lab report engeenring

ENG10003 Mechanics of Structures Virtual Laboratory Session #1 Truss Analysis Introduction There are two parts in this laboratory session. Part 1 is to be completed in your own time and involves the calculation of reactions and member forces by the method of joints and method of sections. Part 2 is to be done by watching the uploaded video and involves loading a pin-jointed truss and measuring the forces within the structural members. These measurements will be compared to your Part 1 calculations. Each student is required to submit a soft copy of this working sheet due in CANVAS on 28 September, which is worth 5% of your total marks for this subject.

PART 1: Calculation of reactions and forces within members of a pin-jointed truss For the pin-jointed truss below,

1. Calculate the reactions. 2. Calculate the forces in members BC, BD and DE by the method of joints. 3. Check your answers to the above-mentioned members by using the method of sections.

(All working for the reactions and structural members must be shown.)

Solve for: Case 1: P = 1 N; W = 0 N Case 2: P = 0 N; W = 1 N

Case 3: P = 1 N; W = 1 N

Student Name: ID No:

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Summary of Results for Part 1

CASE 1

Reactions RAH =______ N; RAV =______ N; RCV =______ N

Internal forces FBC = ______ N; FBD =______ N; FDE =______ N

FAB* = ______ N; FBE* =______ N; FEA* =______ N; FCD* =______ N

*Members AB, BE, EA and CD are optional.

CASE 2

Reactions RAH =______ N; RAV =______ N; RCV =______ N

Internal forces FBC = ______ N; FBD =______ N; FDE =______ N

FAB* = ______ N; FBE* =______ N; FEA* =______ N; FCD* =______ N

*Members AB, BE, EA and CD are optional.

CASE 3

Reactions RAH =______ N; RAV =______ N; RCV =______ N

Internal forces FBC = ______ N; FBD =______ N; FDE =______ N

FAB* = ______ N; FBE* =______ N; FEA* =______ N; FCD* =______ N

*Members AB, BE, EA and CD are optional. Note: Your full-worked solutions MUST be attached to this working sheet.

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PART 2: Experiment to determine reactions and member forces in a model pin-jointed truss In the laboratory session, you will be investigating the truss shown for three different load cases. For each load case, you will need to measure the reactions at A and C (using digital scales provided), and the forces in members BC, BD and DE from the internal member spring displacements. An example of determining Reactions on a Model Truss (with load at Node B) is shown below. . Example Truss with Central Point Load of 118.1 gram or 0.1181 * 9.81 = 1.16 N. The LHS vertical reaction, RAV = (170.3 – 114.5) / 1000 * 9.81 = 0.547 N. The RHS vertical reaction, RCV = (159.6 – 100.9) / 1000 * 9.81 = 0.576 N. Hence, the total is 1.12 N. (This is in close agreement with the value of applied load of 1.16 N) Determining Member Forces using Simplified Photogrammetry. Measuring the elongation or contraction in the spring of these special truss members using a simplified photogrammetric method is a very simple way of experimentally determining their forces (as shown below). Each truss member has a spring inside that deforms a small amount when subjected to load. Consider a member before application of loading. Take a close-up photo of the slot of the member, clearly depicting the internal pointer and its position. Measure distances L0 and a0 on this photo (e.g. using a ruler or the digital calliper provided of the image on your phone if using a phone camera).

Before Application of Load

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Consider the same member after application of loading. Take a close-up photo of the slot of the member that clearly depicts the internal pointer and its position. Measure distances L1 and a1 on this photo or the image on your phone e.g. using a ruler or the digital calliper provided.

After Application of Load Since the actual slot length is 13.0 mm in each of the truss members, the position of the internal pointer from the edge of the slot is in the proportion a/L of the slot length (irrespective whether the photo is rectified or not). The elongation of the member, δm, after application of the load becomes:

δm = 13.0 × −� 𝑎𝑎0 𝐿𝐿0 −𝑎𝑎1𝐿𝐿1� mm

You should familiarize yourself with these members and investigate the difference between how tensile and compressive forces change the measurements.

Stiffness of the spring, Km = ___________ N/mm

Using the spring stiffness (Km) and elongation or contraction δm, the force in each member is determined from:

Fm = (Km × δm) N

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LOAD CASE 1 – MEASURED

P = ___________ gr = ___________ N

Obtain reaction forces and forces in members BC, BD and DE. Other members are optional.

Reactions RAV =______ N; RCV =______ N

Members δBC = ______ mm; δBD =______ mm; δDE =______ mm

F =

K m

δ

FBC = ______ N; FBD =______ N; FDE =______ N

δAB = ______ mm; δBE =______ mm; δEA =______ mm; δCD =______ mm

FAB = ______ N; FBE =______ N; FEA =______ N; FCD =______ N

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LOAD CASE 2 – MEASURED

W = ___________ gr = ___________ N

Obtain reaction forces and forces in members BC, BD and DE. Other members are optional.

Reactions RAV =______ N; RCV =______ N

Members δBC = ______ mm; δBD =______ mm; δDE =______ mm

F =

K m

δ

FBC = ______ N; FBD =______ N; FDE =______ N

δAB = ______ mm; δBE =______ mm; δEA =______ mm; δCD =______ mm

FAB = ______ N; FBE =______ N; FEA =______ N; FCD =______ N

Now that you have completed load cases 1 and 2 – you should be able to estimate the reactions and relevant member forces for load case 3. Complete this on the diagram below. Once you have estimated the reactions and member forces for each load case, you should then load the truss and record your measurements. If your estimated reactions and member forces deviate too much from the measured reactions and member loads – then you have probably made a mistake and will need to go back and re-examine each load case.

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LOAD CASE 3 – MEASURED

P = ___________ N (nominated earlier); W = ___________ N (nominated earlier)

Obtain reaction forces and forces in members BC, BD and DE. Other members are optional.

Reactions RAV =______ N; RCV =______ N

Members δBC = ______ mm; δBD =______ mm; δDE =______ mm

F =

K m

δ FBC = ______ N; FBD =______ N; FDE =______ N

δAB = ______ mm; δBE =______ mm; δEA* =______ mm; δCD =______ mm FAB = ______ N; FBE =______ N; FEA* =______ N; FCD =______ N

Now compare your estimated and measured actions against the calculations performed in Part 1.

Estimated from Load Cases 1 and 2 – Part 2

Hint: apply the superposition principle.

Measured Load from Case 3

Calculated from Load Cases 1 and 2 – Part 1

Hint: scale them up separately based on measured P and W, then apply the

superposition principle.

FBC FBD FDE FAB* FBE* FEA* FCD*

*Members AB, BE, EA and CD are optional.

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CONCLUSIONS: 1. By comparing the estimated actions (reactions and selected member forces) obtained from

Load Cases 1 and 2 with the actual experimental measurements from Load Case 3, please describe and explain the findings?

2. There will be discrepancies between theoretical estimates (Part 1) and actual measurements

(Part 2). Can you think of any possible sources of errors? How can we minimise the discrepancies?

Laboratory Session Feedback: In this practice, rank the parts (on a scale of 1 - lowest to 5-highest) you gained most from:

1. Matching theoretical calculations to actual measured loads. 2. Learning about measurements using photogrammetry. 3. Visualising what a pin-jointed truss actually looks like and seeing how it works. 4. Overall, has this laboratory session helped you understand more about trusses? 5. Other feedback: ____________________________________________________________ __________________________________________________________________________