ÿþb u d y n a s _ S M _ c h 0 9 . q x d 1 2 / 0 1 / 2 0 0 6 1 6 : 1 6 P a g e 2 3 9
F I R S T P A G E S
C h a p t e r 9
9 - 1 E q . ( 9 - 3 ) :
F = 0 . 7 0 7 h l Ä = 0 . 7 0 7 ( 5 / 1 6 ) ( 4 ) ( 2 0 ) = 1 7 . 7 k i p A n s .
9 - 2 T a b l e 9 - 6 : Äa l l = 2 1 . 0 k p s i
f = 1 4 . 8 5 h k i p / i n
= 1 4 . 8 5 ( 5 / 1 6 ) = 4 . 6 4 k i p / i n
F = f l = 4 . 6 4 ( 4 ) = 1 8 . 5 6 k i p A n s .
9 - 3 T a b l e A - 2 0 :
1 0 1 8 H R : S u t = 5 8 k p s i , S y = 3 2 k p s i
1 0 1 8 C R : S u t = 6 4 k p s i , S y = 5 4 k p s i
C o l d - r o l l e d p r o p e r t i e s d e g r a d e t o h o t - r o l l e d p r o p e r t i e s i n t h e n e i g h b o r h o o d o f t h e w e l d .
T a b l e 9 - 4 :
Äa l l = m i n ( 0 . 3 0 S u t , 0 . 4 0 S y )
= m i n [ 0 . 3 0 ( 5 8 ) , 0 . 4 0 ( 3 2 ) ]
= m i n ( 1 7 . 4 , 1 2 . 8 ) = 1 2 . 8 k p s i
f o r b o t h m a t e r i a l s .
E q . ( 9 - 3 ) : F = 0 . 7 0 7 h l Äa l l
F = 0 . 7 0 7 ( 5 / 1 6 ) ( 4 ) ( 1 2 . 8 ) = 1 1 . 3 k i p A n s .
9 - 4 E q . ( 9 - 3 )
" "
2 F 2 ( 3 2 )
Ä = = = 1 8 . 1 k p s i A n s .
h l ( 5 / 1 6 ) ( 4 ) ( 2 )
9 - 5 b = d = 2 i n
F
1 . 4 1 4
7 "
( a ) P r i m a r y s h e a r T a b l e 9 - 1
V F
Äy = = = 1 . 1 3 F k p s i
A 1 . 4 1 4 ( 5 / 1 6 ) ( 2 )
b u d y n a s _ S M _ c h 0 9 . q x d 1 2 / 0 1 / 2 0 0 6 1 6 : 1 6 P a g e 2 4 0
F I R S T P A G E S
2 4 0 S o l u t i o n s M a n u a l " I n s t r u c t o r s S o l u t i o n M a n u a l t o A c c o m p a n y M e c h a n i c a l E n g i n e e r i n g D e s i g n
S e c o n d a r y s h e a r T a b l e 9 - 1
d ( 3 b 2 + d 2 ) 2 [ ( 3 ) ( 2 2 ) + 2 2 ]
J u = = = 5 . 3 3 3 i n 3
6 6
J = 0 . 7 0 7 h J u = 0 . 7 0 7 ( 5 / 1 6 ) ( 5 . 3 3 3 ) = 1 . 1 8 i n 4
M r y 7 F ( 1 )
Äx = Äy = = = 5 . 9 3 F k p s i
J 1 . 1 8
M a x i m u m s h e a r
2
Äm a x = Äx + ( Äy + Äy ) 2 = F 5 . 9 3 2 + ( 1 . 1 3 + 5 . 9 3 ) 2 = 9 . 2 2 F k p s i
Äa l l 2 0
F = = = 2 . 1 7 k i p A n s . ( 1 )
9 . 2 2 9 . 2 2
( b ) F o r E 7 0 1 0 f r o m T a b l e 9 - 6 , Äa l l = 2 1 k p s i
T a b l e A - 2 0 :
H R 1 0 2 0 B a r : S u t = 5 5 k p s i , S y = 3 0 k p s i
H R 1 0 1 5 S u p p o r t : S u t = 5 0 k p s i , S y = 2 7 . 5 k p s i
T a b l e 9 - 5 , E 7 0 1 0 E l e c t r o d e : S u t = 7 0 k p s i , S y = 5 7 k p s i
T h e s u p p o r t c o n t r o l s t h e d e s i g n .
