MSI08 Force in a Statically Indeterminate Cantilever Truss

Faculty : Civil And Environment Engineering Department : Structure And Material Engineering Title :

FORCE IN A STATICALLY INDETERMINATE CANTILEVER TRUSS 10

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

LEARNING OUTCOME 2.1 2.2

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OBJECTIVE 1.1

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

THEORY 3.1 In a statically indeterminated truss, static equilibrium alone cannot be used to calculated member force. If we were to try, we would find that there would be too many “unknows” and we would not be able to complete the calculations 3.2 Instead we will use a method know as the flexibility method, which uses an idea know as strain energy. 3.3 The mathematical approach to the flexibility method will be found in the most appropriate text books. 1 8 5

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2 6 4

3

F

Figure 1 : Idealised Statically Indetermined cantilever Truss Prepared by: Name: Ahmad Zurisman bin Mohd Ali Singnature: Date: Faculty : Civil And Environment Engineering

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FORCE IN A STATICALLY INDETERMINATE CANTILEVER TRUSS • • •

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Basically the flexibility method usues the idea that energy stored in the frame would be the same for a given load wheather or not the redundant member whether or 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 the redundant member. The value fo both are combined to calculate the force in the redundant member and remaining members. The redundant member load in given by: P= fnl ∑ n 2l The remaining member force are then given by: Member force = Pn + f Where, 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)

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

0

354N

250N

-500N

354N

250N

F=250N

Figure 2: Force in the “Released” Truss

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Figure 3 shows the loads in the member due to the unit load being applied to the frame. The redundant member is effectively part of the structure as the idealised in Figure 2

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Figure 3: Forces in the Truss due to the load on the Redundant members 10

PROCEDURE 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.

The thimbwheel on the ‘redundant’ member winded up to the boss and hand – tighten it. The pre-load of 100N applied downward, the load cell was re-zero and carefully zero the digital indicator. A load of 250N was applied and the frame is checked stable and secure. The load returned to zero (the 100N preload leaved). The digital indicator was rechecked and re-zero. Loads were applied in the increment shown in table 1, the strain readings and the digital indicator readings were recorded. The initial (zero) strain reading substracted and table 2 was completed. The equipment member foce at 250 N was calculated and entered into table 3. A graph of Load vs Deflection from Table 1 plotted on the same axis as Load vs deflection when the redundant ‘removed’. The calculation for redundant truss was made much simpler and easier if the tabular method was used tu sum up all of the “Fnl” and “n2l” terms. Table 4 was refered and the values entered and the other terms as required were calculated. Result was entered in to Table 3. Faculty : Civil And Environment Engineering

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FORCE IN A STATICALLY INDETERMINATE CANTILEVER TRUSS

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RESULT Member strains (με) Load (N)

1

2

3

4

5

6

7

8

0 50 100 150 200 250

115 115 119 131 143 155

219 225 231 226 222 217

3 -7 -16 -23 -30 -38

-21 -24 -26 -41 -53 -67

116 113 111 116 120 125

29 35 39 34 29 22

-37 -24 -11 5 16 28

36 28 20 20 37 44

Digital Indicator reading (mm) 0 0.093 0.168 0.210 0.235 0.259

Table 1: Strain Reading and Frame Deflection Member strains (με) Load (N)

1

2

3

4

5

6

7

8

0 50 100 150 200 250

0 0 4 16 28 40

0 6 12 7 3 -2

0 -10 -19 -26 -33 -41

0 -3 -5 -20 -32 -46

0 -3 -5 0 4 9

0 6 10 5 0 -7

0 13 26 42 53 65

0 -8 -16 -16 1 8

Table 2 : True Strain Reading

Redundant removed

Faculty : Civil And Environment Engineering

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FORCE IN A STATICALLY INDETERMINATE CANTILEVER TRUSS

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Member

Experimental Force (N)

Theoretical Force (N)

1 2 3 4 5 6 7 8

237.47 -11.87 -243.40 -273.09 53.43 -41.56 385.89 47.49

124.92 -375.08 -250.00 -625.08 -125.08 176.92 354.00 530.92

Table 3: Measured and Theoretical in the Redundant Cantilever Truss

Member

Length

F

n

Fnl

n2l

Pn

Pn + f

1 2 3 4 5 6 7 8

1 1 1 1 1 1.414 1.414 1.414

250 -250 -250 -500 0 0 354 354

-0.707 -0.707 0 -0.707 -0.707 1 0 1

-176.8 176.8 0.0 353.5 0.0 0.0 0.0 500.6

0.50 0.50 0.00 0.50 0.50 1.41 0.00 1.41

-125.08 -125.08 0.00 -125.08 -125.08 176.92 0.00 176.92

124.92 -375.08 -250.00 -625.08 -125.08 176.92 354.00 530.92

Total

854.1

4.83

P = Total Fnl Total n2l Table 4: table for calculating the Forces in the Redundant Truss

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FORCE IN A STATICALLY INDETERMINATE CANTILEVER TRUSS

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6.0 CALCULATION Calculation for Cross Section Area of the member (m2) ; Diameter, D

= 6 x 10-3 m

From equation ;

A=

πD 2 4

=

π (6 x10−3 ) 2 4 m2

= 2.827x10 −5 Example calculation of experimental forces: Calculation for Member 1 ; F=AEε = (2.827 x 10-5) x (2.10 x 105) x (40) = 237.47 N Example calculation of theoritical forces:

Example for member AD, Fx = 11.414 = 0.707 P=∑Fnl∑n2l =854.14.83

= 176.83 Faculty : Civil And Environment Engineering

Department : Structure And Material Engineering Title :

FORCE IN A STATICALLY INDETERMINATE CANTILEVER TRUSS 20

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DISCUSSION 1.

From table 3, compare your answer to the experimental values. Comment on the accuracy of your result. Refer to table 3, the value of experimental force are different with the theoretical value. There are in member 1,2,4,5,6 and 8. This is because of parallax error and may be the result is affect by the environment in the lab.

2. Compare all of the member forces and the deflection to those from statically determinate frame. Comment on them in terms of economy and safety of the structure. There are positive and negative force value which is tension and compression force at the member. Most of the structure is built with more than their minimum number of truss member so that it will not fail suddenlly if some of their member fail. This can be economy and safe structure. 3. What problem could you for seen if you were to use a redundunt frame in a “real life’ application. (Hint: look at the zero value for the strain reading once you have included the redundant member by winding up thumnut). The redundant frame always use in bridge construction to increase the stability of the bridge because the structure will fail if the load is exceed the ability of the bridge. 7.0 CONCLUSION From the experiment, we can get the value of experimental force for each member in the truss. Besides that, we can compare the experimental force with the theoretical force in the redundant cantilever truss. For the conclusion, the experimental force that we get is different with the theoretical force because of several errors occur.

APPENDIX

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