Question

5. use the force method to determine the reactions at the support draw the Shear and moment diagrams. Assume A is fixed and B is a roller EI is constant Ау Ах Ma By K K ft.k K 15k А 서 3 + 10' 10'

Answer 1

Soin 15K --> + - 1 + 10' 22 - Step-i Cololate degree of static Indeterminacy Denon DSI - No. of Total Unknowns - No. of Available equations of equilibrium DSI 4-3 DSI -Step-iis Identify redundents of the Stellcture. Redundents should be selected in such a way that after removed of redundent, st eucture must remain stable... 115k TRO Step-u) Remove all redundents and make primary stellture. 15K Li L2 PL ΔΙ Now ЗЕТ 3 15:10 PLE 2 EI 158102 3 EI 2 EI Sooo ЕТ 750 EI and Ag tano = A - Latano CS Scanned with CamScanner

and for Small angle tano u o A2 LGO 42 = 750X 10 EI Да 7500 EI - = > So, over all deflection due to lood at point B' is - A+ A2 Sowo ЕТ + 7500 EI a 12500 ET • Step-ciu) Apply redundents on primary stencture (without looding), one at a time. IN RE A = PL BEI Rex 203 3 EI 8 coo RB 3 fI A" Step-(V) weite compatibility equations correspone onding each redundent. to Scanned with CamScanner - At Al = 0

12500 EI + 8000 ЗЕТ RB =0 12500 3f RB х All EI RB = 4.688K n. Step(vi). Now Calculate other reactions using equations of equilibecium. 15k MA Ax=HAT RAZAy .RO = 4.688k Now Efx=0 ch Ax {fy Ay + 4.688 - 15 Ay = 10.31k رأة - | Ez =0 E MA=0 MA + 15 X 10 - 4.688x 20 MA =-66-24 ft.K h. Scanned with CamScanne

Step-wil shear force Diage am. 15k ISK 15K (+) В + + B (-) 13 RB 4.68K 4:688K 4.688k 11 15k 10.31K 10.31K (+) B 772 41.688K 21.688k Resultout SFD Bending moment diagram: 115k A B HCM 150ft-k * Primary stenctuel with Point Lood. +/ + 93.7644-K As 4.688k dll * Preinary Stencture Subjected to RB 11 11 Isk 5.45 46.88 fit-k (+) 56.24 viven peoped conti levele, ft-k Resultant BMD

* Calculation of point of zero moment. But 15k List B А: tx- 14.68K at i distance from point in 15 (10->) - 4.688 (20+2) = 0 150-15% - 93.76 + 4.688% =0 150- 93.76 = 10.3)x YOU ( x = 5.45ft a EE and at point Under 15 K M = 4.688 x lo [ = 146.88 P4-K Scanned with CamScanner