Width b as derived in class re chapter 5 d rawing 2 p

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Unformatted text preview: in class re chapter 5 . D rawing ( 2 p ts), method o f d erivation ( 9 pts) . You must define all terms including Q(y) to get fuJI credit o f derivation. Indicate bow and w here you are using "limit analysis". Note: Clearly showing the use o f "limit analysis" in deriving the shear stress 'txy(x,y)formula is worth 3 points. Clearly showing the use of integration is worth 3 points in the method . D rawing (4 pts): M ethod o f D erivation (12 p ts): -:: i l l- f V o Answer form #1 Formula in terms o f V(x), Q(y), I, and b Answer form #2 Formula in terms o f V(x), A , It, a ndy 'rxv(x,y) = - (/ ( f ) 't.n,(x,y) = At what value o f y does 'txy(x,y) have its maximum magnitude? Maximum magnitude 'txy-nun: {x] o f the shear stress 'txy(x,y) (in terms o f V(x) and A )? y= 't.n'-max (x) = Yr 4 ;J/' /; ( Ipt) ( Ipt) (1 p t) (1 p t) Problem 3 . (20 points). (Like exercise 5.5-7) boy girl P Fig.3A P ,L 5L L=10h b=6h • 5L . 5 L Fig. 3D S tress E lement 5{;;= - . A seesa w C B ~ Conside r Fig. 3A. A seesaw weig hing q=PllOL Ib/in is occupied by two children, each weighing P lb. The center of gravity o f each child is 5L inches from the fulcrum at C. T he board is 20L inches long, h inches thick , and b=6h inches wide. Consider stress element w ith zero angle orientation as shown in Fig. 3 8. Given that L=JOh, determine the maximum bending stres s O'x-m ax in the board as a function of P and h . And, at what point (s) (x,y) does this occur? L F~ .\ :: I<- l! o- P p - 4' Z OL ~ R~::. 2 ~ + i.. 2,. OL . -= 4P 0 ::: 1 d 0 }./< (1­ ) ~ 1- ' -- 0 -- ",J"' ~ '. 2. M ;':- 0 - 2 M ~ 0 \-A . - 0 i :: = ~)( Me) ) • \ f ( -; ) -) \J (i- ) : - '1 X ~t.. ... M ()l) .: -+- "2.- - ~ - '1 y.. - \J (.,., ) k (t) + P 'f -S"L) = _ \' '(. . S L) -­ ~ ~·I 'l...= "2..- ~ + 'l( '"L '2. 0 0 .., ~ .--,- r; 1­ y:. 0L =) /,r lu L o / I ~1 / 1 - \'l.-- 3 - t ~y - !O P l ­ - p ,)( 1 tv" (1- ) - ') - r x :rd; :: '/. '" 0 \ 0 l, ­ OL P ,, 1­ 2. 0L Problem 4. (20 points). (Like exercise 5.4-3) A polyethy lene pipe with outside diameter d = 1.2 inches designed to carry chemical wastes is placed in a trench and bent around a quarter-circular 90 o be nd. See Fig. 4. The bent sect ion o f the pipe is L ft long where L=25rr . Determine the maximum compressive stra in in the pipe created by the 90 o bend. Determ ine without use o f calculator: Fig. 4. ! t q C?i d l; )...... .._ . ct L s: f) - 2 S it - ~ ?i ~o I ) - SCJ n/-z., ~/z.. - - ~ - D. ~ ~ z, tf- J= -~- <J. b 1 "" 2,... I \'­ - 50 o. oo \ P roblem 5. (20 pts). 5(a) 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. 5A with point load P a t e nd. (constr uct FBDs here) p x=O v x =L M( 't ) ~ - ~~* Fig. 5A. Cant ilever with point load P at end. For the structure in Fig. 5A, construct/draw shear force V(x) and Moment M (x) d iagrams. " :=: - ~ L+ ? Y Moment M (x) diagram (5 pts) Shear force V(x) diagram (5 pts) " V PL -­ - ,/ 5(b) 10 points D raw t he s hear force V(x) a nd m oment M (x) d iagrams f or t he simply s upport b eam in Fig. 5B with '0 distributive load q= P /L. . (construct FBDs here) ~;pl ' ! 111 1 L A x=0 .. A ~ x=L ... I B Fig. 5 8. Simply supported beam with distributive load q = P/L . 'K~ For the structure in Fig. 5 8, constr uct/draw shear force V(x) and Moment M (x) diagrams. Shear force V(x) diagram (5 pts) tf) ~ (?- Moment M (x) diagram (5 pts) fJ,(Y'A f L( e ~...
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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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