smc-3714-30-Shear force diagram

ENGINEERING, CS 2024 HSC 6 MC

A shear force diagram is shown.

Which of the following beams is represented in the shear force diagram?

A cantilevered beam with a point load
A simply supported beam with a point load
A cantilevered beam with a uniformly distributed load
A simply supported beam with a uniformly distributed load

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\(D\)

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For a simply supported beam with a uniformly distributed load, the shear force diagram shows a linear variation that begins with a positive reaction at the left support and decreases linearly to a negative value at the right support.
This linear pattern occurs because the distributed load gradually transfers the shear force from one support to the other, with zero shear at the beam’s midspan where the direction of shear changes.

\(\Rightarrow D \)

♦ Mean mark 55%.

ENGINEERING, CS 2023 HSC 22b

The diagram shows a child with a mass of 45 kg hanging 2 metres from the left end of a structure, and an adult with a mass of 85 kg hanging 1 metre from the right end.

Calculate the reactions at \(\text{R}_\text{L}\) and \(\text{R}_\text{R}\). (3 marks)

\begin{array} {ll}
\text{R}_\text{L} = \text{............................... N} & \text{Direction ...............................} \\
& \\
\text{R}_\text{R} = \text{............................... N} & \text{Direction ...............................} \end{array}

Complete the shear force and bending moment diagrams of the scenario described. (3 marks)

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i. \( \text{R}_{\text{L}}=860\ \text{N} \uparrow \)

\( \text{R}_{\text{L}}= 440\ \text{N} \uparrow \)

ii.

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i. \( \stackrel {\curvearrowright} {\sum{ \text{M}}{^{+}_\text{L}}}: \)

\(0\)	\(=(2 \times 450)+(4 \times 850)-(\text{R}_\text{R} \times 5) \)
\(5 \times \text{R}_\text{R}\)	\(=900 + 3400\)
\(\text{R}_\text{R}\)	\(=860\ \text{N} \uparrow \)

\( \sum \text{F}_\text{V} \uparrow:\)

\(0\)	\(= -450-850+860+\text{R}_\text{L} \)
\( \text{R}_{\text{L}}\)	\(= 440\ \text{N} \uparrow \)

ii.

ENGINEERING, CS 2018 HSC 27b

Why would an engineer refer to shear force diagrams and bending moment diagrams when determining the effects of loads on a beam? (4 marks)

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Shear force and bending moment diagrams are graphs used together with structural analysis to assist engineers in the structural design process.
They help quantify the size of shear forces and bending moments on a structural element, such as a beam, at a given point, so possible weaknesses in the element can be determined.
They are used to establish the size, type and material of a beam in a structure so that support can be provided without structural failure.
So SF and BM diagrams help structural engineers decide the geometry and material of design elements.

Show Worked Solution

Shear force and bending moment diagrams are graphs used together with structural analysis to assist engineers in the structural design process.
They help quantify the size of shear forces and bending moments on a structural element, such as a beam, at a given point, so possible weaknesses in the element can be determined.
They are used to establish the size, type and material of a beam in a structure so that support can be provided without structural failure.
So SF and BM diagrams help structural engineers decide the geometry and material of design elements.

ENGINEERING, CS 2018 HSC 27a

A 6-metre beam is loaded as shown.

On the following page, draw the shear force and bending moment diagrams. Support your answer with relevant calculations. Ignore the weight of the beam.

Space for calculations is provided below. (6 marks)

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“

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`text{Shear Force calculations:}`

`text{SF}_1=+↑ SigmaF = 16\ text{kN}`

`text{SF}_2=+↑ SigmaF = 16-15 = 1\ text{kN}`

`text{SF}_3=+↑ SigmaF = 16-15-12 = -11\ text{kN}`

`text{Bending Moment calculations:}`

`text{BM}_1=+↓ SigmaM = 16 xx 2=32\ text{kNM}`

`text{BM}_2=+↓ SigmaM = 16 xx 3-15xx1=48-15=33\ text{kNM}`

`text{BM}_3=+↓ SigmaM = 16 xx 6-15xx4-12xx3=96-60-36=0\ text{kNM}`

ENGINEERING, AE 2019 HSC 24c

A drawing of an aircraft in flight is shown. This aircraft maintains a constant velocity when in level flight.

On the following page, draw a labelled shear force diagram AND a labelled bending moment diagram for this situation. Include a labelled free body diagram to support your answer.

Assume the centre of lift on each wing acts as a point load located 7.5 m from the centre line of the plane.

Calculations can be completed in the space below. (6 marks)

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♦ Mean mark 50%.

ENGINEERING, CS 2022 HSC 23d

A solar panel is to be attached to the roof of a residential garage. A beam of mass 40 kg is shown. The solar panel generates a 25 kg point load as shown.