Question

problem 4

Use the double integration method to solve the following four problems. In each problem you should set x = 0 at the left end of the beam, with x increasing to the right.

Answer 1

® Double integration method :- fage-1 Oog kek 1.5k k— lzir Given that, E=1600ksi and, I . = 864 int Reactions :-

Efy=o » Agt By = xq XOo8) + los Agtby = 5.lk IMAJT=0 A -15x18 + Byx9-6x9x0.8xx) co » By = 5.4 K so, Ag=-0.34

Page 2 - consider à section xxx at a distance à from support k as shown in above figure. we know that, e2dy - Bending moment at ** 1 / RM * ED s ez ordea = B.MK = Ay [x] - (4x2x0.g)* [X-*q] +Byx [x-a] dx2

>> Ele -0.3 [x] – 3.6 [X-6] +504(2-9] Integrating on both sides woor.toa → ER dy dx = -0. 3 = 0.3[0° - 3-6 [X-4° +54 [xam Sa - tao Again, integrating on both sides oort.d then eĉ.y = -0.363 3.6 [1-6] 5.4 [x_q}} 2x3 2x3 tciato » here, C, and Cz are integrating constants by using boundary conditions this values can determine. condition , at x=0 (ie, at support A) y=0 then from equation > EDO : -0.3 x ål bracket term 6 C003 is -ve then whole term Zero Copa so - 2x3 +5o 4 0-97370 2x2 ta (O) to 12-01

page-3 Condition at a=a', i.e., at support 'R', 9=0 then from equation , EIO - -0.3x - 3.6* [9-6] + souxta- 2x3 2x3 +C, xq 3 0= -0.3493-3633 -taci 2x3 – Ci= 5.85 Now equation o becomes Ez egy iga - 02 C° - 9., [.63*7 s14 Expl +5.85 → and equation © becomes 22.4 = -0.35078- 36 Psiq (x2978 2x3 +50854 → equation ® is called slope equation © is deflection equation, 2*3 9 and equation

To get slope at A substitute a=0 in equation Page-4 ③ EI (A)= -0.3xCom 3x02 - 3.6 to 4 SACO Logo + 5.4 tsogs » ERCOA)= Soss OA = 5.85 ED S.SS 1600 x 864* (123) TON=0.00061 Yodiang x= 18' in similarly, substitute slope at a. equation ® To get Ez 2 ) = -0.3x12 - 206518-07% + 5.4 [is que Op = 83,25 togs 王 -83.25 1600x864812~2 Toco -0.00867 radiang

Pages to get deflection at 'c', substitute X = 18 in equatione ofil) = -0.3x - 356! E-36 [18-673 tsou [18-93 2x3 2x3 2x3 +5085*18 El (4c)= -99166-1036-8465601 t 105.3 Acs -567 S67 E2 -567 600x864X12-2 = -0.05906 ft AC = -0.708 inches (-ve sign indicates downward dellection)