Truss Influence Lines - EngineeringWiki

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Truss Influence Lines

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Contents

1 Introduction2 Method for Analysis

2.1 Step I: Support Reaction Analysis

2.2 Step II: Member Analysis for Cut a-a

2.3 Step III: Member Analysis for Cut b-b

3 Example: Warren Truss

4 References

Introduction

In many cases, when analyzing a structure, the applied loads may not always be a constant force located at a fixedlocation. These loads are referred to as live loads.

Trusses, which are used commonly in bridge applications (as well as other applications) are frequently, if notconstantly, exposed to these live loads. When analyzing trusses, the applied loading (including live loads) on thedifferent members of the truss must be calculated in such a way that would account for any combination and/orposition of the live loads, preferably in an easy and efficient manner. Similar to live loading on beams and frames,influence lines can be constructed for the truss members in question (if not all the members).

For the purpose of this analysis, the following trusses are both internally and externally determinate.

Method for Analysis

Suppose that the influence lines of members CD, DH, HI, EF, FK, and KL of the Howe truss[1] below arerequired.



Step I: Support Reaction Analysis

For analysis purposes, the truss will be subjected to a unit load of 1 kN at any arbitrary distance 'x' which is to bemeasured from point 'A'. To begin, the influence lines of the support reactions must be determined using equilibrium.

(1) Solving for (2) Solving for (3) Solving for

The influence lines for the reactions and can now be drawn according to the equations.



The influence lines drawn above illustrate the value of each reaction according to where the unit load is placed.

NOTE: Notice that when the unit load is placed at , reaction is zero while is equal to the unit load, i.e.

is solely supporting the unit load. The same goes for when the unit load is at , while .

LESSON: When the load is at a reaction point, that reaction force solely supports the unit load while all the otherreactions are zero at that point.

Step II: Member Analysis for Cut a-a

In order to find the influence lines of all the members, the 'method of sections' must be utilized. To find the influencelines of members CD, DH, and HI, the truss must be cut along the axis 'a-a'.

All members are drawn assuming they are in tension.

In order to simplify the analysis, the moment will be taken about point H thus eliminating and from the

equation. The remaining force, can then be isolated. To further simplify the process, when the unit load isacting along Section A, , Section B will be analyzed. When the unit load is acting along Section B,

, Section A will be analysed. This technique will allow us to not consider the unit load for that particular

section since it is in fact only acting on the other section[2].

Section B Analysis:

Section A Analysis: Unit load is acting along Section B



Unit load acting along Section A , Assuming counter clockwise rotation aspositive:

(for )

Assuming counter clockwise rotation aspositive:

(for )

Now that is known with respect to the influence diagram can be created. Since influence lines are always

linear [3], the portion of can be drawn by simply connecting the two portions:

Using equilibrium the remaining member forces of the cut can be found with respect to . Similar to the previousmethod for finding force member, , the unit load is placed on the opposite side of the truss from where it isbeing analysed. Again, two equations for each force are found and used to create the influence diagrams for

and .

Section B Analysis:

Unit load acting along Section A , Section A Analysis: Unit load is acting along Section B



for

for

The influence line for the portion can be drawn by connecting the other two portions[3].

When solving for , the unit load is not acting in the x-direction, therefore any of the two sections can be used

while using . Using Section A, this knowledge is exploited to determine the following relationship:

. However, when substituting for and the influence line equation will

be obtained by substituting the respective equations of and for when and .

For x >= 12m: For x



Step III: Member Analysis for Cut b-b

The influence lines for members EF, FK, and KL follow the same procedure for analysis, but this time cutting thestructure along axis 'b-b'.

For (Using Section B)Assuming counter clockwise rotation aspositive:

Note: This makes sense since when ,

EF, FK, and KL are zero force members

For (Using Section A)Assuming counter clockwise rotation aspositive:

for (Using Section B)

for (Using Section A)



for

for

Example: Warren Truss

Determine the influence lines of the indicated members of the Warren truss[4] below.



Solving for

Solving for Solving for

Solving for the reaction force in member

For (Using Section B) For (Using section A)

Solving for the reaction force in member

For (Using Section B) For (Using Section A)



Solving for the reaction force in member and using Section B:

For

For

References

1. Kassimali, Aslam. Structural Analysis. 4th ed. Stamford: Cengage Learning, 92. eBook.



2. Erochko, Jeffrey. Personal Communication, Oct. 16, 2013.

3. 3.0 3.1 Hibbeler, Russ. Structural Analysis. 8th ed. Upper Saddle River: Pearson Prentice Hall, 2012. 232.

eBook.

4. "Heritage Documentation Programs." National Park Service. Historic American Engineering Record, n.d.

Web. 16 Nov 2013. .

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