ECM 2109 Plastic collapse of portal frame lab assignment

ECM 2109 Plastic collapse of portal frame lab assignment

1 Aim 

The aim of this experiment is to examine how structures behave in reality and to see how physical experiments compare with the theory you have been learning in the lectures.

NOTE: Bring this sheet to the Lab – you might need it. 

2 Objectives 

1. To examine the elastic and elasto-plastic behaviour of a portal frame under increasing load.
2. To observe the onset of plasticity and its consequences.
3. To compare the theoretical value of the plastic collapse load for a statically indeterminate

structure with that found in experiment.

3 Apparatus 

The apparatus comprises a loading rig into which has been clamped a model portal frame made of mild steel section with a uniform rectangular section. The loading system is provided by a system of cables which is designed to apply a vertical load at the centre of the beam and a horizontal load at the top of one column.

Two gauges have been placed in order to monitor the horizontal deflection of the beam and its central vertical deflection.

4 Experimental procedure 

The nominal centre-line dimensions of the portal frame are as shown in Figure 1. Nominal dimensions of the cross-section are 12 mm by 3 mm.

Figure 1: Nominal dimensions of the portal frame 

1. Take repeat measurements of the frame and cross-section dimensions to establish the

actual dimensions of the specimen under study.

2. Make sure the loading rig is in good working order. Visually inspect cables for damage.
3. With the frame unloaded, zero the dial gauge readings.
4. Load the frame steadily as follows:
5. a) Use the selector and switch to the horizontal load cell (Load cell #1) by turning the knob on the load cell and increment it slowly by 10 N.  ECM 2109 Plastic collapse of portal frame lab assignment

1. b) Use the selector and switch to the vertical load cell (Load cell #2). Increase the vertical

load by 10 N and use the adjuster knob at the centre to ensure that the loading cable remains precisely vertical.

1. c) Record the deflections when the horizontal and vertical loads are equal.

University of Exeter ECM2109 Structures 

5. Repeat steps 4a), 4b) and 4c) until plastic failure occurs.
6. As the experiment progresses (and later when analysing results) try to observe when

plastic hinges form (this will result in the gradual reduction of the overall stiffness of the structure). The formation of the plastic hinges might not be obvious initially; it should become much clearer at the end of the experiment.

7. Record the load at which collapse occurs (probably somewhere in the range 110 N-150 N) – this is signified by increase in displacement without much increase in load and, more obviously, loss in the already applied force.
8. After collapse, ask supervisory staff to unload the frame and remove it from the loading rig.

Use a set square to verify at which joints the permanent rotation occurred; these joints are the locations of the plastic hinges. Alternatively, if you are running out of time, you could observe the permanent rotation in the unloaded frame while it is still in the rig. You might want to take a photo of the frame at this final stage.  ECM 2109 Plastic collapse of portal frame lab assignment

5 Theoretical calculations 

1. Calculate the static indeterminacy, αs, of the frame. 2. Using the actual size of the members and the value of the yield stress for mild steel, σy,

(which will be provided for you in the lab) find the fully plastic moment Mp for the section. 3. Use the principle of virtual work to calculate the theoretical collapse load of the structure

and establish a critical collapse mechanism.

Consult SZ during office hours or after lectures if you have any questions related to calculations.

6 Presentation of the results 

You are asked each to submit a laboratory report on your experiment. Make use of the guidelines provided in the fluids part of the course (ECM2113) that are now available on the ECM2109 webpage. Things to include are (these are not the section headings for your report):

1. Introduction and aims
2. Theoretical derivations
3. Drawn and explained experimental set up (not just the notional line diagram given herein)
4. Graphs of the loads (on y-axis) against deflections you have measured (on the x-axis).

(Some aspects you might want to consider/comment: Are the graphs linear or piecewise linear? Can you identify at which loads plastic hinges have formed?)

5. Comparison of the measured collapse load with the theoretical value and verification of the

number and locations of the plastic hinges at the end of the experiment. You should critically evaluate all the results. What are the possible sources of discrepancies, if any, between theory and experiment?

Compulsory reading/watching prior to the laboratory work:

• H&S document entitled Safety.pdf 
• Safe operating procedure: Portal Frames STR16 – SOP – 20180305.pdf and risk assessment Portal Frames STR16 – Risk Assessment – 20180305.pdf 

• PortalFrame.mp4: introduction into the apparatus and key features of the experiment

ECM 2109 Plastic collapse of portal frame lab assignment

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