Question

Beam ABC as shown in figure 2 is supported as fixed at A, a cable tie at B and a spring at C carries a uniformly distributed load of 72 kN/m on member AB and a concentrated load of 54 kN on member BC. Using the flexibility method and neglect the axial effects in the bcam, (a) perform the global flexibility matrix of the beam structure, (b) calculate the rotation at B and displacement at C, (c) draw the deflection, shear force and bending moment diagrams of the beam. Given: Modulus of elasticity, E of 200 kN/mm² and moment of inertia, I of 3.54x107 mm for all members. The flexibility coefficient() for the spring and cable is 0.15 mm/kN and 0.027 mm/kN, respectively. Cable 54 KN H 72 kN/m Spring < 8 m Figure 2

Answer 1

(T ! Civer Beam 92 lolm alle 54 KN Spin um x s t um am Giren Data; Mochiles of Elasticity & = 200 kw form Moment of Imentia J. 3.54x100 mm flexibility Coeffe of spring = 0.15 mg/kent = 0.027 mm/lot. Degree of static Indeterminacy: no. of Internal reactions = 3+1+1=5. no. of equilibrium Condition 3 De = 5.3=2 Hance Two Coordinates will be selected. (a) flexibility station Released Beam o su

Conjugate Beaut y $9 Pala 700 768 81/E1 576/EI cs sa Pe n el for The localings deformation in contratos Diemelor 6 AL- shear in Conjugate Bearn at a AL - PA - 768 AL & Shear at B in A'B't shear at B in Bc. ET JAL = 263 + 100 - 3 Apply cript force in Coordinate direction Conjugate Beam E22 = 2 + + 8 + 4 + 2 x + 1 2 + + 6 2 et

Apply Onit force in Coordinate Direction Released structure with onit load in Conjugation direction O Anjugate Beam B L x 8 = BEI Pflection at c and Rotation at B ARB GUIN 79 Kolm &= & S

72x 84 - 5.2mm [ 8X 200X3154410 = S. + S BEI LO) (-)-100 (. +1 s- 5.49mm. £, - Sits - 5.+ 5.49 E = 10.69mm Deflection at "." – 10.60mm &