Question

For the structural system shown in the figure determine the value of the deflection and slope at point C, apply the virtual working method with unit load

5kw/m. C B A 40 KN 2.80m 3.00m pom 5.80m

Answer 1

- 5 kolm IS B *3m. A с 2.8 m 40KN © To find deflection at Ĉ by virtual work method apply unit load oto of 1kN (1) deflection at 'c' is given as Yc -S Moda El foor CB 604 4.42-8) measuring from'c' 40 a 1.x m for BA (2.84 x 25.8) m 40 x 5(x-2.8) (x-2-8) 2 m = 1x so yc = $ 140x) (3x)dx (40 x) (-2)dx + x[102.5682.95€ EI 12.8 ET

S. 8 Y c = 15-40 x² dx + (-40x2+2.52(-2-839.]dx 7 E12 28 Yo te 28 (-40%?dat JF-402+2.5x+19.62 -14 ? JETORP2 '13 2.8 3 + -40%} + 2.5" +19.623 3 9- 2487.86 CKN-M3) E (kN/m2). I (m) (m) Ans b slope at 'c' is find by applying unit moment at free end 'c unit moment 5 kNm KN А B k -3 m 40KN tom= IkNam k ☆ 5.8m

Seation CB (oux &2:8)m n = More 40x m = - 1 KN-m For secticon BA (2.8L245.8) + Myce 4ox - 5(2-218)2 403 2.5(X-218) 2 imz I KN-m So slope at & is Go mmar I EI Ac = EI -218 5.8 (-1) (4090dx + (-1) [40x- 215(2-21852] dze 125 218 fc = 1 EI 75.8 40x dze + f tox+2.52241916-142 bles 2.8 - 4002 local EL + -4022+2.523 + 1.9162-1472/518 2 2 3 2 to 2.8 OF 650 -3 (kN-m) EI radian fKNfm2umf)