Question

use castiglianos theorem

10- Determine the reaction at the roller support and draw the shear and bending moment diagrams for the beam and loading shown. Ans: Ry=5P/161 L/2- 1/2-

Answer 1

Р to RA H 959 11 591 11119 2 BPL Here 3 number of Reaction number of useful oq 2. a Mimber of Reaction < number of sekel equation This is statically Indeterminate structor. of So we use comptability ean in the form deflection. Total deflector a zen

Ist cale (ave to downurod kole) 06 Perabolo Straight line sue to point losed at cantilever beam Formula & seflection (Y) LIL3 361 Slope (0) EL Apply this formula + Ya Adresword P(42) ² tomo (5) SED T = (tono) (4) Tor Small versation P23 + PL 3 24ED IGEI 2923 + 3 PL? 48 EI 5123 48ER 294 case [ due to upward force) 3 ord L RA Dupwaar RA (4) 3 RAL 3 3ER BEL For total deflection res 5P13 БР RAL RA If 48 € BEI

raw the She a fonte mende 11 conside, the (SF) xx Section xx hom the left side 5P (Sf)e-*= TE 5P. - P - АТР Draw the Bending moment X sign comention eig 2 5P X Eve A vé (BM)-2 SP lagging Beading Нет" Banding (B) 2.0 (BM) = 1/2 16 5PL 32 RAI

(B1). RAXX - P(x-4) 5PL SPL IPL 3 PL Find Benthony moment to Raxu - P(x-4) (BH)x- 5px - Px + PL 5pm - 16px PL 2 1 lipn A PL 768 7 84 0.72.0