Question

Instrucciones Se tiene una viga simplemente apoyada de acero W12x26 según el AISC 360-16, que tiene una luz de 1.50 m y que soporta una carga concentrada en el centro de la luz de 15 KN. Para esta viga: 1. Calcular las deformaciones por cortante mediante el método de Castigliano 2. Calcular las deformaciones por flexión mediante el método de Castigliano.

There is a simply supported vean of W12x26 steel according to AISC 360-16. which has a light of 1.50 m and that supports a concentrated load in the center of the light of 15KN. For this beam

1: calculate shear deformations using the castiglian method
2: calculate flexion deformations using the castiglian method

Answer 1

page- IS KN somm K 150 mm fb 2 and . for AISC 360-16 we have , E = 2x 105 mpa 2x103 Nimm? we have a = 77200 MPa I 77200N/mm2 - Now, as per castigliano's theorem. # du = 4, Where is strain 2 energy of beam. a and A is the deflection or say deformation due to application of Load apli, na Annon We also know that strain energy can be due to axi al force , Bending moment, (flexureri shear force a in this question ble are only concerned With shear deformations and flexural deformation so, ine will calculate only shear 6 strain energy and flexural strain energy. gorz Kvz du take k= 6 Ushear = 8th J2AG , 5 (3u² drl - Ushear = J5AG 2 cha c oce et de la 1 - 0 A = area of crossection of beam and 6 = shear Modulud of beam

Page 2 flexura flexure = - p m 2 dr I LEI m= Bending moment at any section V = shear force at any section E = young's modulus of elasticity I = moment of Inertia of c-s of een beam HOMMUHAMMA Now, we have a A Cine area of crossection of beam) = 12x26 Let say 12 and 26 are in mm" hence 2 A = 312mm 750mm / 15KN. 750 mm 46 - = I 12x26 - 17576mmy 12 115KN X2 5KN Cºnso | ty. -750mm- calculath of flexural strain energy Uflexure = 1 m2 dr =s med t (me by REI beam - AB

as por castigliano flexural deformation. - ap J JP ET Now he can calculate defor moth by taking two parts AC and BC We can also twice the flexural deformation dur to strain energy in. part AC only. therefore flexural deformation - JAC M = mx xp = VAR Om - 705 = 7.50 750 flexural de formth = 216.5n) (705) du 2 (2x105) (17576) calculate it you will get answer shear de formation similarly to Ushear du J AG deflection due to shear - du 6v de OP AG asper castigliano xix. = & VA . d v zo VA

page-4 ce whole equatson for Shear deformation becomes Zero. 9. there will be no shear de formath 11 LITER