T a b l e 9 - 4 :
Äa l l = m i n [ 0 . 3 0 ( 5 0 ) , 0 . 4 0 ( 2 7 . 5 ) ] = m i n [ 1 5 , 1 1 ] = 1 1 k p s i
T h e a l l o w a b l e l o a d f r o m E q . ( 1 ) i s
Äa l l 1 1
F = = = 1 . 1 9 k i p A n s .
9 . 2 2 9 . 2 2
9 - 6 b = d = 2 i n
F
7 "
P r i m a r y s h e a r
V F
Äy = = = 0 . 5 6 6 F
A 1 . 4 1 4 ( 5 / 1 6 ) ( 2 + 2 )
S e c o n d a r y s h e a r
( b + d ) 3 ( 2 + 2 ) 3
:
T a b l e 9 - 1 J u = = = 1 0 . 6 7 i n 3
6 6
J = 0 . 7 0 7 h J u = 0 . 7 0 7 ( 5 / 1 6 ) ( 1 0 . 6 7 ) = 2 . 3 6 i n 4
M r y ( 7 F ) ( 1 )
Äx = Äy = = = 2 . 9 7 F
J 2 . 3 6
b u d y n a s _ S M _ c h 0 9 . q x d 1 2 / 0 1 / 2 0 0 6 1 6 : 1 6 P a g e 2 4 1
F I R S T P A G E S
C h a p t e r 9 2 4 1
M a x i m u m s h e a r
2
Äm a x = Äx + ( Äy + Äy ) 2 = F 2 . 9 7 2 + ( 0 . 5 5 6 + 2 . 9 7 ) 2 = 4 . 6 1 F k p s i
Äa l l
F = A n s .
4 . 6 1
w h i c h i s t w i c e Äm a x / 9 . 2 2 o f P r o b . 9 - 5 .
9 - 7 W e l d m e n t , s u b j e c t e d t o a l t e r n a t i n g f a t i g u e , h a s t h r o a t a r e a o f
A = 0 . 7 0 7 ( 6 ) ( 6 0 + 5 0 + 6 0 ) = 7 2 1 m m 2
M e m b e r s e n d u r a n c e l i m i t : A I S I 1 0 1 0 s t e e l
S u t = 3 2 0 M P a , S e = 0 . 5 ( 3 2 0 ) = 1 6 0 M P a
k a = 2 7 2 ( 3 2 0 ) - 0 . 9 9 5 = 0 . 8 7 5
k b = 1 ( d i r e c t s h e a r )
k c = 0 . 5 9 ( s h e a r )
k d = 1
1 1
k f = = = 0 . 3 7 0
K 2 . 7
f s
S s e = 0 . 8 7 5 ( 1 ) ( 0 . 5 9 ) ( 0 . 3 7 ) ( 1 6 0 ) = 3 0 . 5 6 M P a
E l e c t r o d e s e n d u r a n c e : 6 0 1 0
S u t = 6 2 ( 6 . 8 9 ) = 4 2 7 M P a
S e = 0 . 5 ( 4 2 7 ) = 2 1 3 . 5 M P a
k a = 2 7 2 ( 4 2 7 ) - 0 . 9 9 5 = 0 . 6 5 7
k b = 1 ( d i r e c t s h e a r )
k c = 0 . 5 9 ( s h e a r )
k d = 1
k f = 1 / K = 1 / 2 . 7 = 0 . 3 7 0
f s
.
S s e = 0 . 6 5 7 ( 1 ) ( 0 . 5 9 ) ( 0 . 3 7 ) ( 2 1 3 . 5 ) = 3 0 . 6 2 M P a = 3 0 . 5 6
T h u s , t h e m e m b e r s a n d t h e e l e c t r o d e a r e o f e q u a l s t r e n g t h . F o r a f a c t o r o f s a f e t y o f 1 ,
F a = Äa A = 3 0 . 6 ( 7 2 1 ) ( 1 0 - 3 ) = 2 2 . 1 k N A n s .
