Question

60 in 150 lbf 5 lbf/in 3. The cantilever shown in the figure consists of two structural-steel channels with a weight of 0.833 lbf/in. Both distributed load of 5 lbf/in and a point load of 150 lbf are applied to the beam as shown above. Using Castigliano's theorem find the deflection at A and compare to the deflection calculated using the superposition method. Include weight of the channels. (l3.70 in4) R A simply supported beam has a concentrated moment MA applied at the left support and 4 a concentrated force F applied at the free end of the overhang on the right. Determine the deflection equations in regions AB and BC.

Answer 1

Given that Faten I 2.0 in4 E 20. o MPsi SingCaigiano heore tigut treat the end teacex as vaiadle F Aho in e -Fx 2.91X M-Fx 5-833. 2 60 S(Fx+2.914x)(x)dx M ET ET 무- KPd (150/6)2.a4)(60) 30l0) (3-70) 2o. 182 irn Cin the ciecon o the \50 1b borce) -O.182 in

By Superpoiton methad deblechion at A Cwtat 8ED St 1so(60 83 30) $2 O 182 ir) Fao boh -the mekhodk MA beamg (region azoand BC tor thi bea with a lo (asith by SupeosiHen mthoa, aa (x2-aattnd 1393eRapat A(221) Far (d Fax MA

MA s-x F- a(3x-1)) Mal (ud)E-A) Aa(o-A)) 6EI 6ET