Which method is used for calculating deflection of beam which has several loads?
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Today, any routine software package will do it in a fraction of a second and give you a hundred percent accurate answer irrespective of the complexity of the structure, the properties of the members and the distribution and nature of the loading on the structure.
The direct stiffness method is used to develop the algorithm.
During the pre computer era, we had crude methods to estimate the deflection, not calculate it exactly. No one was actually interested in knowing the exact value.
For beams, with point loads and distributed loads all mixed up, and spread out over the span you can get by with ML^2/( 10EI) as a quick first approximation.
M is the maximum moment. L is the span, E is the modulus of elasticity and I is the moment of inertia of the beams cross section.
For frames, to calculate sway, you need more experience and judgement.
For a rough first guess, forget gravity loads on the frame. They don’t result in much lateral deflection.
Consider the lateral wind loads or the crane surge loadings.
If it is a single aisle portal frame:
Consider the windward column and calculate the cantilever deflection at the tip
(PL^3/(3EI) for point loads and PL^3/(8EI) for udl
This will be the extreme upper limit for the value of deflection.
Divide it by two since two columns resist the lateral load.
This will be the first approximation.
Then tweak this value. Since the structure is not a free cantilever the actual value will obviously be less. But how much less? That takes practice and judgement and depends on the Height to width ratio of the frame.
The taller the frame, the nearer it is to half the cantilever deflection.
The wider the aisle, the lesser it is. With some practice and judgement and also experience you can nail it down to within +/- 15 percent accuracy.
Experts have found ways to further polish these results but all this knowledge is now outdated and computer software has made these techniques irrelevant.
Crude methods like this work well during preliminary designs and that is how old veterans worked during the pre-computer era. All those structures analysed and designed by them using classical non computer oriented methods, are still standing.
While doing my ME in structures at Roorkee in 1972–74, I used to watch in amazement my old and pre - eminent Teacher (Dr. O. P Jain) analyse on the blackboard a multi bay, multi storeyed building frame with nothing more than a piece of chalk in his hands and not even a calculator, and arrive at the moments and axial forces in critical members with an accuracy sufficient to proportion the columns sizes safely. Working with with just three significant digits was enough those days because, when the loads were uncertain what purpose did more accuracy serve? Computer analysis experts who dabbled with main frame computers and fem software could at best improve the accuracy by 10 to 15 percent.
The direct stiffness method is used to develop the algorithm.
During the pre computer era, we had crude methods to estimate the deflection, not calculate it exactly. No one was actually interested in knowing the exact value.
For beams, with point loads and distributed loads all mixed up, and spread out over the span you can get by with ML^2/( 10EI) as a quick first approximation.
M is the maximum moment. L is the span, E is the modulus of elasticity and I is the moment of inertia of the beams cross section.
For frames, to calculate sway, you need more experience and judgement.
For a rough first guess, forget gravity loads on the frame. They don’t result in much lateral deflection.
Consider the lateral wind loads or the crane surge loadings.
If it is a single aisle portal frame:
Consider the windward column and calculate the cantilever deflection at the tip
(PL^3/(3EI) for point loads and PL^3/(8EI) for udl
This will be the extreme upper limit for the value of deflection.
Divide it by two since two columns resist the lateral load.
This will be the first approximation.
Then tweak this value. Since the structure is not a free cantilever the actual value will obviously be less. But how much less? That takes practice and judgement and depends on the Height to width ratio of the frame.
The taller the frame, the nearer it is to half the cantilever deflection.
The wider the aisle, the lesser it is. With some practice and judgement and also experience you can nail it down to within +/- 15 percent accuracy.
Experts have found ways to further polish these results but all this knowledge is now outdated and computer software has made these techniques irrelevant.
Crude methods like this work well during preliminary designs and that is how old veterans worked during the pre-computer era. All those structures analysed and designed by them using classical non computer oriented methods, are still standing.
While doing my ME in structures at Roorkee in 1972–74, I used to watch in amazement my old and pre - eminent Teacher (Dr. O. P Jain) analyse on the blackboard a multi bay, multi storeyed building frame with nothing more than a piece of chalk in his hands and not even a calculator, and arrive at the moments and axial forces in critical members with an accuracy sufficient to proportion the columns sizes safely. Working with with just three significant digits was enough those days because, when the loads were uncertain what purpose did more accuracy serve? Computer analysis experts who dabbled with main frame computers and fem software could at best improve the accuracy by 10 to 15 percent.
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