b u d y n a s _ S M _ c h 0 9 . q x d 1 2 / 0 1 / 2 0 0 6 1 6 : 1 6 P a g e 2 4 2
F I R S T P A G E S
2 4 2 S o l u t i o n s M a n u a l " I n s t r u c t o r s S o l u t i o n M a n u a l t o A c c o m p a n y M e c h a n i c a l E n g i n e e r i n g D e s i g n
9 - 8 P r i m a r y s h e a r Ä = 0 ( w h y ? )
S e c o n d a r y s h e a r
T a b l e 9 - 1 : J u = 2 Àr 3 = 2 À( 4 ) 3 = 4 0 2 c m 3
J = 0 . 7 0 7 h J u = 0 . 7 0 7 ( 0 . 5 ) ( 4 0 2 ) = 1 4 2 c m 4
M = 2 0 0 F N · m ( F i n k N )
M r ( 2 0 0 F ) ( 4 )
Ä = = = 2 . 8 2 F ( 2 w e l d s )
2 J 2 ( 1 4 2 )
Äa l l 1 4 0
F = = = 4 9 . 2 k N A n s .
Ä 2 . 8 2
9 - 9
R a n k
J u a 3 / 1 2 a 2 a 2
f o m = = = = 0 . 0 8 3 3 5
l h a h 1 2 h h
a ( 3 a 2 + a 2 ) a 2 a 2
f o m = = = 0 . 3 3 3 3 1
6 ( 2 a ) h 3 h h
( 2 a ) 4 - 6 a 2 a 2 5 a 2 a 2
f o m = = = 0 . 2 0 8 3 4
1 2 ( a + a ) 2 a h 2 4 h h
1 8 a 3 + 6 a 3 + a 3 a 4 1 1 a 2 a 2
f o m = - = = 0 . 3 0 5 6 2
3 a h 1 2 2 a + a 3 6 h h
( 2 a ) 3 1 8 a 3 a 2 a 2
f o m = = = = 0 . 3 3 3 3 1
6 h 4 a 2 4 a h 3 h h
2 À( a / 2 ) 3 a 3 a 2 a 2
f o m = = = = 0 . 2 5 3
Àa h 4 a h 4 h h
T h e s e r a n k i n g s a p p l y t o f i l l e t w e l d p a t t e r n s i n t o r s i o n t h a t h a v e a s q u a r e a r e a a × a i n
w h i c h t o p l a c e w e l d m e t a l . T h e o b j e c t i s t o p l a c e a s m u c h m e t a l a s p o s s i b l e t o t h e b o r d e r .
I f y o u r a r e a i s r e c t a n g u l a r , y o u r g o a l i s t h e s a m e b u t t h e r a n k i n g s m a y c h a n g e .
S t u d e n t s w i l l b e s u r p r i s e d t h a t t h e c i r c u l a r w e l d b e a d d o e s n o t r a n k f i r s t .
9 - 1 0
I u 1 a 3 1 1 a 2 a 2
f o m = = = = 0 . 0 8 3 3 5
l h a 1 2 h 1 2 h h
I u 1 a 3 a 2
f o m = = = 0 . 0 8 3 3 5
l h 2 a h 6 h
I u 1 a 2 1 a 2 a 2
f o m = = = = 0 . 2 5 1
l h 2 a h 2 4 h h
b u d y n a s _ S M _ c h 0 9 . q x d 1 2 / 0 1 / 2 0 0 6 1 6 : 1 6 P a g e 2 4 3
F I R S T P A G E S
C h a p t e r 9 2 4 3
I u 1 a 2 1 a 2 a 2
f o m = = ( 3 a + a ) = = 0 . 1 6 6 7 2
l h [ 2 ( 2 a ) ] h 6 6 h h
b a d 2 a 2 a
x = = , y = = =
¯ ¯
2 2 b + 2 d 3 a 3
2 d 3 a a 2 2 a 3 2 a 3 a 2 a 3
I u = - 2 d 2 + ( b + 2 d ) = - + 3 a =
3 3 9 3 3 9 3
I u a 3 / 3 1 a 2 a 2
f o m = = = = 0 . 1 1 1 1 4
l h 3 a h 9 h h
Àa 3
I u = Àr 3 =
8
I u Àa 3 / 8 a 2 a 2
f o m = = = = 0 . 1 2 5 3
l h Àa h 8 h h
T h e C E E - s e c t i o n p a t t e r n w a s n o t r a n k e d b e c a u s e t h e d e f l e c t i o n o f t h e b e a m i s o u t - o f - p l a n e .
