Three force body method: Beam with angled load

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William Haynes

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Question statement

{geogebra_applet("xfpyfgd9",[['split', split], ['θ',theta+'°']])}

A beam is loaded with a {F} force at a {theta}° angle from the horizontal, as shown. Distance $\overline{AB}$ is {AB}, and $\overline{BC}$ is {BC}.

Use the three-force body method to determine the magnitudes of the reactions at pin $A$ and roller $C$ .

Give any introductory information the student needs.

			Name	Type	Generated Value

split	number	0.7
L	quantity	quantity(3, "m")
theta	integer	15
F	quantity	quantity(95, "kN")

			Name	Type	Generated Value

h	quantity	quantity(0.2411542731880107, "m")
alpha	number	4.5958253922
K	quantity	quantity(95.30643696104013254622660947939482826238, "kN")
A	quantity	quantity(92.05894887225966096831736997943651301846, "kN")
C	quantity	quantity(17.21146649931759873353372870915296805875, "kN")

			Name	Type	Generated Value

			AB	quantity	quantity(2.1, "m")
			BC	quantity	quantity(0.9, "m")

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(0.2..0.8#0.5)

JME function reference

Description

percentage position of point B

Describe what this variable represents, and list any assumptions made about its value.

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Generated value: `number`

0.7

→ Used by:

This variable doesn't seem to be used anywhere.

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1. Gap Gap 0. Engineering Accuracy with units
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2. Gap Gap 1. Engineering Accuracy with units
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$A$ = Gap 0. $\qquad C$ = Gap 1.

Advice

Given:

$F$ = {F}
$\theta$ = {theta}°
$\overline{AB}$ = {AB}
$\overline{BC}$ = {BC}
Force $\mathbf{C}$ acts straight up, due to the roller.

Required:

magnitudes of $\mathbf{A}$ and $\mathbf{C}$.

Procedure:

Start by drawing a clear diagram representing the situation and locate point "$x$" where the lines of action of $\mathbf{F}$ and $\mathbf{C}$ intersect. In three-force-bodies, the line of action of $\mathbf{A}$ must pass through that point too.
Draw the line of action of $\mathbf{A}$ and define $\alpha$.
Find $h$, using: \[\tan\theta = \frac{h}{\overline{BC}}\]
Find $\alpha$: \[\tan\alpha =\frac{h}{(\overline{AB} + \overline{BC})}\]
Rearrange the forces into a force triangle, tip-to-tail, and label it.
Use the law of sines to solve for the unknown magnitudes. \[ \frac{F}{\sin (90 + \alpha)} = \frac{A}{\sin (90° - \theta)} = \frac{C}{\sin (\theta-\alpha)}\]

Give a worked solution to the whole question.

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This question is used in the following exams:

Chapter 5 Exercises by William Haynes in Engineering Statics.
Chapter 05 Exercises by Michael Proudman in Engineering Statics.
15. 2 and 3 Force Bodies by Michael Proudman in Engineering Statics.
studio 4 - Chapter 5 Exercises by Jay McCormack in studio 4.
studio 4 - Chapter 5 Exercises by Jay McCormack in Jay's workspace.
15. 2 and 3 Force Bodies by William Haynes in Engineering Statics.

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Three force body method: Beam with angled load

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William Haynes 4 years, 11 months ago

William Haynes 4 years, 11 months ago

William Haynes 4 years, 11 months ago

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Three force body method: Beam with angled load

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

William Haynes 4 years, 11 months ago

William Haynes 4 years, 11 months ago

William Haynes 4 years, 11 months ago

Error in variable testing condition

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Warning

Generated value: number

Parts

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Generated value: `number`