Beam with Spring Support - IStructE Certificate in Structural Behaviour Course

Question from IStructE's Structural Behaviour Course, as part of the Certificate in Structural Behaviour.
This is a question from the Structural Behaviour Course, which asks you to calculate the vertical deflection of the truss using whatever method you want. Here we chose the method of conservation of energy.
Recorded by Tim Lai, founder of The Structural Exam.
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Thumbnail image from the Structural Behaviour Course

[@TheStructuralExam]

09:18 CORRECTION: This capital Delta should be equal to x rather than -x due to the fact that delta is already a downwards direction, and then at 10:06, the equation should read x = -0.0225 - 0.9x. The final answer remains the same.

[@gamingfps1611]

wrong again hhhh it should be x = 0.0225-0.9x >>>1.9x=0.0225>>x=0.01184 downward and the positive is downward

[@sairanjan3341]

I’ll be taking my exam in aug 2020. Thanks a lot for the videos, it’s been teaching me a lot of techniques.

[@waqarfarooqui618]

Alternatively, 1) Compute stiffness of the beam (kb) = load/ deflection= {250kN / ( deflection of 6m simply supported beam for the point load of 250kN)} , 2) Stiffness of spring is 10kN/mm (ks) ; 3) Compute total stiffness = kb+ks = ktot 4) Load / ktot = 11.8mm.; Springs are in parallel because same load is not seen by the two springs , therefore ktot = kb + ks; otherwise it would have been an inverse adddition

[@rajivrajak3815]

how have you supposed beam deflection as spring?

[@waqarfarooqui618]

Beam deflection is not spring rather beam can be idealised as spring. Spring constant is the stiffness of the beam. Assumption is that the load not very high otherwise there will be plastic behaviour

[@DrJQureshi]

This is an interesting solution. I was about to upload a KZbin video on this topic, and I'll now include this as well. Thanks for the information!

[@alinam7142]

Thank you 😊 please post more

[@andreamusacchi2626]

Great example this one!

[@ahmedaga4754]

Hi ... What should i do if i take c as redunant?

[@yoshicrafto2242]

Thanks

[@temia7944]

Thanks for the explanation, am I right to say this is a good example of a idealized bridge with a pier in the middle?

[@TheStructuralExam]

An idealised bridge and pier would more likely be modelled with no deflection at the central support.

[@arthurmorgan5945]

Hi, thanks for the content. I don't understand how you say 10kn/0.001M. The question says "the spring displaces by 1mm for every 10kN acting on it". So surely that is 0.001m/10kN and not the other way around?

[@TheStructuralExam]

Do a dimensional analysis on F=kx. k must have units of force per unit displacement

[@ahmadelshukri5023]

The last equation not ok .... I think positive value according to your step .... thanks