I f y o u h a v e a s q u a r e a r e a i n w h i c h t o p l a c e a f i l l e t w e l d m e n t p a t t e r n u n d e r b e n d i n g , y o u r
o b j e c t i v e i s t o p l a c e a s m u c h m a t e r i a l a s p o s s i b l e a w a y f r o m t h e x - a x i s . I f y o u r a r e a i s r e c -
t a n g u l a r , y o u r g o a l i s t h e s a m e , b u t t h e r a n k i n g s m a y c h a n g e .
9 - 1 1 M a t e r i a l s :
A t t a c h m e n t ( 1 0 1 8 H R ) S y = 3 2 k p s i , S u t = 5 8 k p s i
M e m b e r ( A 3 6 ) S y = 3 6 k p s i , S u t r a n g e s f r o m 5 8 t o 8 0 k p s i , u s e 5 8 .
T h e m e m b e r a n d a t t a c h m e n t a r e w e a k c o m p a r e d t o t h e E 6 0 X X e l e c t r o d e .
D e c i s i o n S p e c i f y E 6 0 1 0 e l e c t r o d e
C o n t r o l l i n g p r o p e r t y : Äa l l = m i n [ 0 . 3 ( 5 8 ) , 0 . 4 ( 3 2 ) ] = m i n ( 1 6 . 6 , 1 2 . 8 ) = 1 2 . 8 k p s i
F o r a s t a t i c l o a d t h e p a r a l l e l a n d t r a n s v e r s e f i l l e t s a r e t h e s a m e . I f n i s t h e n u m b e r o f b e a d s ,
F
Ä = = Äa l l
n ( 0 . 7 0 7 ) h l
F 2 5
n h = = = 0 . 9 2 1
0 . 7 0 7 l Äa l l 0 . 7 0 7 ( 3 ) ( 1 2 . 8 )
M a k e a t a b l e .
N u m b e r o f b e a d s L e g s i z e
n h
1 0 . 9 2 1
2 0 . 4 6 0 ’! 1 / 2 "
3 0 . 3 0 7 ’! 5 / 1 6 "
4 0 . 2 3 0 ’! 1 / 4 "
D e c i s i o n : S p e c i f y 1 / 4 " l e g s i z e
D e c i s i o n : W e l d a l l - a r o u n d
b u d y n a s _ S M _ c h 0 9 . q x d 1 2 / 0 1 / 2 0 0 6 1 6 : 1 6 P a g e 2 4 4
F I R S T P A G E S
2 4 4 S o l u t i o n s M a n u a l " I n s t r u c t o r s S o l u t i o n M a n u a l t o A c c o m p a n y M e c h a n i c a l E n g i n e e r i n g D e s i g n
W e l d m e n t S p e c i f i c a t i o n s :
P a t t e r n : A l l - a r o u n d s q u a r e
E l e c t r o d e : E 6 0 1 0
T y p e : T w o p a r a l l e l f i l l e t s A n s .
T w o t r a n s v e r s e f i l l e t s
L e n g t h o f b e a d : 1 2 i n
L e g : 1 / 4 i n
F o r a f i g u r e o f m e r i t o f , i n t e r m s o f w e l d b e a d v o l u m e , i s t h i s d e s i g n o p t i m a l ?
9 - 1 2 D e c i s i o n : C h o o s e a p a r a l l e l f i l l e t w e l d m e n t p a t t e r n . B y s o - d o i n g , w e v e c h o s e n a n o p t i m a l
p a t t e r n ( s e e P r o b . 9 - 9 ) a n d h a v e t h u s r e d u c e d a s y n t h e s i s p r o b l e m t o a n a n a l y s i s p r o b l e m :
T a b l e 9 - 1 : A = 1 . 4 1 4 h d = 1 . 4 1 4 ( h ) ( 3 ) = 4 . 2 4 h i n 3
P r i m a r y s h e a r
V 3 0 0 0 7 0 7
Äy = = =
A 4 . 2 4 h h
S e c o n d a r y s h e a r
d ( 3 b 2 + d 2 ) 3 [ 3 ( 3 2 ) + 3 2 ]
T a b l e 9 - 1 : J u = = = 1 8 i n 3
6 6
J = 0 . 7 0 7 ( h ) ( 1 8 ) = 1 2 . 7 h i n 4
M r y 3 0 0 0 ( 7 . 5 ) ( 1 . 5 ) 2 6 5 7
Äx = = = = Äy
J 1 2 . 7 h h
1 4 2 8 7
2
Äm a x = Äx + ( Äy + Äy ) 2 = 2 6 5 7 2 + ( 7 0 7 + 2 6 5 7 ) 2 =
h h
A t t a c h m e n t ( 1 0 1 8 H R ) : S y = 3 2 k p s i , S u t = 5 8 k p s i
M e m b e r ( A 3 6 ) : S y = 3 6 k p s i
T h e a t t a c h m e n t i s w e a k e r
D e c i s i o n : U s e E 6 0 X X e l e c t r o d e
Äa l l = m i n [ 0 . 3 ( 5 8 ) , 0 . 4 ( 3 2 ) ] = 1 2 . 8 k p s i
4 2 8 7
Äm a x = Äa l l = = 1 2 8 0 0 p s i
h
4 2 8 7
h = = 0 . 3 3 5 i n
1 2 8 0 0
D e c i s i o n : S p e c i f y 3 / 8 " l e g s i z e
W e l d m e n t S p e c i f i c a t i o n s :
P a t t e r n : P a r a l l e l f i l l e t w e l d s
E l e c t r o d e : E 6 0 1 0
T y p e : F i l l e t A n s .
