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Course 38579

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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.

The truss is unstable and indeterminate.

The truss is stable and indeterminate.

100%

The truss is unstable and determinate.

The truss is stable and determinate.

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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 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 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 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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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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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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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 (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 P16.

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

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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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