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This document describes the method of substitute members for analyzing complex trusses. [1] It is difficult to use other methods like method of sections or joints for complex trusses. [2] The method of substitute members involves imagining removing a member and replacing it with an imaginary member elsewhere, then determining member forces. [3] The example problem demonstrates applying this method to determine all member forces in a complex truss.

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Andrea Alcantara
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640 views3 pages

Andrea 1

This document describes the method of substitute members for analyzing complex trusses. [1] It is difficult to use other methods like method of sections or joints for complex trusses. [2] The method of substitute members involves imagining removing a member and replacing it with an imaginary member elsewhere, then determining member forces. [3] The example problem demonstrates applying this method to determine all member forces in a complex truss.

Uploaded by

Andrea Alcantara
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© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Theory of structures/ L6 Dr.

Ali Al-Rifaie
___________________________________________________________________________________

Complex trusses

It is hard to use method of sections and method of joints to analyze a complex truss as the solution

requires writing several equations for each section or joint taken from the truss and then solving the

complete set of equations simultaneously. Therefore, a more direct method for analyzing a complex

truss named the method of substitute members can be presented here.

Procedure for analysis

1. Determine the reactions at the supports of truss

2. Imagine how to analyze the truss by the method of joint by removing a member from a joint

with a three members and replace it by an imaginary member elsewhere in the truss.

3. Determine the forces (S'i) in all members due to the external loads using joint method.

4. Remove the external loading and place equal but opposite collinear unit load on the truss at the

two joints from which the member was removed.

5. Determine the force in each member due to the unit load.

6. If the effects of the above two loadings are combined, the force in the ith member of the truss

will be S i = S 'I + x si (1)

This equation can be applied on the imaginary (substituted) member that was replaced the

removed one. Since the imaginary member does not actually exist on the original truss, so S i ,

the force in this member in equation (1) equal to zero. Then x can be determined.

7. Use equation (1) to find the force in all members by substitute the value of x obtained in the

previous step.

1
Theory of structures/ L6 Dr. Ali Al-Rifaie
___________________________________________________________________________________

Problem 1. Determine the forces in all the members of the


complex truss shown. State if the members are in tension or
compression. Hint: Substitute member AD with one placed
between E and C.

Solution:

member S'I si x si Si = S'I + x si


AB 848.53 -1 -1421.86 -573.33
BC 848.53 -1 -1421.86 -573.33
CD 0 -1.115 -1585.37 -1585.37
ED 0 -0.8165 -1160.94 -1160.94
EF 1005.27 -1.04 -1478.73 -473.46
AF 1373.21 -1.41 -2004.82 -631.61
EC 747.9 -.526 -747.9 0
FC -1231.19 1.27 1805.76 574.57
EB -1200 1.41 2004.82 840.82
DA (removed member) 0 1 1421.86 1421.86

2
Theory of structures/ L6 Dr. Ali Al-Rifaie
___________________________________________________________________________________

Class work: Suggest another member to be removed then solve the complex truss

Homework: See example in page 112.

Solve problems 3.34, 3.35, 3.46 page 131-134

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