L e n g t h o f b e a d : 6 i n
L e g s i z e : 3 / 8 i n
b u d y n a s _ S M _ c h 0 9 . q x d 1 2 / 0 1 / 2 0 0 6 1 6 : 1 6 P a g e 2 4 5
F I R S T P A G E S
C h a p t e r 9 2 4 5
9 - 1 3 A n o p t i m a l s q u a r e s p a c e ( 3 " × 3 " ) w e l d m e n t p a t t e r n i s o r o r . I n P r o b . 9 - 1 2 , t h e r e
w a s r o u n d u p o f l e g s i z e t o 3 / 8 i n . C o n s i d e r t h e m e m b e r m a t e r i a l t o b e s t r u c t u r a l A 3 6 s t e e l .
D e c i s i o n : U s e a p a r a l l e l h o r i z o n t a l w e l d b e a d p a t t e r n f o r w e l d i n g o p t i m i z a t i o n a n d
c o n v e n i e n c e .
M a t e r i a l s :
A t t a c h m e n t ( 1 0 1 8 H R ) : S y = 3 2 k p s i , S u t = 5 8 k p s i
M e m b e r ( A 3 6 ) : S y = 3 6 k p s i , S u t 5 8 8 0 k p s i ; u s e 5 8 k p s i
F r o m T a b l e 9 - 4 A I S C w e l d i n g c o d e ,
Äa l l = m i n [ 0 . 3 ( 5 8 ) , 0 . 4 ( 3 2 ) ] = m i n ( 1 6 . 6 , 1 2 . 8 ) = 1 2 . 8 k p s i
S e l e c t a s t r o n g e r e l e c t r o d e m a t e r i a l f r o m T a b l e 9 - 3 .
D e c i s i o n : S p e c i f y E 6 0 1 0
T h r o a t a r e a a n d o t h e r p r o p e r t i e s :
A = 1 . 4 1 4 h d = 1 . 4 1 4 ( h ) ( 3 ) = 4 . 2 4 h i n 2
x = b / 2 = 3 / 2 = 1 . 5 i n
¯
y = d / 2 = 3 / 2 = 1 . 5 i n
¯
d ( 3 b 2 + d 2 ) 3 [ 3 ( 3 2 ) + 3 2 ]
J u = = = 1 8 i n 3
6 6
J = 0 . 7 0 7 h J u = 0 . 7 0 7 ( h ) ( 1 8 ) = 1 2 . 7 3 h i n 4
P r i m a r y s h e a r :
V 3 0 0 0 7 0 7 . 5
Äx = = =
A 4 . 2 4 h h
x
y
r x r
x
y
r y
x
S e c o n d a r y s h e a r :
M r
Ä =
J
M r M r x
Äx = Ä c o s 4 5 æ% = c o s 4 5 æ% =
J J
3 0 0 0 ( 6 + 1 . 5 ) ( 1 . 5 ) 2 6 5 1
Äx = =
1 2 . 7 3 h h
2 6 5 1
Äy = Äx =
h
b u d y n a s _ S M _ c h 0 9 . q x d 1 2 / 0 1 / 2 0 0 6 1 6 : 1 6 P a g e 2 4 6
F I R S T P A G E S
2 4 6 S o l u t i o n s M a n u a l " I n s t r u c t o r s S o l u t i o n M a n u a l t o A c c o m p a n y M e c h a n i c a l E n g i n e e r i n g D e s i g n
2
Äm a x = ( Äx + Äx ) 2 + Äy
1
= ( 2 6 5 1 + 7 0 7 . 5 ) 2 + 2 6 5 1 2
h
4 2 7 9
= p s i
h
R e l a t e s t r e s s a n d s t r e n g t h :
Äm a x = Äa l l
4 2 7 9
= 1 2 8 0 0
h
4 2 7 9
h = = 0 . 3 3 4 i n ’! 3 / 8 i n
1 2 8 0 0
W e l d m e n t S p e c i f i c a t i o n s :
P a t t e r n : H o r i z o n t a l p a r a l l e l w e l d t r a c k s
E l e c t r o d e : E 6 0 1 0
T y p e o f w e l d : T w o p a r a l l e l f i l l e t w e l d s
L e n g t h o f b e a d : 6 i n
L e g s i z e : 3 / 8 i n
A d d i t i o n a l t h o u g h t s :
S i n c e t h e r o u n d - u p i n l e g s i z e w a s s u b s t a n t i a l , w h y n o t i n v e s t i g a t e a b a c k w a r d C w e l d
p a t t e r n . O n e m i g h t t h e n e x p e c t s h o r t e r h o r i z o n t a l w e l d b e a d s w h i c h w i l l h a v e t h e a d v a n -
t a g e o f a l l o w i n g a s h o r t e r m e m b e r ( a s s u m i n g t h e m e m b e r h a s n o t y e t b e e n d e s i g n e d ) . T h i s
w i l l s h o w t h e i n t e r - r e l a t i o n s h i p b e t w e e n a t t a c h m e n t d e s i g n a n d s u p p o r t i n g m e m b e r s .
9 - 1 4 M a t e r i a l s :
M e m b e r ( A 3 6 ) : S y = 3 6 k p s i , S u t = 5 8 t o 8 0 k p s i ; u s e S u t = 5 8 k p s i
A t t a c h m e n t ( 1 0 1 8 H R ) : S y = 3 2 k p s i , S u t = 5 8 k p s i
Äa l l = m i n [ 0 . 3 ( 5 8 ) , 0 . 4 ( 3 2 ) ] = 1 2 . 8 k p s i
D e c i s i o n : U s e E 6 0 1 0 e l e c t r o d e . F r o m T a b l e 9 - 3 : S y = 5 0 k p s i , S u t = 6 2 k p s i ,
Äa l l = m i n [ 0 . 3 ( 6 2 ) , 0 . 4 ( 5 0 ) ] = 2 0 k p s i
D e c i s i o n : S i n c e A 3 6 a n d 1 0 1 8 H R a r e w e l d m e t a l s t o a n u n k n o w n e x t e n t , u s e
Äa l l = 1 2 . 8 k p s i
D e c i s i o n : U s e t h e m o s t e f f i c i e n t w e l d p a t t e r n s q u a r e , w e l d - a l l - a r o u n d . C h o o s e 6 " × 6 " s i z e .
