Question

1. (19 pts) The cantilever beam is subjected to a distributed load w (unit N/m) as shown in the figure. (a) True or false: If the beam is slender, i.e., length, L >> thickness, t, it is reasonable to neglect the shear strain energy, Us, compared with bending energy, UN. ) (b) What are the reaction forces at supports A and B? (c) What is the moment as a function of location along the beam AB? (d) Use energy method to determine the deflection at the midpoint of AB, > 60 N/m В 8m — 4m -

Answer 1

QUES a) True, yes we can neglent shear strain energy if the beaun ir slender L b) 8N/m À Z B - 6mě om um EMB=0 - RAX12 – 118*60*[ {x8 + 4] - 4x4x60x{ *4=C RA X12 = 1600 + 320 Кө а 100 м Efy=0 RA+ RE = < x 12*60 cs Scanned with RB = 360 -160 = 200 N CamScanner

AD c) i) Bending moment equation fort span taking support A as origin - Raxal - 3-**4*60*27 () B.M B.M = RAxa - 1.250x² upto point D. range of a d=0 to 8m ii) B.M equation for span BD taking support B as origin B.M - RB x2 - x 60 nx x 60 do X I Ź = 200xx - 2.5x x3 ra range of a 0 a=0 to um = 0 to upto point D d) Using to Energy method (unit bad method) determine the deflection at the mid- sspand wid? AB. CamScannd

applying unit wad at 5 por mid- e B 6M RA = RB = % member origin range on Mo_ WEL bg, origin M 91 auge 0.512 GEL ABAC A 0-6m RAxa - 1.25x² PEL CD - 6-8m Axa-1.25 1² 0.5x-1(x-6) 0-4m 200 xx - 2.50² 051X YEL BD B sine ormule. 7 M.M-da EL (16074- 1 15x?) (0.5x4).dou ( 2.5xu 60xx-1.252 31 (160oo-1:25 *)(0.54 - 17(4-6)) -de/EL. + "%(200*4 2.5n%)*(0.5**) cales ca Scanced with CamScanner

A = 4788+ 3420 + 1877.33 El at mid-span AB a £ 10085.33 Eli deflection ay Ics Scanned with | CamScanner