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Friday, 13 October 2017

Moment Redistribution for Design of Continuous Beams


Design of structural members requires a lot of analysis and checks. Beams are a fundamental part of any structure and their design requires consideration of forces and their effects on the beam as a whole. 
As a part of the structure, beams can be considered as two types single span or continuous span. The only differentiating element between the two types of beams is the consideration of beam a continuous or discontinuous. If the beam is taken as discontinuous then the effects of loading acting only on the span are to be considered, like the bending moment in the beam will be only due to the load present in the span and will not have any counteracting effect. These often lead to uneconomical designs as when the beams are designed as continuous the positive moment created by the load in one bay creates a negative loading in the other bay. In this fashion, the combined effect of loading creates a balance in the other adjoining span. Well, engineers have figured this out and have successfully exploited this phenomenon for designing economical structures to save material and cost.

As seen from the image above a lot of material is saved by designing the beam for net forces and actions instead of designing by the conventional single bay/span method.

How to perform MDM:

Moment distribution is performed by formulating a table wherein the moments are distributed by considering the stiffness factors and the fixed end moments of the spans. The moment is distributed until the moment at both the sides of a continuous joint are equal.
Check out the video below to learn more about the method:

Now once you've completed the calculation of moments from the beam you can formulate a table and then by considering the beams separately in each span calculate the reactions and then formulate the SFD and BMD. Now in order to design the members for worst case scenario. You can refer the image below to determine the load cases:

As a part of my BE termwork, I'd performed a similar analysis and determined the moments by considering the different cases. After performing the analysis I'd prepared a table of the moments:

By iterating the above sequence for the different cases I calculated the moments at the different sections of the beam. Once MDM is completed you are now to redistribute the moments to take the benefit of loading patterns. Up to 30% of the moments on the continuous supports can be redistributed to the adjoining spans. and by doing this the point of contraflexure can be shifted in order to make a structure more economical.

Now in-order to redistribute the moment select any continuous support, suppose you want to redistribute 20% of moments at support E, multiply the moment on support E by (100-20)% and then apply it on the span. Later by applying the loading calculate the reactions on the supports and then find the final bending moments.:
Check out the Video below to learn how to calculate the support reactions:
Calculate the reactions and then plot the corresponding bending moment diagrams for all the corresponding load cases. Perform the same sequence for all the cases, at the end it is recommended that you make a table to compare and evaluate the worst combination for design.

Now once you have the worst combination of Bending moment you can design the beams by considering the moments and the loading. Use the general design procedures for the design of flexural members under specifications as per IS 456.

Thanks for Reading....
Until Then Keep it Halal!

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