Portal Frame Analysis

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University of Manchester
University of Manchester
NISHANT AGARWAL

The report primarily discusses results obtained from the conducted experiments and includes computed data from the Kingston computer program. The value of the plastic moment capacity of each experiment was obtained; Obtained value was used to find the yield strength of the structures and compare them to typical values for mild steel. The important data is summarized in a table; followed by a list of important formulae. All individual results are listed in the appendix at the end.

NISHANT AGARWAL

The report primarily discusses results obtained from the conducted experiments and includes computed data from the Kingston computer program. The value of the plastic moment capacity of each experiment was obtained; Obtained value was used to find the yield strength of the structures and compare them to typical values for mild steel. The important data is summarized in a table; followed by a list of important formulae. All individual results are listed in the appendix at the end.

Structures: Collapse of Portal Frame
Structures: Collapse of Portal Frame

TABLE OF CONTENTS:
0. Symbols

1. Development of a Plastic Hinge

2. Discussion
3.1 Cantilever Arm
3.2 Beam Mechanism
3.3 Sway Mechanism
3.4 Combined Mechanism

3. Interaction Diagram

4. Bending Moment Diagrams

5. Conclusion

6. Bibliography

7. Appendix

0. Symbols
b Width (mm)
d Thickness (mm)
h Height (mm)
W Vertical Load (kN)
H Horizontal Load (kN)
fy Yield Strength (N/mm2)
Mp Plastic moment capacity ( kN-mm)

1. Development of A Plastic Hinge

A plastic hinge is formed when the yielding has spread throughout the entire cross section of a member, reducing rotational stiffness to zero. (Todd, 2000) When a member reaches it’s maximum yield stress, it does not result in failure. The member continues to take additional load and as the load continues to increase, more and more fibers reach the yield stress and the stress distribution is as shown above. Eventually the whole of the cross section reaches the yield stress. The moment corresponding to this state is known as the plastic moment of the cross section and is denoted by Mp. (Kumar)

2. Discussion
This report discusses four experiments. First, determining the value of the plastic moment capacity (Mp) of a cantilever. Followed by, obtaining collapse loads for the beam, sway and combined mechanism. The results of the last three experiments are plotted together to form an interaction diagram. The table below summarizes the important results recorded and calculated during the course of the experiment. Mechanism| fy| Mp| Wc| Hc|

Cantilever| 394.1| 10.6889| 0.049| -|
Beam| 356.589| 10.35| 0.276| -|
Sway| 478.634| 12.375| -| 0.165|
Combined| 328.697| 8.915| 0.214| 0.0713|

2.1 Cantilever Arm
Plastic Hinge
Plastic Hinge
Deflected Shape
Deflected Shape

Fig 2.1 (b) Deflected and deformed arm.
Fig 2.1 (b) Deflected and deformed arm.
Fig. 2.1 (a) Cantilever Arm
Fig. 2.1 (a) Cantilever Arm

Fig.(I. B) Collapsed Cantilever Arm, (Kingston)
Fig.(I. B) Collapsed Cantilever Arm, (Kingston)
Fig.(I. A) Deformed Cantilever Arm
Fig.(I. A) Deformed Cantilever Arm
Notes And Comments:
The above is a statically determinate structure. Hence, only one plastic hinge will form. The plastic moment capacity is obtained by plotting Moment- vertical deflection graph; it is read off as the value that initiates the ‘plateau’ formation. The computed value fy of 394.1 N/mm2, is within the required range of yield strength for mild steel, i.e. (360 – 430 N/mm2). NOTE: Before commencing the experiment, the cantilever strip was bent at about 20mm off its edge to prevent the weight hanger from slipping off. The hanger was then loaded and deflections measured till collapse of the cantilever arm....
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