Question

Chapter 10, Concept Question 058 Which boundary condition is true for this cantilever beam, where the origin is at A? 18 kips 200 kip-ft . B с 6 ft 9 ft deflection = 0 at x = 6 ft slope = 0 at x = 6 ft deflection O at x = 0 slope O at x = 15 ft slope = O at x = 0

Answer 1

58 18 kips 2ookip-ft A B Line Diagram, BA A B A 'Deflected shape. As the loading will cause ofward deflection; there will AA value and QA value as shown. However support c is a sigid support lie Fixed support); it is not down ward from its original position. Hence Ac =0; due to sigidity of the support, Loc=0 / re there will be no any sotation at support going upwardor moreover ci A taking section from choosing Now, when A as origin we are as shown 0ܠܠܢ 2

(Slope - (Slope = o at a=154 : Answer. other options are can eliminate of watching from deflected shape of beam,

flowever we will find to recheck and o: Moment at a foo from A in AB Maa 200 kott In span Be Mx = 200+ 18 (4-6) 6 <asist 362 EI 200 Er с Ā oft B got let's solue defleefion and slope using Moment method. area A "Able Able = Deflection at B with respect to e fangent drawn from which is horizontal) So, Able z do = AB at x=oft- Dole Moment of prea of M about B. between ΕΓ B and C. ABl. = & Cameo + 32) x3 x( 3 x( 34 362 + 20) 70 362 ET 200 EI

Ople Slope at Ble a= 6ft. is Oble Slope at B with respect to & fangent drawn from C. Area of in diagram between Bande Er B 200 362 Oble x9 tc Er A FOBIC 70

Similarity are can find and o at other locations Note- for a Cantilever beam; it is preferred to use Moment - Area Method to find A and O. A this fuick and easy method to find Aando for cantilever beam. "J very

2ookip-ft 59 A oft 6ft B 8А AA Catetelling Deflected shape A Slope = = 0 at x = 15ft/ Ans. Other options can be eliminated by watching deflected shape flower calcolate deflection at u= 6ft Using Moment area Method 200 ЕТ C A IB ABLE TOA Deflee tion at B with respect to tangent drawn from & (which is horizontal) Moment of Area B of H diagram about B. Cable ET

8100 Δg/s 200 EI 200 yox ΕΓ tive sign means upward deflection, Ao = 8100 to at he 66t. EI • Atu=15ft; Oc= slope at c = 0. . Atur oft; OA ? (let's find OA with Moment Area method) dale slope at a with respect to tangent drown from e Cie horizontal). So, dale - OA A B DAT PALE M Area of t diagram between A and C. dale 200x1540. EI Snelgrily slope and deflection at a=64 hat can be found (s and to).

can Moment - Area Method find I and o at others beam; Similarity are locations Note- for a Cantilever it is preferred to use to find and O. de this į a very fuick and easy method to find Dauda for cantilever beam, ЗоkN B M Deflection so at xeo a Answer, OB AH Again use Moment Area Method to recheck; in the Same we solved eallar problems Eau OH mannes

1 40 kib-ft ID goff! B 69 666 H А > se Deflection o, AB de at x=0 Answer, को AH or B M2 TRC 79 A 12 & Fu=0 RA+ Re = W0 EMA=0 (: support A is hinge resist moment) Rex d - we we xe - Rc = it will not Wil > RA = 2 we.

3. Convention Sign Thic B (4) Re fagging Hogging Moment as-ive RA=3 we 2 we moment as tive 8. Mx= RAX - wx x x ocas Mx? 3 wer wa? 2 Æ Mn = - wx2 + 3wex 3wla I Aus