The forces in each member of the truss.
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Answer to Problem 12.1P
The forces in each member of the truss are shown below.
The force in member AE is,
The force in member BF is,
The force in member EF is,
The force in member AB is,
The force in member CE is,
The force in member BD is,
The force in member DE is,
The force in member BC is,
The force in member AF is,
The force in member BE is,
The force in member CD is,
Explanation of Solution
Check the determinacy of the truss as shown below.
Here, number of members are
Substitute
Hence, the given truss is statically indeterminate by
The following diagram shows the free body diagram of the truss.
Figure-(1)
Write the equation for moment about A.
Here, vertical reaction at C is
Write the equation for sum of vertical forces.
Here, vertical reaction at A is
Substitute
Consider the force in diagonal members FB is in tension and AE is in compression.
Here, force in member AE and FB are
Use the method of section and cut the section as shown in figure below and calculate the forces in the members.
Figure-(2)
Calculate the angles as shown below.
Here, the angle between the members FA and FB is
Consider the joint F.
Write the Equation for sum of vertical forces.
Substitute
Write the equation for the sum of horizontal forces.
Here, force in member FE is
Substitute
Consider joint A.
Figure-(3)
Calculate the angles as shown below.
Write the equation for sum of vertical forces.
Substitute
Here, force in member FA is
Write the Equation for sum of horizontal forces.
Substitute
Here, force in member AB is
Consider the force in diagonal members BD is in tension and EC is in compression.
Here, force in member BD and EC are
Use the method of section method and cut the section as shown in figure below and calculate the forces in the members.
Figure-(4)
Calculate the angles as shown below.
Write the Equation for sum of vertical forces.
Substitute
Here, force in the member BD and CE are
Write the equation for moment about B.
Here, force in the member ED is
Substitute
Write the Equation for moment about E.
Here, force in the member BC is
Substitute
Write the Equation for sum of vertical forces.
Substitute
Here, force in the member BE is
Consider the joint C.
Angles will be same as calculated at joint B.
Figure-(5)
Write the Equation for sum of vertical forces.
Here, force in the member CD is
Substitute
Conclusion:
Therefore, the forces in each member of the truss are shown below.
The force in member AE is,
The force in member BF is,
The force in member EF is,
The force in member AB is,
The force in member CE is,
The force in member BD is,
The force in member DE is,
The force in member BC is,
The force in member AF is,
The force in member BE is,
The force in member CD is,
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Chapter 12 Solutions
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