Distributed Loads: trapezoidal loading

Error

There was an error loading the page.

Contributors

William Haynes

Feedback

From users who are members of Engineering Statics :

William Haynes

said

Ready to use

5 years ago

History

○

William Haynes 4 years, 3 months ago

Published this.

○

William Haynes 5 years ago

Gave some feedback: Ready to use

○

William Haynes 5 years ago

Created this.

There is only one version of this question that you have access to.

There is one other version that you do not have access to.

Question statement

{geogebra_applet('xgjx2s8s',[['a', a 10/L], ['b', b 10/L],['c', c 10/L],['showfbd','false']])}

$\var{qty(L,unit[0])}$ long beam $AB$ is subjected to a distributed load which

varies uniformly from $\var{Q0}$ at $x=\var{QA}$ to $\var{QW}$ at $x=\var{QB}$ , and
is constant $\var{QW}$ between $x=\var{if(c<b,QC,QB)}$ and $x=\var{if(c<b,QB,QC)}$ .
varies uniformly from $\var{QW}$ at $x=\var{QB}$ to $\var{Q0}$ at $x=\var{QA}$ .

Determine the reactions at $A$ and $B$ .

Give any introductory information the student needs.

			Name	Type	Generated Value

WT	number	480
WR	number	80
WTot	number	560
xR	rational	27/2
xT	rational	9
RB	number	337.5
RA	number	222.5
check	boolean	true

			Name	Type	Generated Value

QxR	quantity	quantity(13.5, "ft")
QxT	quantity	quantity(9, "ft")
Qw	quantity	quantity(80, "lbs/ft")
QWr	quantity	quantity(80, "lbs")
QWt	quantity	quantity(480, "lbs")
QRA	quantity	quantity(222.5, "lbs")
QRB	quantity	quantity(337.5, "lbs")
QA	quantity	quantity(1, "ft")
QB	quantity	quantity(13, "ft")
QC	quantity	quantity(14, "ft")
Q0	quantity	quantity(0, "lbs/ft")

			Name	Type	Generated Value

a	integer	1
b	integer	13
c	integer	14
w	integer	80
L	integer	16
unit	list	[ "ft", "lb" ]

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
abs(a-b) w /2

JME function reference

Description

weight of the triangular load

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

Can an exam override the value of this variable?

Generated value: `number`

480

← Depends on:

→ Used by:

QWt
RA
RB
WTot

This variable doesn't seem to be used anywhere.

Parts

Find Reactions Gap-fill
1. Gap A Engineering Accuracy with units
  Add
2. Gap B Engineering Accuracy with units
  Add

Gap-fill

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

$A = $ A $B = $ B

Advice

{geogebra_applet('xgjx2s8s',[['a', a 10/L], ['b', b 10/L],['c', c 10/L],['showfbd','true']])}

Draw a free body diagram of the beam, replacing the distributed loads with equivalent concentrated loads at the centroids of the triangle and rectangle.
Determine locations of the centroids and the 'area' under the loading curve for each part.
$\begin{align}\\ W_R &= \var{QWR} & x_R &= \var{QxR} \\ W_T &= \var{QWT} &x_T &= \var{QxT}\end{align}$
Find the reactions
$\begin{align}\\ \Sigma M_A &= 0 \\W_R x_r + W_T x_T &= B L \\ B &= \frac{W_R x_r + W_T x_T}{L} \\&= \var{QRB} \\ \\ \Sigma F_y &= 0 \\ A + B &= W_T + W_R \\ A &= W_T + W_R - B \\ &= \var{QRA} \end{align}$
You may check your answer by finding $A$ using $\Sigma M_B = 0$. You should get the same result either way.

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
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet

This question is used in the following exams:

Chapter 7 Exercises by William Haynes in Engineering Statics.
Chapter 07 Exercises by Michael Proudman in Engineering Statics.
22. Distributed Loads by Michael Proudman in Engineering Statics.
22. Distributed Loads by William Haynes in Engineering Statics.

Loading...

Error

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

William Haynes 4 years, 3 months ago

William Haynes 5 years ago

William Haynes 5 years ago

Error in variable testing condition

Error

Warning

Generated value: `number`

Parts

Gap-fill

Loading...

Error

Distributed Loads: trapezoidal loading

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

William Haynes 4 years, 3 months ago

William Haynes 5 years ago

William Haynes 5 years ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Gap-fill

Generated value: `number`