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Course 38579

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Figure P4 shows a rigid frame fixed at point A. A single force of magnitude

3000\,\text{N}3000 N is applied at point B, acting along the direction shown (defined by the 3–4–5 triangle).

The horizontal member has a length of 10 m, and the vertical member has a height of 12 m.

Determine the reaction moment (M_A) at the fixed support A. Use the sign convention for forces and moments shown in the figure (i.e. a counter clockwise moment is considered positive).

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

Figure P4. Cantilever beam with applied forces

$M_A = - (3000)(10) = - 30{,}000\,\text{Nm}$ M_A = - (3000)(10) = - 30{,}000\,\text{Nm}

$M_A = \frac{3}{5}(3000)(12) + \frac{4}{5}(3000)(10) = 45{,}600\,\text{Nm}$ M_A = \frac{3}{5}(3000)(12) + \frac{4}{5}(3000)(10) = 45{,}600\,\text{Nm}

$M_A = \frac{4}{5}(3000)(12) - \frac{3}{5}(3000)(10) = 10{,}800\,\text{Nm}$ M_A = \frac{4}{5}(3000)(12) - \frac{3}{5}(3000)(10) = 10{,}800\,\text{Nm}

$M_A = - \frac{3}{5}(3000)(12) - \frac{4}{5}(3000)(10) = - 45{,}600\,\text{Nm}$ M_A = - \frac{3}{5}(3000)(12) - \frac{4}{5}(3000)(10) = - 45{,}600\,\text{Nm}

$M_A = \frac{4}{5}(3000)(12) + \frac{3}{5}(3000)(10) = 46{,}800\,\text{Nm}$ M_A = \frac{4}{5}(3000)(12) + \frac{3}{5}(3000)(10) = 46{,}800\,\text{Nm}

$M_A = - \frac{4}{5}(3000)(12) + \frac{3}{5}(3000)(10) = - 10{,}800\,\text{Nm}$ M_A = - \frac{4}{5}(3000)(12) + \frac{3}{5}(3000)(10) = - 10{,}800\,\text{Nm}

$M_A = \frac{4}{5}(3000)(10) - \frac{3}{5}(3000)(12) = 2{,}400\,\text{Nm}$ M_A = \frac{4}{5}(3000)(10) - \frac{3}{5}(3000)(12) = 2{,}400\,\text{Nm}

$M_A = (3000)(10) = 30{,}000\,\text{Nm}$ M_A = (3000)(10) = 30{,}000\,\text{Nm}

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Consider the free-body diagram of the beam shown in

Figure P3

The beam is in equilibrium. The support reactions are shown, together with the external uniformly distributed load

, applied at the position indicated.

Which of the following correctly represents the

moment equilibrium equation about point B? Take L₁ = 3.5 m, and L₂ = 2.5 m.

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

Figure P3. Beam free-body diagram

$\sum M_B = 0:\; 6\,A_y - 1.75\,q= 0$ \sum M_B = 0:\; 6\,A_y - 1.75\,q= 0

$\sum M_B = 0:\; -6\,A_y + 2.5\,q= 0$ \sum M_B = 0:\; -6\,A_y + 2.5\,q= 0

$\sum M_B = 0:\; 6\,A_y + 3.125\,q= 0$ \sum M_B = 0:\; 6\,A_y + 3.125\,q= 0

$\sum M_B = 0:\; -6\,A_y + 3.125\,q= 0$ \sum M_B = 0:\; -6\,A_y + 3.125\,q= 0

$\sum M_B = 0:\; -6\,A_y - 3.125\,q= 0$ \sum M_B = 0:\; -6\,A_y - 3.125\,q= 0

$\sum M_B = 0:\; 6\,A_y - 3.5\,q= 0$ \sum M_B = 0:\; 6\,A_y - 3.5\,q= 0

$\sum M_B = 0:\; -6\,A_y + 1.25\,q= 0$ \sum M_B = 0:\; -6\,A_y + 1.25\,q= 0

$\sum M_B = 0:\; -6\,A_y + 6.125\,q= 0$ \sum M_B = 0:\; -6\,A_y + 6.125\,q= 0

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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, F₁and 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

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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

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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. 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.

Figure P17. Frame system for free-body diagram construction (not to scale). Version 5124.

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Consider the

truss bridge

shown in

Figure P15. All joints are pin-connected. Both supports at A and B are pin supports. External loads of magnitude F are applied at locations 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

truss bridge

shown in

Figure P14

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 P14. Pin-connected truss bridge.

The truss is unstable and indeterminate.

100%

The truss is stable and indeterminate.

The truss is unstable and determinate.

The truss is stable and determinate.

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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.

100%

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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

F_EQ

due to the triangular distributed load?

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

Figure P11. Simply supported beam with triangular distributed load

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

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Consider the diagram of a

simply supported beam shown in

Figure P10. This beam has different dimensions to in the previous question.

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

0 kN/m at point B (at the right edge of the beam), to a magnitude of w₂ = 9 kN/m at mid-span of the beam. The span of this beam from point A to point B, L = 12.0 m

. The beam is in equilibrium.

Determine the

magnitude of the equivalent point load (F_EQ)

due to the triangularly distributed load.

Select the correct value of F

_EQ
(in kN).

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

F_EQ = 27.00 kN

100%

F_EQ = 108.00 kN

F_EQ = 216.00 kN

F_EQ = 54.00 kN

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Course 38579

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

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.

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.

Want instant access to all verified answers on learning.monash.edu?

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.

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.

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.