Mohammad Sohel Akhtar, Structural Engineer, New Delhi, India“Feel the structure”
Here,at the end of this article, you will find an attachment having calculations to find out the fixed end moments for a single span fixed beam which is subjected with a point load at it’s centre.
Principle of superposition and compatibility equation has been used to find the fixed end moments. You will be astonished ,how tricky it has been to convert an indeterminate beam to few determinate beams. All converted determinate beams when added represents the same indeterminate beam and calculating deflection individually for each converted determinate beams and adding them all at specified location so that equation of compatibility can be formed will help us to find out the internal forces like moments & shear .
To understand the entire concept, please go through the attached calculation sheet and i am 100% sure, you will find it very different from any text books. Also, you may not have the same procedure in the text books as most of the text book does not go in so much deep to find out fixed end moments in simpler manner.I have explained step by step the entire concept.
In the calculation sheet, i have not explained how to determine BMD & M/EI diagram as it is not our subject of analysis. Our focus of analysis is to determine fixed end moments. Anyway, please visit my previous blogs in the Category of deflection calculation in which i gone in details for the formation of BMD & M/EI diagram.
People are scared on analyzing complex indeterminate structure because they think it a complex. If using good judgement,you are able to convert any indeterminate beam to simpler determinate beams, then i ensure you that your half of work is done and you will be solving only simple equations.
As a structural engineer, we should not ignore analysis of cantilever beams subjected with different kind of loading. You will notice, if you are able to solve for cantilever beams then you will be able to a frame structure. Firstly, building is nothing but a vertical cantilever and during analysis of any frame, we should have a great judgement and skill to convert frames into vertical cantilever and horizontal beams so that it can be converted into a determinate beams . After this rest of this will be solving of algebraic equations only.
As in similar manner, for structural dynamics,you are dealing with second order liner differential equations and after getting response at any instant of time as a maximum displacement, velocity & acceleration for dynamic loading or initial displacement to the structure, your work become simple because after that you are only doing static analysis and your structure analysis becomes a static problem.
This is the Series-1 for fixed end moments calculation for central point loads and i will be coming with varieties of loading pattern in a single span fixed beam to find out it’s fixed end moments.
You need to understand the concept of fixed end moments because during analysis of beams and frames using slope deflection methods and moment distribution methods, it is essential to know the quickest method to find out the fixed end moments.
Mohammad Sohel Akhtar(Structural Engineer), Delhi, India