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Tried with a finer mesh but still the same results.

Hi all, I'm fairly new to the Abaqus program so go easy on me. The issue is, I'm getting the same failure load in a simply supported beam (4 point bending) even if I reduce the spacing of stirrups. From stress contours I can observe that any steel rebars are not yielding indicating there's no...

@rb1957 No I initially wanted to study the derivation of fixed straight beam and then moved on to curved beams. In the book that roby suggested has everything I need. But seems like there's no derivation in it so I can study it. I will use FEA (abaqus) later but for now I just need to study it...

Perpendicular to the plane of curvature so there will be torsion.

Forgot to tell its a horizontally curved beam. And gonna try superposition method also after trying moment area method to verify. Also for superposition can I use pin-pin with load and pin-pin with imposed end rotations instead of pin-fix as u suggested?

Below I attached the arrangement of the beam.

Thanks for all of your replies. I was able to find the support reactions easily by applying Castigliano's theorem. and then as rb1957 said integrating starting from v(x) solves the problem. But the main problem I was trying to solve was the deflection of fix-fix CURVED beam, which I'm not sure...

Does anyone have the derivation procedure for deflection formula of a clamped-clamped beam as shown in attached figure. https://files.engineering.com/getfile.aspx?folder=2a0efc53-5bc0-43ca-89db-6b304f45f1a9&file=Screenshot_20200506-232710.jpg

It was designed to fail in shear with low shear r/f. It has 2 m span and simply supported. Control beams failed in shear and after applyingg CFRP, failure mode became flexural. Four point bending arrangement was used for testing.

Its a 200 X 200 section with 2T12 r/f at top and bottom each. CFRP layer thickness is 0.168 mm and epoxy adhesive layer can be assumed as 1mm. CFRP fabric is embedded in the epoxy layer. For this case CFRP is applied (wrapped) 450mm at each end.

This is not for some client. It's an old experimental research of mine. I meant the plotted results. I'm just trying to understand it in a more theoretical level. Or maybe launch a new research since nowhere this is explained. The biggest difference were shown in slopes of regions before...

It affect the deflection somehow. Maybe adhesive layer around the beam can affect the deflection due to bending forces I think. Agree there need to be at least anchoring for u-socketed FRP,specially when wrapping is not possible in slab-beam systems.

I'm familiar with ACI 440.2R. The issue is not for flexurally strengthened RC beams by applying FRP at the soffit. It's for shear strengthened beams by u-socketing or wrapping. Somehow this affect the deflection of the beam. Maybe adhesive layer at soffit at FRP wrapped regions affect the...

Apparently it does affect the deflection of the beam.Have a look at the attached figure. Obviously the deflection was reduced after applying FRP. And this is not even FRP sheets or laminate, its just uni-directional CFRP fabric. My guess is that it increase the Eeff of the beam where FRPs are...

Hi, Does anyone know a code or a guide to calculate deflection of an externally FRP strengthened RC beam. More specifically shear strengthened by FRP u socket or wrapping. Looking around everywhere but having no luck. Anything close to this subject is OK so I can study them.

I solved it guys. Turns out Castigliano’s method is not needed at all. All I was missing was the information that torsion at mid is always zero no matter where the load is applied. Applied when Θ=Φ, MΘ=0 and when Θ=Φ/2, TΘ=0 to equilibrium equations and that’s it! But I still wander how to apply...

@retired13 Mb is the support reaction. MΘ is the moment along the beam which related Θ by quilibrium equations. And system is not symmetrical, the load can be anywhere on the beam. I'll try only considering the part between support and load.

@rb1957 I will use Abaqus after figuring it out in more theoretical level. @retired13 I was imagining something like U socket support at each end. U socket walls will restrain the torsion but still allow it to rotate by flexural moment. So I simply eliminated Mb support reaction from all four...

I tried eliminating Mb components but it's wrong apparently.

Both ends are restrained for torsion of course. Only pinned for Flexural moment. If you saw the calculation for fixed condition it gives perfect results. Just eliminated Mb by removing Mb components of those equations to make it pinned but getting wrong results.