Method of joints: cantilever truss

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Question statement

The truss shown supports three loads, $A = \var{A}$ , $B=\var{B}$ , and $C=\var{C}$ . Use the method of joints to find the forces in all members. Indicate tension or compression.

Give any introductory information the student needs.

			Name	Type	Generated Value

units	string	lb
A	quantity	quantity(1000, "lbs")
B	quantity	quantity(800, "lbs")
C	quantity	quantity(600, "lbs")
AB	quantity	quantity(2000, "lbs")
AC	quantity	quantity(1732.050807568878, "lbs")
BC	quantity	quantity(692.8203230275512, "lbs")
BD	quantity	quantity(2400, "lbs")
CD	quantity	quantity(1385.640646055101834821957073204813156563, "lbs")
CE	quantity	quantity(2771.281292110204517410978536602406578282, "lbs")
check	quantity	quantity(-0.0000000000003781231502437835354143790287515030303972, "lbs")

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random(['N', 'kN', 'lb'])

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Gap-fill

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Analyze joint $A$ and find $AB$ and $AC$.

$AB =$ Gap 0. Gap 1. $AC =$ Gap 2. Gap 3.

Advice

Procedure

Start with a joint with two unknowns, in this case $A$. Draw a free body diagram of the joint and solve for the two unknowns. Move to an adjacent joint with two unknowns and repeat. Continue in this manner until all the unknowns are found.

When drawing free body diagrams, the force of a member acts along the axis of the member. A force pushing towards the joint indicates compression, and a force pulling away indicates tension. An incorrect assumed direction will result in a negative value.

After all the forces in the members are found you can check your answer by calculating the external reactions at $D$ and $E$, and verifying that joints $D$ and $E$ are in equilibrium.

$\begin{align}A\!: \Sigma F_y &= 0 & A\!: \Sigma F_x &= 0 \\AB_y &= A& AC&= AB_x \\AB \sin 30° &= A & &= AB \cos 30° \\AB &= \dfrac{\var{disp(A)}}{\sin 30°} & &= \var{disp(AB)} \cos 30° \\&= \var{siground(AB,4)} \text{ (T)} & &= \var{siground(AC,4)} \text{ (C)}\end{align}$

$\begin{align}B\!: \Sigma F_{y'} &= 0& B\!: \Sigma F_{x'}&= 0\\BC &= B_{y'}&BD&= B_{x'} + AB \\ &= B \cos 30° & &= B \sin 30°+ AB\\ &= {\var{disp(B)}} \cos 30°&&= \var{disp(B)} \sin 30°+ {AB}\\&= \var{siground(BC,4)} \text{ (C)}& &= \var{siground(BD,4)} \text{ (T)}\ \\\end{align}$

$\begin{align}C\!: \Sigma {F_y} &= 0 & C\!: \Sigma {F_x} &= 0\\ -CD_y-BC_{y} -C &=0 & CE + CD_x &= BC_x + AC\\ CD \sin 60°&= -(BC \sin 60° +C)& CE &= AC + BC_x - CD_x\\CD&= -\frac{{\var{disp(BC)}} \sin 60° + \var{C}}{\sin 60°} & &= \var{disp(AC)} + \var{disp(BC)} \cos 60° -(\var{disp(-CD)}) \cos 60° \\ &= \var{-disp(CD)} \text{ (C)} & &= \var{siground(CE,4)} \text{ (C)} \\&= \var{siground(CD,4)} \text{ (T)} \end{align}$

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This question is used in the following exams:

Chapter 06 Exercises by Michael Proudman in Engineering Statics.
28. Method of Joints by Michael Proudman in Engineering Statics.
Trusses by Robert Birch in Robert's workspace.
Chapter 6 Exercises by William Haynes in Engineering Statics.
28. Method of Joints by William Haynes in Engineering Statics.

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Method of joints: cantilever truss

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

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Checkpoint description

William Haynes 5 years, 10 months ago

William Haynes 5 years, 10 months ago

William Haynes 5 years, 10 months ago

Error in variable testing condition

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Generated value: string

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Generated value: `string`