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Course 38579

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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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Consider the pulley system shown in

Figure P6

The system consists of fixed pulleys at the ceiling and a movable pulley block supporting a mass

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.

Figure P6. Rope pulley system

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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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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

equivalent stiffness, k_e

, of the system?

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

Select the correct answer.

Figure P8. Spring and mass system.

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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.

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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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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 a

beam shown in

Figure P9

A trapezoidal distributed load with peak magnitude

q₁ = 12 kN/m

is applied over the entire span from A to C. The beam is in equilibrium.

Determine the

magnitude of the equivalent point load (F_EQ) due to the trapezoidal distributed load. Take L₁ = L₃ = 2 m, and L₂ = 1.2 m.

Select the correct value of F

_EQ
(in kN).

Figure P9. Simply supported beam with distributed load

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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

kk (in the appropriate units) of ONE spring.

Select the correct answer.

Figure P7. Mass–spring system in static equilibrium

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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.

F3 = 25 kN and M1 = 70 kNm, determine the magnitude and sign of the reaction moment (M_A) at the fixed support A. Ensure that you 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 kN·m)

Figure P5. Cantilever beam with applied moment and force.

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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.

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.