A t t a c h m e n t l e n g t h :
l 1 = 6 + a = 6 + 6 . 2 5 = 1 2 . 2 5 i n
T h r o a t a r e a a n d o t h e r p r o p e r t i e s :
A = 1 . 4 1 4 h ( b + d ) = 1 . 4 1 4 ( h ) ( 6 + 6 ) = 1 7 . 0 h
b 6 d 6
x = = = 3 i n , y = = = 3 i n
¯ ¯
2 2 2 2
b u d y n a s _ S M _ c h 0 9 . q x d 1 2 / 0 1 / 2 0 0 6 1 6 : 1 6 P a g e 2 4 7
F I R S T P A G E S
C h a p t e r 9 2 4 7
P r i m a r y s h e a r
V F 2 0 0 0 0 1 1 7 6
Äy = = = = p s i
A A 1 7 h h
S e c o n d a r y s h e a r
( b + d ) 3 ( 6 + 6 ) 3
J u = = = 2 8 8 i n 3
6 6
J = 0 . 7 0 7 h ( 2 8 8 ) = 2 0 3 . 6 h i n 4
M r y 2 0 0 0 0 ( 6 . 2 5 + 3 ) ( 3 ) 2 7 2 6
Äx = Äy = = = p s i
J 2 0 3 . 6 h h
1 4 7 6 0
2
Äm a x = Äx + ( Äy + Äy ) 2 = 2 7 2 6 2 + ( 2 7 2 6 + 1 1 7 6 ) 2 = p s i
h h
R e l a t e s t r e s s t o s t r e n g t h
Äm a x = Äa l l
4 7 6 0
= 1 2 8 0 0
h
4 7 6 0
h = = 0 . 3 7 2 i n
1 2 8 0 0
D e c i s i o n :
S p e c i f y 3 / 8 i n l e g s i z e
S p e c i f i c a t i o n s :
P a t t e r n : A l l - a r o u n d s q u a r e w e l d b e a d t r a c k
E l e c t r o d e : E 6 0 1 0
T y p e o f w e l d : F i l l e t
W e l d b e a d l e n g t h : 2 4 i n
L e g s i z e : 3 / 8 i n
A t t a c h m e n t l e n g t h : 1 2 . 2 5 i n
9 - 1 5 T h i s i s a g o o d a n a l y s i s t a s k t o t e s t t h e s t u d e n t s u n d e r s t a n d i n g
( 1 ) S o l i c i t i n f o r m a t i o n r e l a t e d t o a p r i o r i d e c i s i o n s .
( 2 ) S o l i c i t d e s i g n v a r i a b l e s b a n d d .
( 3 ) F i n d h a n d r o u n d a n d o u t p u t a l l p a r a m e t e r s o n a s i n g l e s c r e e n . A l l o w r e t u r n t o S t e p 1
o r S t e p 2 .
( 4 ) W h e n t h e i t e r a t i o n i s c o m p l e t e , t h e f i n a l d i s p l a y c a n b e t h e b u l k o f y o u r a d e q u a c y
a s s e s s m e n t .
S u c h a p r o g r a m c a n t e a c h t o o .
9 - 1 6 T h e o b j e c t i v e o f t h i s d e s i g n t a s k i s t o h a v e t h e s t u d e n t s t e a c h t h e m s e l v e s t h a t t h e w e l d
