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Course 38579

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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_1 = 20\,\text{m}, x_2 = 12\,\text{m}x_2 = 12\,\text{m}, x_3 = 10\,\text{m}x_3 = 10\,\text{m}
  • y_1 = 6\,\text{m}y_1 = 6\,\text{m}, y_2 = 10\,\text{m}y_2 = 10\,\text{m}y_3 = 3\,\text{m}y_3 = 3\,\text{m}
  • F_1 = 20\,\text{kN}F_1 = 20\,\text{kN}
  • F_2 = 40\,\text{kN}F_2 = 40\,\text{kN}
  • F_3 = 15\,\text{kN}F_3 = 15\,\text{kN}
  • w_1 = 3\,\text{kN/m}w_1 = 3\,\text{kN/m}
  • M_1 = 10\,\text{kN}\cdot\text{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 (xx and yy 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 xx is to the right.
  • Positive yy is upward.
  • Anti-clockwise moments are taken as positive.

Figure P16.

Beam system for free-body diagram construction (not to scale).

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Consider the

truss bridge

shown in

Figure P14

.

All joints are pin-connected. The supports at

A and B are both pin supports. External loads of magnitude F are applied on the top chord of the truss at five locations, as shown in the figure.

Determine the number of

zero force members in this truss. 

Select the correct number.

Figure P14. Pin-connected truss bridge.

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Consider the

roof truss

 shown in

Figure P13

.

All joints are pin-connected. The left and right supports are

both

pin supports.

Determine the

structural classification

of the truss.

Select the correct statement.

Figure P13. Pin-connected truss bridge.

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Determine the mass of A required to keep the system in equilibrium if block B has a mass of 3030 kg? Consider the gravitational acceleration to be g=9.8g=9.8 m/s2. Provide your answer in kg to 4 decimal places.

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Determine the mechanical advantage of the following pulley system. The mechanical advantage here is defined as the weight of A divided by the force at B.

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Determine the mass of the block required to keep the system in equilibrium if FF is 500500 N. Consider the gravitational acceleration to be g=9.8g=9.8 m/s2. Provide your answer in kg to 4 decimal places.

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Consider the following structure and determine the resultant force (in N) acting at point O to 4 decimal places.

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Two forces are applied to the construction bracket as shown. Determine the angle θ (in degrees) to 4 decimal places which makes the resultant of the two forces completely vertical.

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Which of the following statements is false for the figure below?

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Which of the following equations represents the resultant vector of two forces F_1 F_1 and F_2 F_2 acting at an angle  \theta \theta apart starting from the same origin? i.e. calculate F1 + F2. Refer to the image below for an illustration. Remember that when adding vectors, the tail of one vector needs to connect to the head of another.

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