Question

Draw the Shear Force (V) and Bending Moment (MI) diagrams of statically indeterminate beam shown in figure using “Force Method”. The (roller) support at "B" settles 35 mm. The moment of inertia is given by (1) for regions "AB", "BC" and "CD"; however it is equal to (21) for the region “DE”. ("B" is the roller and “E" is the fixed type of support). [The flexural rigidity: EI=40000 kNm] 60 KN y 10 kN/m A - Tu (21) 1.5m 11 1m 3m K X *

Answer 1

o as Sol The roller Support at "B" settles 35mm. Degree of sotie indeterminacy - 4-3-1. Take "ve as Reduandent Pore and the Reduandent shown bellow. ཡིད 10 kN/m !... ) he Reduandont structure with given loading structure Gokn A CI (F) (2I) t + + * 1.5m 1m Im 3m B E (21) (I) (7) c (I) D ť * * 3m im im. 1.5m Reduandert structure with unit vertical loading Member / origin I limits EI M m A AB 0-115 1 1xfr-1-5) 1 0 BC 1.5-25 A CD A 2.5-3,5 1 -60(1-2.5) 2-60(a-2.5) _9x(n-1-5) 1x(2-1-5) DE A 3.5-6.5 - 10 x(-3.5) 2

3.5 -box(x-2.5) (n-115) du ALS Mman EI EI 215 605 + X (artis)dy REGO -60x(x-2,5) – 5(x-3,5)) ZEI 3.5 AL 50 -7605 -8005 BEI EI SEI displacement due loading. & ffantes) Si 31.5 = JE (*-1.5)da EI liš EI 2.5 6.5 *S (2-1979 da ZEI 3.5 Sirp 1 +7 +39= 133 GEI BEI 3EI 261 As a displacement at Node due to Settlements As3 -0.035m EI = Hoooo kam As -0.035 x 40000 . - Hoo EI EI P1x & Compotability Egretion? Fx S= 6541 >> V3 x 133 -14ool honey- -8005 881 GEI

VB 2 -315x = -9585 -18.017 kw indicates downward direction) 532 (Negative s fgcozy Vet VB = 60+ 10x3 = 9 E = 90+18.017 = 108.017 Kn EME=07 Vzx 5 - 60x4-10x3² +Me=o 27 Me - 375.085KN. shear force diagram (w), E - 18.017 (Eve) 78.017 bo 108.17 Berding Moment diagram A c B tvel Eve) 196.034 - 18.017 (-ve) 375.085