Question

3 Figure 3 shows a statically indeterminate Wo structure. Using the integration method together with elastic curve theory, determine :- A a) Equation of the shear force. [3 marks] bord b) Equation of the bending moment. [2 marks] - L- c) Equation of the slope [3 marks] Figure 3 d) Equation of the deflection [3 marks] e) Determine the forces at points A and B. [2 marks] f) The slope and deflection at x = L/2 [2 marks] Note: No marks will be awarded when using positive shear and bending moment methods.

Answer 1

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we have to apply compo consistency concept A support A for which we have to calculate Deflection at A The Given Loading pattern cloesn't has any empirical Relation to solve it tience Reshaping the Load wo Hence changing the Load with its Modified equivalent Load- Triangular Load JILLER - Uniformly Distributed 1 1 1 1 1 1 LOO wo wie - NL - RAL3=0 30E QE 3E] Triangular UDL Uproard Reaction Assumea ороолол Downwasa 120 E -11 NL =) RA = L > RA -11 xhL 120 Tzone 40 I negative shows Assumed Direction is wrona)

Hence suuctue becomes INL WO (2) equation of shear force t ho Veress line ts (nox) (c)-nor ЧО At section kore mor] I wore Vick)= linh we would NL nok?) took UDL Triangula Load equation of moment: Mere Rase (hox] v] [eg] - noe? MCR) = 1 Wolk tl wor wo ī & Distance of Cenuoio 3 from section.

(C Equation of slope: using Double integration Method Eld²y = MC alrea Integrating once- El ay to w ser two Rey - Worstai EJ Cy)= | NL K3 + wors-wore uo6 DOL 2u Boundary condition Atr=0 y=0 Atr= L y =0 At K = dy=0 ak using condition in K=O y=0 EDCO: O +C2 C2=0 K=Ly=0 E] Co= 1x NLY twole - WOLY tou 120 2u uo o d will tOIL

Ciz – In find NON putting values of C & Ca we will Requied equation't © Ez dyshock?s moeten word deurs equation of Deflection: 12OL 24 ette E] Lauo El dy = I [ 1 LR3 +wors - woah - a wr] =y I hire 2 © {fy=0 RAARB= √ [no] [L] RB = WOL-RA WOL + [ W now [RB= 31. nad Hence forces At Point A & RA= -|INL [Downwand] е зі сомалар СО Point B uo uo

(6) Deflection at re= Į Put r= ļ in equation & slope Also for slope & Deflection LLLLLLLLL cu un 1 adulte two le-No (4) 3 2UL dowe 4018. Wow would nous] EJL 326 384 1920E] J -Deblection:- WLX 120 2uo 2 hox] -ll wie 3840 E]