kN}\cdot\text{m}

Instructions

• Show all external loads acting on the beam.
• 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.