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Unformatted text preview: and L ' \ :: r / ..... .£:t-['-('L D IT·. z: () ~ h ' '------ .i->: N. :i'- \ R~ \ -... ), ¥ , :", Lt--A '1 ~ - MA i \ ~ L =- 0 ~ kll ': '~ L ~ P l1. LL 1 - ::. Q ~ M It':;"- 1.. z: ~ ~ 2.. 1.. Fig . 2A . Cantilever with point load P at end. F or the s tructure in Fig. 2A, c onstruct/draw s hear force V(x) a nd M oment M ix) d iagrams. ru rz.,; !.j. V- - .y,' ~ (I ~ M(1)l 1 : - 4 ( L - )1 )=0 ~ \ f ( y. ) 0;: 4 ( L-'lC ) :.. ? - ~ 1 Z: M " CM- ~ Y'- ~' ..J- ) ;;; - kC'i- ) - _ _~ v ej ) i F -:.\1 ( "!- ) ( L - , z, ' --( l - '1)7 y Shear force V(x) diagram (5 pts) 2 =>~ ( ~ ) ; Moment M(.\:) diagram (S pts) v ~) ~ ~ • , i il L­ ·~""' ----"'· L,. 7 - - "i )t 2(b) 10 points D raw t he s hear force V(x) a nd m oment M (x) d iagrams for t he c antilever beam in Fig. 2B w ith m oment load M l=P*L. (construct FBDs here) Determine reactions at Wall in terms of P and L '. F ig.2B . Cantilever with moment load M1=P*L. F or the s tructure in Fig. 2B, c onstruct/draw s hear force V(.\:) a nd M oment M (x) d iagrams . C \"\ ,.,.. :J ~ J !Vb ) L F · : :.0 - - \/('1. ) - ~, L H )l C + <>-- \ /t..,. ) ~~\v+- ) -..4 Shear force V(.\:) diagram (5 pts) v\ . r , M ('It) ~ ""';> \i (~ ) ~ 0 -::- D : . - tv1 ~ - \v1 ~ .~ - F'I, Moment M (x) diagram (5 pts) - . -.._~ l.. . X 2 M (~ ) 2. Problem 3. (20 points). Chapter 7 (Like Problem 7.7-18) A steel cantilever beam ( E = 400 GPa (i.e., 40031 09Pa) and v =113) o f rectangular cross section (width b= 25 rnm, height h = 120 mm) is loaded by a force P that acts at the mid-height o f the beam and is inclined at an angle a to the vertical (see figure). The force P and the angle a are given such that P>O and the angle a satisfies 90 ">a >0. The length L satisfies L=10h. E = 400 G Pa and v =113 p. -, 0_ r' t J I Y y J) II Cross Section b= 25 mm & h = 120 rom 'fI,. = p ~ ~ / I.'-----c ------------Jl~l__x p S tress Element ~ 1 ;:' P t .JO 0\ A=bh ;. ,1 .::;. L~> The axial force P and the angle a are given for this problem. Even though this problem statement has numbers and data in the' "L statement o f the problem, determine the methods o f solution below w ithout the use of a calculator. You are free to use numbers as you wish in setting up and giving the method of solution, but avoid using a calculator to compute actual numbers . -- Give the method o f solution and equations for determining the maximum shear stress 't max in the bar. Give the (x,y) locations where the maximum shear stress ' t max in the bar occurs. That is, given the axial force P and the angle a, how do we find out what the maximum shear stress 't m a , in the bar will be? What equations are needed ? What is the method o f solution? [As part o f solution, you must show x-face and y -face points of stress element on Mohr circle diagram for this problem.] lSI '\)e:\--~r V'oAA' ' A.L F R D rI\ ~~' 6- ) ; V & ) -- ~k. c,v.T M i r<t.:'): U p t4&')...
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This note was uploaded on 09/18/2013 for the course AME 3143 taught by Professor Staff during the Fall '11 term at The University of Oklahoma.

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