Cantilever beam

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Keith Tarnowski 5 years, 9 months ago

Created this as a copy of Equilibrium of a rigid body: cantilever beam.

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('dpvndcem',[['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 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	4
A	number	0.6
B	number	0.9
units	string	mm
FA	vector	vector(0,50)
magA	integer	50
MagC	integer	40
theta_c	integer	340
FC	vector	Vector with 2 components
M	integer	-100
debug	boolean	false

			Name	Type	Generated Value

OA	quantity	quantity(2.4, "m")
OC	quantity	quantity(4, "m")
OB	quantity	quantity(3.600000000000001, "m")
MA	quantity	quantity(120, "m^2")
MC	quantity	quantity(-54.723222932106978, "m^2")
MB	quantity	quantity(-100, "m^2")
MO	quantity	quantity(34.723222932107, "m^2")
FO	vector	Vector with 2 components
dirO	quantity	quantity(-135.983306927937434, "deg")
angle_from_ref	list	List of 4 items

			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:

units

→ Used by:

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Gap 0. Engineering Accuracy with units
  Add
2. Gap Gap 1. Choose one from a list
  Add
Part b) Gap-fill
1. Gap Gap 0. Engineering Accuracy with units
  Add
2. Gap Information only
  Add
3. Gap Gap 1. Angle quantity
  Add

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.

$M_O$ = Gap 0. Gap 1. {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.

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

Part	Test	Passed?
Gap-fill
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
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet
Information only
Angle quantity
Angle quantity		Hasn't run yet

This question is not used in any exams.

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Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

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Checkpoint description

Keith Tarnowski 5 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

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Cantilever beam

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Keith Tarnowski 5 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`