force in a statically indeterminate cantilever truss

Faculty : Civil And EnvironmentEngineering

Page 01

Department : Structure And MaterialEngineering

Edition 2Checking No

Title :

FORCE IN A STATICALLYINDETERMINATE CANTILEVERTRUSS

Effective Date 11/07/2005AmendmentDate

5/7/2005

1.0 OBJECTIVE

1.1 To observe the effect of redundant member in a structure and understand themethod of analysing type of this structure.

2.0 LEARNING OUTCOME

2.1 Aplication of engineering knowledge in practical aplication.2.2 To enchance technical competency in structure engineering through

laboratory aplication.

3.0 THEORY3.1 In a statically indeterminated truss, static equilibrium alone cannot be used

to calculated member force. If we were to try, we would find that therewould be too many “unknows” and we would not be able to complete thecalculations

3.2 Instead we will use a method know as the flexibility meethod, which usesan idea know as strain energy.

3.3 The mathematical approach to the flexibility method will be found in themost appropriate text books.

Figure 1 : Idealised Statically Indetermined cantilever Truss

Prepared by:Name: Ahmad Zurisman bin Mohd Ali

Singnature:

Date:

1

2

34

5 78

F

6


Page 02



Title :



5/7/2005

Basically the flexibility method usues the idea that energy stored in the framewould be the same for a given load wheather or not the redundant member whetheror not.

In other word, the external energy = internal energy. In practise, the loads in the frame are calculated in its “released” from (that is,

without the redundant member) and then calculated with a unit load in place of theredundant member. The value fo both are combined to calculate the force in theredundant member and remaining members.

The redundant member load in given by:

P = lnfnl

2

The remaining member force are then given by:

Member force = Pn + fWhere,

P = Redundant member load (N)L = length of members (as ratio of the shortest)n = load in each member due to unit load in place of redundant

member (N)

F = Force in each member when the frame is “release” (N)

Figure 2 shows the force in the frame due to the load of 250 N. You should be ableto calculate these values from Experiment : Force in a statically determinatetruss

Figure 2: Force in the “Released” Truss

-250N

250N

250N-500N

0 354N354N

F=250N


Page 03



Title :



5/7/2005

Figure 3 shows the loads in the member due to the unit load being applied to theframe.

The redundant member is effectively part of the structure as the idealised inFigure 2

Figure 3: Forces in the Truss due to the load on the Redundant members

4.0 PROCEDURE

1. Wind the thimbwheel on the ‘redundant’ member up to the boss and hand –tighten it. Do not use any tools totighten the thumbwheel.

2. Apply the pre-load of 100N downward, re-zero the load cell and carefully zero thedigital indicator.

3. Carefully apply a load of 250N and check the frame is stable and secure.4. return the load to zero ( leaving the 100N preload). Recheck and re-zero the

digital indicator. Never apply loads greater than those specified on theequipment.

5. Apply loads in the increment shown in table 1, recording the strain readings andthe digital indicator readings.

6. Substract the initial (zero) strain reading ( be careful with your signs) andcomplete table 2.

7. Calculate the equipment member foce at 250 N and enter them into table 3.8. Plot a graph of Load vs Deflection from Table 1 on the same axis as Load vs

deflection when the redundant ‘removed’.9. The calculation for redundant truss is made much simpler and easier if the tabular

method is used tu sum up all of the “Fnl” and “n2l” terms.10. Refer to table 4 and enter in the values and carefully calculated the other terms as

required.11. Enter your result in to Table 3.

0

01

1


Page 04



Title :



5/7/2005

5.0 RESULT

Member strains (με)

Load(N)

1 2 3 4 5 6 7 8 DigitalIndicator

reading (mm)050100150200250

Table 1: Strain Reading and Frame Deflection

Member strains (με)

Load(N)

1 2 3 4 5 6 7 8

050100150200250

Table 2 : True Strain Reading


Page 05



Title :



5/7/2005

Member Experimental Force (N) Theoretical Force (N)

12345678

Table 3: Measured and Theoretical in the Redundant Cantilever Truss

Member Length F n Fnl n2l Pn Pn + f

1 12 13 14 15 16 1.4147 1.4148 1.414

Total

P = Total FnlTotal n2l

Table 4: table for calculating the Forces in the Redundant Truss


Page 06



Title :



5/7/2005

6.0 DISCUSSION AND CONCLUSION

1. From table 3, compare your answer to the experimental values. Comment onthe accuracy of your result……………………………………………………………………………..

……………………………………………………………………………..

……………………………………………………………………………..

……………………………………………………………………………..

……………………………………………………………………………..

2. Compare all of the member forces and the deflection to those from staticallydeterminate frame. Comment on them in terms of economy and safety of thestructure.……………………………………………………………………………..

……………………………………………………………………………..

……………………………………………………………………………..

……………………………………………………………………………..

……………………………………………………………………………..

1. What problem could you for seen if you were to use a redundunt frame ina “real life’ aplicatioin. (Hint: look at the zero value for the strain readingonce you have included the redundant member by winding up thumnut).………………………………………………………………………….

………………………………………………………………………….

………………………………………………………………………….

………………………………………………………………………….

………………………………………………………………………….

force in a statically indeterminate cantilever truss

Documents