Moment of inertia: 2 angles forming box beam

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Created this as a copy of Moment of inertia: built-up beam with angles.

Name	Status	Author	Last Modified
Moment of inertia: built-up beam with angles	Ready to use	William Haynes	22/03/2021 14:13
Moment of inertia: 2 angles forming box beam	Ready to use	William Haynes	22/03/2021 14:13

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Question statement

{geogebra_applet('u9qngrny',[['h',h],['w',w],['t',t],['P',centroid]])}

A built-up beam is made up of two {name} angles welded together to form a box beam.

Use this table of properties for the angle sections.

Give any introductory information the student needs.

			Name	Type	Generated Value

name	string	L7 $\times$ 4 $\times$ 3/4
A_L	quantity	quantity(7.69, "in^2")
Ixx	quantity	quantity(37.8, "in^4")
Iyy	quantity	quantity(9.05, "in^4")
xbar	quantity	quantity(1.01, "in")
ybar	quantity	quantity(2.51, "in")
dimensions	list	[ 7, 4, 3/4 ]
applet	ggbapplet	HTML node

			Name	Type	Generated Value

Ibar_y'	quantity	quantity(37.8, "in^4")
Ibar_x'	quantity	quantity(9.05, "in^4")
d_x	quantity	quantity(1.365, "in")
d_y	quantity	quantity(0.99, "in")
Ix	quantity	quantity(33.173938, "in^4")
Iy	quantity	quantity(104.2564005, "in^4")
kx	quantity	quantity(1.468656888424513839234286519423459394777, "in")
ky	quantity	quantity(2.603593601619253744511992890528654449271, "in")

			Name	Type	Generated Value

index	integer	5
debug	boolean	false
rotated	boolean	true
centroid	vector	vector(2.51,1.01)
h	integer	4
w	integer	7
t	rational	3/4

			Name	Type	Generated Value

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
["L9  $\\times$  4  $\\times$  1/2","L8  $\\times$  6  $\\times$  5/8","L8  $\\times$  6  $\\times$  1/2","L8  $\\times$  4  $\\times$  3/4","L8  $\\times$  4  $\\times$  1/2","L7  $\\times$  4  $\\times$  3/4","L7  $\\times$  4  $\\times$  5/8","L7  $\\times$  4  $\\times$  1/2","L7  $\\times$  4  $\\times$  3/8","L6  $\\times$  4  $\\times$  7/8","L6  $\\times$  4  $\\times$  3/4","L6  $\\times$  4  $\\times$  1/2","L6  $\\times$  4  $\\times$  3/8","L5  $\\times$  3  $\\times$  5/8","L5  $\\times$  3  $\\times$  1/2"][index]

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: `string`

L7 $\times$ 4 $\times$ 3/4

← Depends on:

index

→ Used by:

Statement

Parts

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

Find the moment of inertia and radius of gyration with respect to the x axis.

$\bar{I}_x =$ $\bar{I}_x$ $\quad k_x =$ $k_x$

Find the moment of inertial and radius of gyration with respect to the y axis.

$\bar{I}_y =$ $\bar{I}_y$ $\quad k_y =$ $k_y$

Advice

Channel properties from table

$\begin{align}\text{Area:}& &A&= \var{A_L}\\\text{Centroid:} & &\bar{x} &= \var{xbar} & \bar{y} &= \var{ybar}\\\text{MOI:} && \bar{I}_{xx} &= \var{ixx} & \bar{I}_{yy} &= \var{Iyy}\end{align}$

These properties are for angle sections oriented with the long side vertical.

Find moment of inertia

$\bar{I}_y = 2 \, [ \bar{I} + A d^2]$ where,

$\bar{I} = \var{latex(if(rotated,safe('\\bar{I}_{xx}'),safe('\\bar{I}_{yy}')))} =\var{Ibar_y'}$

$A =\var{A_L}$, and

$d = \left(\dfrac{w+t}{2}-\var{latex(if(rotated,safe('\\bar{y}'),safe('\\bar{x}')))} \right)= \var{d_x}$, so

$\bar{I}_y = \var{disp(Iy)}\\$

$\bar{I}_x = 2 \, [ \bar{I} + A d^2]$ where,

$\bar{I} = \var{latex(if(rotated,safe('\\bar{I}_{yy}'),safe('\\bar{I}_{xx}')))} =\var{Ibar_x'}$

$A =\var{A_L}$, and

$d =\left( \dfrac{h}{2}-\var{latex(if(rotated,safe('\\bar{x}'),safe('\\bar{y}')))}\right) = \var{d_y}$, so

$\bar{I}_x = \var{disp(Ix)}\\$

Find Radii of gyration

$k_x = \sqrt{\dfrac{\bar{I}_x} {2 A}} = \var{disp(kx)} \qquad k_y = \sqrt{\dfrac{\bar{I}_y} {2 A}} = \var{disp(ky)}$

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This question is used in the following exams:

Chapter 10 Exercises by Michael Proudman in Engineering Statics.
42. Standard Sections by Michael Proudman in Engineering Statics.
41. Standard Sections by William Haynes in Engineering Statics.
Chapter 10 Exercises by William Haynes in Engineering Statics.

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Moment of inertia: 2 angles forming box beam

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Taxonomy: mathcentre

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Taxonomy: Context

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William Haynes 4 years, 2 months ago

William Haynes 4 years, 7 months ago

William Haynes 4 years, 7 months ago

William Haynes 4 years, 7 months ago

William Haynes 5 years, 10 months ago

William Haynes 5 years, 10 months ago

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Moment of inertia: 2 angles forming box 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, 7 months ago

William Haynes 4 years, 7 months ago

William Haynes 4 years, 7 months ago

William Haynes 5 years, 10 months ago

William Haynes 5 years, 10 months ago

Error in variable testing condition

Error

Warning

Generated value: string

Parts

Gap-fill

Generated value: `string`