plastic bending of portals-miet1071-2012

School of Aerospace, Mechanical and Manufacturing Engineering

Laboratory Experiment

Subject Code and Name: MIET1071, Solid Mechanics 3

Experiment Title: Plastic Bending of Portals Course Coordinator: Dr. Monir Takla Tutor’s Name: ________________________________ Student Name: ________________________________ Student Number: ________________________________ Date: ________________________________

School of Aerospace, Mechanical and Manufacturing Engineering, RMIT University 2

Title: Plastic Bending of Portals

SUMMARY (written by student)


1. Learning Objectives of the Experiment • Demonstration of Plastic Bending of Portals • Observing Positions of Plastic Hinges • Examining Load-Deflection Relationship • Measuring Collapse Load • Comparing Collapse Load to Theory • Writing up a technical report • Review of theoretical knowledge 2. Introduction to Experiment In this experiment you are asked to set up and perform experiments related to the plastic bending of portals, then compare the results to the simple Plastic Design theory. The experiment clearly demonstrates the principles involved and gives practical support to your studies.


3. Description of Equipment Figure 1 below shows the Plastic Bending of Portals experiment set up in a Test Frame. It consists of a specimen steel portal frame held firmly at the bottom corners by two fixing blocks (ensuring an encastre fixing). Two load cells load the specimen frame by wires and adjustable pulleys. These ensure the loads pull the frame in the correct direction. Each of the pulley mounting plates has a long travel digital indicator attached. This accurately measures the deflection of the specimen frame in the horizontal and vertical directions. The experiment hardware fits onto a Structures Test Frame.

Figure 1


Figure 2 below shows the different components of the experimental testing equipment.

Figure 2


4. Description of Experiment Fix a specimen portal frame (two uprights with a cross-beam at the top) to the bottom cross-piece of a test frame. The test frame also holds horizontal and vertical screw mechanisms with electronic load cells for loading the portal frame. Set the portal frame load conditions by arranging the load cell screw mechanisms to provide either single or combined loads. Load the portal frame manually by adjusting the screw mechanisms. The electronic load cells connect to a Digital Force Display that shows the horizontal and vertical loads as the portal frame deforms. Two long-travel digital deflection indicators measure the portal frame deformation. Continue to load the portal frame until it is in the fully plastic condition, that is, it has undergone plastic collapse. Monitor the collapse load, deformations, and note where plastic hinges formed during collapse. The square portal frame with encastre fixings has three redundancies. If it forms four plastic hinges it will turn into a mechanism and collapse. Alternatively, if any individual member fails as a beam it will effectively fail as a structure. In this experiment you will load specimen portals vertically and then horizontally. In both cases you will observe the positions of the plastic hinges, examine the load deflection relationship and compare the collapse load to theory. Part 1: Vertical Loading Take a specimen portal and check the corners are reasonably square and its legs are straight. If they are not, you need to use another frame. If the frame is a little distorted_ make a note of any distortion so you can make a comparison before and after the test. Measure the section of the frame and calculate a value for the second moment of Area, I, in m4 Remove the clamp plates and locate the ends of the specimen portal into the fixing blocks. Ensuring the clamp plates are square, clamp the specimen using a clamp plate and screw in each block. Find the centre of the portal top beam and mark it with a pencil. Find the longer wire and position the small diameter pin underneath the pencil mark position with the offset end toward the indicator anvil. Clamp it to the frame using the clamp pin and two screws. Rest the indicator anvil on the pin. Pass the wire around the adjustable pulley and secure the end into the load cell clevis using two clevis shear screws. Using a combination of the adjustable Pulley and the load cell, make sure the wire comes vertically down from the frame, around the pulley, then horizontally across to the load cell. Look at the digital force display readout to ensure the Frame is not Pulled during these adjustment. Ensure there is no load on the wire and zero both the load cell and the indicator. Wind the load cell handwheel to pull the frame and cause a measured deflection of 1 mm, take a reading of the force required. Continue to wind the load cell to cause deflections in 1 mm steps until there is very little or no increase in load for each increment of deflection. Enter your results into Table 1.


Deflection Force (mm) (N)

0 0 1 2 3 4 5 6

7 8 9 10 11 12 13 14 15 16 17 18 19 20

Table 1 Results for Part 1 Plot a graph of force versus deflection. From your results, comment on the shape of the resulting plot and note the collapse load. Release the load and carefully remove the portal, sketch the shape of the collapsed portal making note of the positions of the hinges that have formed. Save the portal for later tests. How many hinges have formed? Has the portal failed completely (turned into a mechanism) or has only one part of the structure failed? Part 2: Horizontal Loading Take another (new) portal and fix it into the blocks (as you did in Part 1). Find the shorter wire and position the small diameter pin into the right-hand corner with the offset end toward the indicator anvil. Clamp it to the frame using the clamp pin and two screws. Pass the wire around the adjustable pulley and secure the end into the load cell clevis using two clevis shear screws. Using the adjustable pulley and d the load cell, make sure the wire comes horizontally from the frame. around the pulley, then vertically up to the load cell. Check the digital force display to ensure the frame is not pulled during these adjustments. Check there is no tension in the wire, ensure the indicator anvil is pushed up to the pin, then zero both the load cell and the indicator.


Wind the load cell handwheel to pull the frame and cause a measured deflection of one mm. Take a reading Of the force required. Continue to wind the load cell to cause deflections in 1 mm steps, checking that the indicator anvil stays in contact with the pin. Carry on until there is very little or no increase in load for each increment of deflection Enter your results into Table 2.

Deflection Force (mm) (N)

0 0 1 2 3 4 5 6

7 8 9 10 11 12 13 14 15 16 17 18 19 20

Table 2 Results for Part 2 Plot a graph of force versus deflection. From your results, comment on the shape of the resulting plot. Note the collapse load. Release the load and remove the portal and sketch the shape of the collapsed portal making note of the positions of the hinges that have formed. How many hinges have formed? Has the portal failed completely (turned into a mechanism) or has only one part of the structure failed? Sketch bending moment diagrams for both load cases and compare with the two modes of failure. Are these what you expected? Could you use the bending moment diagram to predict the positions of the plastic hinges?


5. Theoretical Background To compare the collapse loads to theory we can use the following equations (for a portal with a height to width ratio of 2:3.

V = 8Mp/L H= 6 Mp/L

Where:

V = Vertical load to cause collapse (N) H = Horizontal load to cause collapse (N) Mp = Plastic Moment (Nm) L=Width of frame (m)

Reference: Hibbeler, R.C., Mechanics of Materials, Sixth International Edition, Prentice Hall Useful Literature for this lab work: Nash, W.A., Strength of Materials, Third Edition, Mc Graw-Hill, 1994. Takla, M., Mechanics of Solids III, Resource Material, Unit 9.


6. Calculation of Results (Written by student) [The report must contain all raw results and calculated results must be presented as well as sample calculations]


7. Discussion [Students to discuss the results, their accuracy, their significance, any abnormalities or restrictions that existed in the experiments]


8. Conclusions [The experiment has stated aims and objectives. What conclusions were drawn in relation to those aims? What other conclusions were drawn from the experiment]


9. Student Comments [Students comments/suggestions are welcome to improve the learning outcomes from this experiment]