Force Method for Indeterminate Structures - Intro to Structural Analysis

Learn how to calculate the reaction forces for indeterminate structures using the Force Method (sometimes called the flexibility method).
The force method is an intuitive way of computing reactions for systems with low degrees of indeterminacy. Supports are removed until the resulting structure is determinate, and then forces are applied at the removed supports to ensure that the displacements at those locations are zero, thereby satisfying the original constraints. These external forces are equivalent to the reaction forces.
For the two examples conducted here, the necessary displacements are available from common deflection tables. However, for more complex problems, the setup for the force method lends itself nicely to using the principle of virtual work (PVW) to find all the displacements. See here for how to compute displacements using PVW:
• Deflection of Frames u...

[@gianlucacastro5281]

Such a well done video, thank you for it!

[@abdulrasheedabdul-lateef7054]

This is the best explanation of the force method. Thank you

[@aiqnvc8883]

Thank you for your video! It is really inspiring!!

[@mahindagamage3135]

You made life easy, Thanks

[@ahmedsalamaali4137]

Best explanation ever

[@StructuresProfH]

I'm humbled. Thank you!

[@Civilbabu2000]

Thank you sir i'm from India... You have explained it very well sir😍😍😍

[@StructuresProfH]

You are welcome!

[@aibibiabuova764]

Thank youuuu

[@AyaulymB040]

Thanks!

[@akramfadulalla2653]

I have been looking for an example for a fixed fixed frame. Third-degree determinacy with uniform loading. If you could do a similar example that would be great.
Thanks

[@brianmtshali4615]

Thank you!
Please do for indeterminate trusses

[@StructuresProfH]

Good idea. I'll put that in the pipeline for this summer.

[@muhammadtaha2401]

Where can I located the tables for deflection and flexibility?

[@alviniwenofu506]

Please can you share where you got it

[@patrikengas6479]

hey, (i'm just taking a peek into the next semester curriculum), but one thing i dont get is why you use this method to find support reactions, are they initially unknown?

[@StructuresProfH]

Yes, the reactions are unknown. For an indeterminate structure, equilibrium alone is not enough to solve for the reactions, so that's why we need the force method (or other techniques for indeterminate structural analysis).

[@allandionisio671]

sorry, I don't understand at 8:55 why is -51WL4/1152. where can i find tha value or that formula

[@StructuresProfH]

That is the deflection at the middle point of a cantilever of length L under a distributed load w. Formulas for simply supported beams and cantilevers are tabulated in a bunch of places, even Wikipedia: en.m.wikipedia.org/wiki/Deflection_(engineering)
(This wiki link has the formula as a function of x, but a simple substitution of x = L/2 should get the formula I used). Of course, you can always calculate these deflections using some other method, like moment-area if you wish - it’s just a lot more work.

[@paulpolycap2112]

A clamped beam AB of constant flexural rigidity is shown in Fig. 2.9a. The beam is subjected
to a uniform distributed load of
wKN / m
and a central concentrated moment
.
Draw shear force and bending moment diagrams by force method.
help with that

[@jasonRhawt]

Are you able to upload the tables you used?

[@StructuresProfH]

I don't have one that's copyright free (I usually teach structural analysis from Hibbeler's textbook, and that has a table on the front cover). However, you can find typical tables just about anywhere. This website has most of the common cases: mechanicalc.com/reference/beam-deflection-tables

[@paulpolycap2112]

A clamped beam AB of constant flexural rigidity is shown in Fig. 2.9a. The beam is subjected
to a uniform distributed load of
wKN / m
and a central concentrated moment
.
Draw shear force and bending moment diagrams by force method.
help with that