Question

Problem 4 (25 points) An overhang beam with negligible weight is loaded as shown. Knowing that the flexural rigidity of the beam is EI = 100 x 10 Nm?, (a) derive the elastic curve for section AB of the beam and (b) determine the slope at supports A and B. 10 KN 5 kN/m M 40 kN-m B 4 m - 2 m (a) V = (b) A = es =

Answer 1

Cioen do to : 10Oxle Wm2 EI= drow the the body diagram of in shown System the as figure baloo lokp БЕРIm Il 9 to kom A I po Ay am Bola Í 2m Ay st E Fn =0 Anzo T CEMA π =o Il Ayx q tlox2 5 X 4x4 t 40 Ay 15kw (9 - tp Efy=1 Z 509 710 Ay t By ist by : 30 Ay= 15kp (9)

moment find the Bending equation for AR = 15m 502 Mor = Ayxat 5 X z Xn 2 2 from bending moment eguation ЕТ لاہے 150- 5n2 dna 2 integrate the above eguotion EI du 15 2 2 crid nh t cl an 2 EI du 5 nata an -0. again integrate th above eg otion, EIU= d a 3 oly Elt tant Cz EIVE 15 n3 - 6 5 ne tcin + C2 24 I EI OG 1 5 24 at tanter elastic cune

Where Ciť z ar constants of in tpralon Apply th boundary ondition in eg Jso put the calu in eg 11 EI(O) = 15 ход 5 tcixo + C2 2=0 apply the second boundong ondition nizam, in 11 €1(0) 158 93 Х ee + CIX & to 24 디그 -26.6666 67 Soi equation of elastic cune for AD becomes vend C 15m3 EI nt 6 29 - 26.666667

from ego slope equation for АД ist do Jn 1 1 EI 15 m2 N 5 na 2 - 26.666667 put n = in ea (ell to find the slope ot point os given QAS dom) a zo dos 15x02 Exo 3 - 26.666667 2 OA= - 26.666667 Ер m ). EI OA A- 26.666667X 103 am? 100X106 sme DAS - 2.666667 Ylo red Slope of A point

a in pal qm Similarly eg point B nem to find the slop. 'du IN EI given - 15892 5x4 ² 26.66667 2 QB = 40 knmz ЕТ OBS 40x102 (m2) (m2) 100 X 106 axlo rad 11 slope B point