Question

Problem 2 Consider a simply supported symmetric I beam ABCD carrying a uniformly distributed load w and a concentrated load F as shown in Figure 2. Young's modulus of the beam is 200 GPa. F 8 kN 8cm 3cm 3cm 7 m 5 m 3 m 2cm W= 6 kN/m 6cm A D B 2cm 7TITT TITIT Figure 2 1) Replace the support C with the reaction force Rc, and using static equilibrium find the reactions at point A and B in terms of Rc 2) Using the boundary conditions, calculate the deflection of the beam (as a function of x, measured from the left support, A) in terms of the unknown reaction, Rc. 3) Use the zero-deflection condition at point C to calculate the unknown reaction, Rc 4) Calculate the final values of the reaction forces at A and B 5) Calculate the net deflection and slope at point D.

Answer 1

Sm 3 m f-8KN GHN/M RC 3rm Lut RA ) At peint A , Rex7ReXR 8X1s 422 RG = 120-12 P +147 7 267 -12 R 7 *ent St' RA = 5K -64+ 147 7 5Ret 93 RA - N 2) Kp EL

2 -MM A 0 middle point behucen ARB at dy Mat that boint M 7x37 2 +C dy dn (E e-lej ET 21-2 B 21-2RA + - M (7) [ 49 2E1 7 8A 721-RA) 2ET EI 3 63-2 8EI

RA- 5ets83 7 21-215R+83) /7 2147-10R-66 7EI - 1of-19 Fr EI C 5R+83 63 SED u41-1066-166 &ET F35-108) 2 SEI 19 - 1 0 dy -N t ET 7/-19-10P -N24 + 2 75 8 851 3) at c, y - O 9A3 MC = 24 KNm 2 - I 24 245- T38

S2a5-10P) 24(2) (19-10P1C) 8 # O 13475-490 R 14400 t (-15 96-8408) 521 1330 2 19 KN u) RA 5 Re ra3 7 5x1-9+8.3 7 = 13.21 kN Re = 207-12 R 2R17-12X19 3419 KN