Question

4. If E - 200 GPa, b = 1.2 m, L = 4 m, h = 2 m, and M = 1 kNm, determine the maximum deflection and slope at the supports. < Beam> N M PDF 4 m <Cross Section > Z 2 m 1.2 m

Answer 1

M B 2=4.0m By AY given 2m L = ym b = 1.2m 1.2m h = 2m M = I KNim E= 200 Gpa Step!! Defemine support realhom Ay and By Eff=0 -( Ay & By=0 EMA = 0 Mt By x L=0 M =-By xL By AY = - By L Step 2: M M x I M I

Ma Bending moment at Mac = Mx-M I -(2) Mac = M 2 - 1) Step3! EI chy Mac d22 = EI di M( 2 - 1) dx2 I dy dx Mil an t-x)+c, M x ²) + G x +(2 tb ( EIY 23 62 y so G=0 at a co at x=2 o= m m3)+52 "1-4-32%) +42 in the CIXL

С. ZW 3 7 + Jur 3 І тур - ті. • 1 ( t -*) + т. EIY А. Step 4! Slope cet A , то EI OA = 0+ ML 3 хаіх Qaulxh ML РА ЗЕ. 3x 2 рехI T= x 1. 2- со, 8 mУ exp" mmЧ . I 4 xio 2 3x 20e7163 x 87р ! 8.33x10 9 rad

Step 5: OB at x=2=um EI OB = M ( 22 - 2) + 1 M2 2 + ML 3 --302 +212 - 6 ML 6 EI OB OB - ML 6EL 106x 4x1000 6x200x10 x 8x10" OB = 4. 167X10 9 sad maximum deflection dr Step 6! To Determine O= ML x2 22 - 2) at ML 3 x2 4 -->) + 3 2x 4 05 0.12522_2 + 1.33 a = 10 685m

Ex = nta - :) + ML. 3 мех w_589° зх. ) ) J EI Гrt thаt - нача*)] + 2 = 7 (-). 2 203+ . 2467) şio 9+3 2оо хоро хір" Sh: 9 I may х/6 mm І.