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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 'txynun: {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 5.57)
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'xm 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 5.43) 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 quartercircular 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.
 Fall '11
 STAFF

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