Moment of inertia of composite shape - triangle and rectangles

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Question statement

{geogebra_applet('wsef7939',[['A',A],['B',B],['C',C]])}

Consider the composite shape shown. Grid units are [{units}].

Determine the total area of the shape, and its Moment of Inertia and Radius of Gyration with respect to the x-axis.

Give any introductory information the student needs.

			Name	Type	Generated Value

A	vector	vector(-5,3)
B	vector	vector(8,9)
C	vector	vector(-8,0)
units	string	m
debug	boolean	false
axis	string	x

			Name	Type	Generated Value

h1	quantity	quantity(9, "m")
b2	quantity	quantity(8, "m")
h2	quantity	quantity(9, "m")
b3	quantity	quantity(13, "m")
h3	quantity	quantity(3, "m")
b1	quantity	quantity(8, "m")
removed	boolean	true
A1	quantity	quantity(72, "m^2")
A2	quantity	quantity(36, "m^2")
A3	quantity	quantity(19.5, "m^2")
A_t	quantity	quantity(88.5, "m^2")
expression	string	\sin(x)

			Name	Type	Generated Value

I1x	quantity	quantity(1944, "m^4")
I2x	quantity	quantity(486, "m^4")
I3x	quantity	quantity(29.25, "m^4")
I_t	quantity	quantity(2400.75, "m^4")
kx	quantity	quantity(5.208370056367711340865818837587448721297, "m")

			Name	Type	Generated Value

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
vector(random(C[0]..10 except B[0] ),random(1..B[1]))

JME function reference

Description

This points sets the coordinates of the second triangle, at (x,0) and (x(b),y)

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

Can an exam override the value of this variable?

Generated value: `vector`

vector(-5,3)

← Depends on:

→ Used by:

b3
h3
removed

Statement

Parts

Area Gap-fill
1. Gap Area Engineering Accuracy with units
  Add
Moment of Inertia Gap-fill
1. Gap $I_x$ Engineering Accuracy with units
  Add
Radius of gyration Gap-fill
1. Gap $k_x$ Engineering Accuracy with units
  Add

Gap-fill

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

$A$ = Area {A_t}

Advice

Consider the shape to be made of three parts.

$\qquad \var{b1} \times \var{h1}$ rectangle.
$\qquad \var{b2} \times \var{h2}$ triangle.
$\qquad \var{b3} \times \var{h3}$ {if(removed,'negative','')} triangle.

Area:

$A_1 = b_1 h_1 = \var{A1}$

$A_2 = \frac{1}{2} b_2 h_2= \var{A2}$

$A_3 = \frac{1}{2} b_3 h_3= \var{A3}$ {if(removed,'Removed','')}

$A = \Sigma A_i = \var{A_t}$

Moment of inertia wrt x-axis:

$\begin{align}I_x &= \Sigma I_x \\ &= \frac{b_1 h_1^3}{3} + \frac{b_2 h_2^3 }{12} + \var{if(removed,'–','')} \frac{b_3 h_3^3}{12}\\&= (\var{siground(I1x,4)}) + (\var{siground(I2x,4)}) + (\var{if(removed,'–','')}\var{ siground(I3x,4)})\\&= \var{siground(I_t,4)}\end{align}$

Radius of gyration wrt x-axis:

$k_x = \sqrt{\dfrac{I_x}{A}} = \var{siground(kx,4)}$

Give a worked solution to the whole question.

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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
Gap-fill
Gap-fill		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet

This question is used in the following exams:

Chapter 10 Exercises by Michael Proudman in Engineering Statics.
23. Moment of Inertia by Michael Proudman in Engineering Statics.
Chapter 10 Exercises by William Haynes in Engineering Statics.
23. Moment of Inertia by William Haynes in Engineering Statics.

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Moment of inertia of composite shape - triangle and rectangles

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

William Haynes 6 years, 5 months ago

William Haynes 6 years, 5 months ago

William Haynes 6 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: `vector`

Parts

Gap-fill

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Error

Moment of inertia of composite shape - triangle and rectangles

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

William Haynes 6 years, 5 months ago

William Haynes 6 years, 5 months ago

William Haynes 6 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: vector

Parts

Gap-fill

Generated value: `vector`