p a t t e r n s o f T a b l e 9 - 3 c a n b e a d d e d o r s u b t r a c t e d t o o b t a i n t h e p r o p e r t i e s o f a c o m t e m -
p l a t e d w e l d p a t t e r n . T h e i n s t r u c t o r c a n c o n t r o l t h e l e v e l o f c o m p l i c a t i o n . I h a v e l e f t t h e
b u d y n a s _ S M _ c h 0 9 . q x d 1 2 / 0 1 / 2 0 0 6 1 6 : 1 6 P a g e 2 4 8
F I R S T P A G E S
2 4 8 S o l u t i o n s M a n u a l " I n s t r u c t o r s S o l u t i o n M a n u a l t o A c c o m p a n y M e c h a n i c a l E n g i n e e r i n g D e s i g n
p r e s e n t a t i o n o f t h e d r a w i n g t o y o u . H e r e i s o n e p o s s i b i l i t y . S t u d y t h e p r o b l e m s o p p o r t u n i -
t i e s , t h e n p r e s e n t t h i s ( o r y o u r s k e t c h ) w i t h t h e p r o b l e m a s s i g n m e n t .
S e c t i o n A A
A b 1
1 "
2
8 " d
1 0 1 8 H R
8 "
A
A 3 6 b
a
B o d y w e l d s A t t a c h m e n t w e l d
1 0 0 0 0 l b f
n o t s h o w n p a t t e r n c o n s i d e r e d
U s e b 1 a s t h e d e s i g n v a r i a b l e . E x p r e s s p r o p e r t i e s a s a f u n c t i o n o f b 1 . F r o m T a b l e 9 - 3 ,
c a t e g o r y 3 :
A = 1 . 4 1 4 h ( b - b 1 )
x = b / 2 , y = d / 2
¯ ¯
b d 2 b 1 d 2 ( b - b 1 ) d 2
I u = - =
2 2 2
I = 0 . 7 0 7 h I u
V F
Ä = =
A 1 . 4 1 4 h ( b - b 1 )
M c F a ( d / 2 )
Ä = =
I 0 . 7 0 7 h I u
Äm a x = Ä 2 + Ä 2
P a r a m e t r i c s t u d y
L e t a = 1 0 i n , b = 8 i n , d = 8 i n , b 1 = 2 i n , Äa l l = 1 2 . 8 k p s i , l = 2 ( 8 - 2 ) = 1 2 i n
A = 1 . 4 1 4 h ( 8 - 2 ) = 8 . 4 8 h i n 2
I u = ( 8 - 2 ) ( 8 2 / 2 ) = 1 9 2 i n 3
I = 0 . 7 0 7 ( h ) ( 1 9 2 ) = 1 3 5 . 7 h i n 4
1 0 0 0 0 1 1 7 9
Ä = = p s i
8 . 4 8 h h
1 0 0 0 0 ( 1 0 ) ( 8 / 2 ) 2 9 4 8
Ä = = p s i
1 3 5 . 7 h h
1 3 1 7 5
Äm a x = 1 1 7 9 2 + 2 9 4 8 2 = = 1 2 8 0 0
h h
f r o m w h i c h h = 0 . 2 4 8 i n . D o n o t r o u n d o f f t h e l e g s i z e s o m e t h i n g t o l e a r n .
