Equilibrium of a rigid body: cantilever beam

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Name	Status	Author	Last Modified
Equilibrium of a rigid body: cantilever beam	Ready to use	William Haynes	07/02/2024 18:41
Cantilever beam	draft	Keith Tarnowski	05/06/2019 11:04
Keith's copy of Equilibrium of a rigid body: cantilever beam	draft	Keith Tarnowski	05/06/2019 16:23

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Question statement

{geogebra_applet('v5xfnaym',[['A',A],['B',B],['L',L],['units','"'+units[1]+'"'],['fa',FA], ['fc',FC], ['M',M]])}

A beam of length $L$ = {L} {units[1]} is supported by a fixed (cantilever) support at $O$ . Detemine the reactions at $O$ when the beam supports these loads:

$A$ = {magA} {units[0]}, $B$ = {abs(M)} {units[0]}-{units[1]} and $C$ = {magC} {units[0]}, as shown.

Give any introductory information the student needs.

			Name	Type	Generated Value

L	integer	2
A	number	0.4
B	number	0.8
units	list	[ "lb", "ft" ]
FA	vector	vector(0,20)
magA	integer	20
MagC	integer	20
theta_c	integer	80
FC	vector	Vector with 2 components
M	integer	-300
debug	boolean	false

			Name	Type	Generated Value

OA	quantity	quantity(0.8, "ft")
OC	quantity	quantity(2, "ft")
OB	quantity	quantity(1.6, "ft")
MA	quantity	quantity(16, "lbs*ft")
MC	quantity	quantity(39.392310120488318, "lbs*ft")
MB	quantity	quantity(-300, "lbs*ft")
MO	quantity	quantity(244.607689879512, "lbs*ft")
FO	vector	Vector with 2 components
dirO	quantity	quantity(265, "deg")

			Name	Type	Generated Value

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
if(units[1]='ft',random(2..12#2),random(1..5))

JME function reference

Description

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

Can an exam override the value of this variable?

Generated value: `integer`

← Depends on:

This variable doesn't seem to be used anywhere.

Parts

Moment at O Gap-fill
1. Gap $M_O$ Engineering Accuracy with units
  Add
2. Gap Direction Choose one from a list
  Add
Force at O Gap-fill

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

Determine the magnitude and direction of the moment at the fixed support at $O$.

$M_O$ = $M_O$ Direction {format(MO)}

Advice

Draw a free body diagaram of the beam, then apply the equations of equilibrium.

$\Sigma M = 0$

$M_O + M_A + M_B + M_C = 0$

$M_A = d_1 A_y$ = ({OA}) ({qty(abs(FA[1]),units[0])}) = {abs(MA)} {if(sign(MA)>0,'counterclockwise','clockwise')}

$M_B =$ {abs(MB)} {if(sign(MB)>0,'counterclockwise','clockwise')}

$M_C = L C_y$ = ({OC}) ({format(qty(abs(FC[1]),units[0]))}) = {format(abs(MC))} {if(sign(MC)>0,'counterclockwise','clockwise')}

$ M_O = - ( \var{format(MA)} + \var{format(MB)} + \var{format(MC)} ) = \var{format(abs(MO))}$ {if(sign(MO)>0,'counterclockwise','clockwise')}

$\Sigma F_x = 0$

$O_x + A_x + C_x = 0$

$O_x = 0 - C_x = \var{format(qty(abs(FO[0]), units[0]))}$ {if(sign(FO[0])>=0,'right','left')}

$\Sigma F_y = 0$

$O_y + A_y + C_y = 0$

$O_y = - (A_y + C_y) = - ( \var{FA[1]} + \var{siground(FC[1],4)} )= \var{format(qty(abs(FO[1]), units[0]))} $ {if(sign(FO[1])>=0,'up','down')}

Resolve $O_x$ and $O_y$ to get

Force $O = \var{format(qty(abs(FO), units[0]))} $ at an angle of {format(dirO)} from the positve x-axis.

Give a worked solution to the whole question.

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Part	Test	Passed?
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Gap-fill		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet
Choose one from a list
Choose one from a list		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Angle quantity 2020
Angle quantity 2020		Hasn't run yet
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Engineering Accuracy with units
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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.
13. Equilibrium of Rigid 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.
Chapter 5 Exercises for studio 4 by Jay McCormack in 23-24 Studio 4 Statics Practice.
13. Equilibrium of Rigid Bodies by William Haynes in Engineering Statics.

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Equilibrium of a rigid body: cantilever beam

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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William Haynes 4 years, 2 months ago

William Haynes 4 years, 6 months ago

William Haynes 4 years, 11 months ago

William Haynes 4 years, 11 months ago

William Haynes 6 years, 5 months ago

William Haynes 6 years, 6 months ago

William Haynes 6 years, 6 months ago

Error in variable testing condition

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Warning

Generated value: `integer`

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Gap-fill

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Equilibrium of a rigid body: cantilever beam

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

William Haynes 4 years, 2 months ago

William Haynes 4 years, 6 months ago

William Haynes 4 years, 11 months ago

William Haynes 4 years, 11 months ago

William Haynes 6 years, 5 months ago

William Haynes 6 years, 6 months ago

William Haynes 6 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`