Equivalent Force-couple system: Bracket

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{applet}

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			Name	Type	Generated Value

xa	number	4
yb	number	4.5
yc	number	2.25
theta	integer	-40
units	string	lb
A	integer	130
D	integer	75

			Name	Type	Generated Value

B	vector	Vector with 2 components
M	number	113.8864421876
beta	number	-57.8689511978
vecA	vector	Vector with 2 components

			Name	Type	Generated Value

applet	ggbapplet	HTML node
params	dict	Dictionary with 7 entries
debug	boolean	false

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(2.5..5#0.25)

JME function reference

Description

x coord of point A (origin at D)

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

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Generated value: `number`

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M
params

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Force Gap-fill
Couple Gap-fill
1. Gap Magnitude Engineering Accuracy with units
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2. Gap Direction Choose one from a list
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Replace the forces acting at $A$ and $D$ with an equivalent force-couple system acting at point $B$ .

Advice

1. Replace forces $A$ and $D$ with a single equivalent force $\mathbf{B} = \mathbf{A} + \mathbf{D}$ acting at point $B$.

This force will have the same translational effect as the original systems, therefore:

$B_x = A_x + D_x = + \var{A} \cos \var{abs(theta)}° + 0 = \var{ea(B[0])}$ {units}

$B_y = A_y + D_y =\var{latex( if(theta >=0, "+", "-"))} \var{A} \sin \var{abs(theta)}° - D = \var{ea(B[1])}$ {units}

$B = \sqrt{B_x^2 + B_y^2} = \var{ea(abs(B))}$ {units}

$\beta =\tan^{-1}\left( \left \vert\frac{ \var{ea(B[1])}} {\var{ea(B[0])}}\right \vert \right) = \var{ea(abs(beta))}° $

2. Force $\mathbf{B}$ acting at point $B$ produces no moment about that point, so a concentrated moment $\mathbf{M}$ must be included to maintain equivalence.

The magnitude and direction of this moment is equal to the moment produced by the original forces $A$ and $D$ about point $B$.

$\begin{align}M &= \pm A_x(\var{yB}) \pm A_y(\var{xA}) \pm D_x(\var{yb}) \pm D_y (0)
\\&= + (\var{ea(vecA[0])} \text{ lb}) ( \var{yb}\text{ in}) \var{latex( if(theta >=0, "+", "-"))} (\var{abs(ea(vecA[1]))}\text{ lb}) (\var{xA} \text{ in}) + (0)(\var{yb} \text{ in}) + (\var{D}\text{ lb})( 0)
\\&= \var{latex( if(M >=0, "+", "-"))} \var{ea(abs(M))} \text{ in-lb}
\\&= \var{abs(ea(M))} \text{ in-lb } \var{if(M>=0," CCW"," CW")} \end{align}$

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Equivalent Force-couple system: Bracket

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

William Haynes 1 year, 10 months ago

William Haynes 1 year, 10 months ago

William Haynes 1 year, 11 months ago

Error in variable testing condition

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Warning

Generated value: number

Parts

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Generated value: `number`