Truss: zero force members

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Question statement

{applet()}

Scripts in part seems to cause breakage of marking algorithm - moved it to advise section.

Loads: down is positive

{f}

Loads and reactions: down is positive

{loads[0]} = {f[loads[0]]} {loads[1]} = {f[loads[1]]} {supports[0]} = {reactions[0]} {supports[1]} = {reactions[1]} $\Sigma M_A:$ = {13 x[loads[0]]+ 17 x[loads[1]] + reactions[0] * x[supports[0]] + reactions[1] * x[supports[1]]}

Forces in members: Tension is positive

{m}

Joint Equilibrium:

Joint A: {polar(f["A"], -90) + polar(AB,0) + polar(AG,30)}

Joint B: {polar(f["B"], -90) + polar(AB,180) + polar(BC,0) + polar(BG,120) + polar(BH,60) }

Joint C: {polar(f["C"], -90) + polar(BC,180) + polar(CD,0) + polar(CH,120) + polar(CN,60) }

Joint D: {polar(f["D"], -90) + polar(CD,180) + polar(DE,0) + polar(DO,120) + polar(DL,60)}

Joint E: {polar(f["E"], -90) + polar(DE,180) + polar(EF,0) + polar(EL,120) + polar(EM,60)}

Joint F: {polar(f["F"], -90) + polar(EF,180) + polar(FM,150)}

Joint G: {polar(f["G"], -90) + polar(GH,30) + polar(AG,-150) + polar(BG,-60)}

Joint H: {polar(f["H"], -90) + polar(HN,0) + polar(CH, -60) + polar(BH,-120) + polar(GH, -150) + polar(HI, 30)}

Joint I: {polar(f["I"], -90) + polar(IJ,30) + polar(NI,-60) + polar(HI,-150)}

Joint J: {polar(f["J"], -90) + polar(JK,-30) + polar(JO,-60) + polar(JN,-120) + polar(IJ,-150)}

Joint K: {polar(f["K"], -90) + polar(KL,-30) + polar(KO,-120) + polar(JK,150)}

Joint L: {polar(f["L"], -90) + polar(LM,-30 ) + polar(EL, -60) + polar(DL,-120) + polar(LO, 180) + polar(KL, 150)}

Joint M: {polar(f["M"], -90) + polar(FM,-30) + polar(EM,-120) + polar(LM,150)}

Joint N: {polar(f["N"], -90) + polar(NI,120 ) + polar(HN, 180) + polar(JN,60) + polar(CN,-120)}

Joint O: {polar(f["O"], -90) + polar(KO, 60) + polar(LO, 0) + polar(JO,120) + polar(DO, -60)}

Give any introductory information the student needs.

			Name	Type	Generated Value

points	list	List of 15 items
members	list	List of 27 items
loads	list	[ "O", "I" ]
supports	list	[ "A", "C" ]
f	dict	Dictionary with 15 entries
m	dict	Dictionary with 27 entries
x	dict	Dictionary with 15 entries
reactions	list	[ 11.875, -41.875 ]
zeroForce	list	List of 27 items
num_ans	number	18

			Name	Type	Generated Value

AB	number	-20.5681033399
AG	number	23.75
BC	number	-20.5681033399
BG	number	0
BH	number	0
CD	number	-3.7527767497
CH	number	-7.3612159322
CN	number	-40.9918691125
DE	number	0
DL	number	-3.7527767497
DO	number	3.7527767497
EF	number	0
EL	number	0
EM	number	0
FM	number	0
GH	number	23.75
HI	number	11
HN	number	14.7224318643
IJ	number	19.5
JK	number	-6.5
JO	decimal	dec("1.876388374866283387723786829305214252943e+1")
JN	number	-26.2694372481
KL	number	-6.5
KO	number	0
LO	number	7.5055534995
LM	number	0
NI	number	-14.7224318643

			Name	Type	Generated Value

answers

list

List of 27 items

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
["A","B","C","D","E", "F","G","H","I","J", "K","L","M","N","O"]

JME function reference

Description

names of the points

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

Can an exam override the value of this variable?

Generated value: `list`

[ "A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M", "N", "O" ]

This variable doesn't seem to be used anywhere.

Parts

Choose several from a list

Choose several from a list

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

Select all {num_ans} zero-force members to receive full credit.

Minimum marks

Maximum marks

(no maximum)

Show correct answer on reveal?

Show score feedback icon?

Advanced settings

Number of display columns

Minimum answers

Maximum answers

What to do if wrong number of answers selected:

Custom marking matrix?

Custom matrix expression

Show choice feedback state?

Marking method

For each choice, specify the number of marks to add or subtract when the student picks it.

Variable list of choices?

List of choices

Shuffle order of choices?

Advice

Look for situations like 1a) and 2a) in the diagram below.

In figure 1a), members $AB$ and $AC$ share the same line of action and member $AD$ is zero-force. If a load is added to $A$, then member $AD$ must pick up load to support it and will not be zero-force.

If figure 2a), members $AB$ and $AC$ do not share the same line of action and both must be zero-force to maintain equilibrium of joint $A$. If a load is added at $A$ as shown in figure 2b) then $AB$ and $AC$ will pick up load to maintain equilibrium.

When a member is identified as zero-force, then it may produce zero-force members at adjacent joints.

Give a worked solution to the whole question.

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This question is used in the following exams:

Chapter 06 Exercises by Michael Proudman in Engineering Statics.
29. Special Loading Conditions by Michael Proudman in Engineering Statics.
29. Special Loading Conditions by William Haynes in Engineering Statics.
Chapter 6 Exercises by William Haynes in Engineering Statics.

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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William Haynes 4 years, 4 months ago

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William Haynes 4 years, 7 months ago

William Haynes 4 years, 7 months ago

William Haynes 5 years, 3 months ago

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William Haynes 5 years, 4 months ago

Error in variable testing condition

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Generated value: `list`

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Truss: zero force members

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

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Checkpoint description

William Haynes 4 years, 4 months ago

William Haynes 4 years, 4 months ago

William Haynes 4 years, 4 months ago

William Haynes 4 years, 6 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, 3 months ago

William Haynes 5 years, 3 months ago

William Haynes 5 years, 4 months ago

Error in variable testing condition

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Generated value: list

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Advanced settings

Generated value: `list`