I u 1 9 2
f o m = = = 6 4 . 5
h l 0 . 2 4 8 ( 1 2 )
A = 8 . 4 8 ( 0 . 2 4 8 ) = 2 . 1 0 i n 2
I = 1 3 5 . 7 ( 0 . 2 4 8 ) = 3 3 . 6 5 i n 4
b u d y n a s _ S M _ c h 0 9 . q x d 1 2 / 0 1 / 2 0 0 6 1 6 : 1 6 P a g e 2 4 9
F I R S T P A G E S
C h a p t e r 9 2 4 9
h 2 0 . 2 4 8 2
v o l = l = 1 2 = 0 . 3 6 9 i n 3
2 2
I 3 3 . 6 5
= = 9 1 . 2 = e f f
v o l 0 . 3 6 9
1 1 7 9
Ä = = 4 7 5 4 p s i
0 . 2 4 8
2 9 4 8
Ä = = 1 1 8 8 7 p s i
0 . 2 4 8
4 1 2 7
.
Äm a x = = 1 2 8 0 0 p s i
0 . 2 4 8
N o w c o n s i d e r t h e c a s e o f u n i n t e r r u p t e d w e l d s ,
b 1 = 0
A = 1 . 4 1 4 ( h ) ( 8 - 0 ) = 1 1 . 3 1 h
I u = ( 8 - 0 ) ( 8 2 / 2 ) = 2 5 6 i n 3
I = 0 . 7 0 7 ( 2 5 6 ) h = 1 8 1 h i n 4
1 0 0 0 0 8 8 4
Ä = =
1 1 . 3 1 h h
1 0 0 0 0 ( 1 0 ) ( 8 / 2 ) 2 2 1 0
Ä = =
1 8 1 h h
1 2 3 8 0
Äm a x = 8 8 4 2 + 2 2 1 0 2 = = Äa l l
h h
Äm a x 2 3 8 0
h = = = 0 . 1 8 6 i n
Äa l l 1 2 8 0 0
D o n o t r o u n d o f f h .
A = 1 1 . 3 1 ( 0 . 1 8 6 ) = 2 . 1 0 i n 2
I = 1 8 1 ( 0 . 1 8 6 ) = 3 3 . 6 7
8 8 4 0 . 1 8 6 2
Ä = = 4 7 5 3 p s i , v o l = 1 6 = 0 . 2 7 7 i n 3
0 . 1 8 6 2
2 2 1 0
Ä = = 1 1 8 8 2 p s i
0 . 1 8 6
I u 2 5 6
f o m = = = 8 6 . 0
h l 0 . 1 8 6 ( 1 6 )
I 3 3 . 6 7
e f f = = = 1 2 1 . 7
( h 2 / 2 ) l ( 0 . 1 8 6 2 / 2 ) 1 6
C o n c l u s i o n s : T o m e e t a l l o w a b l e s t r e s s l i m i t a t i o n s , I a n d A d o n o t c h a n g e , n o r d o Ä a n d à . T o
m e e t t h e s h o r t e n e d b e a d l e n g t h , h i s i n c r e a s e d p r o p o r t i o n a t e l y . H o w e v e r , v o l u m e o f b e a d l a i d
d o w n i n c r e a s e s a s h 2 . T h e u n i n t e r r u p t e d b e a d i s s u p e r i o r . I n t h i s e x a m p l e , w e d i d n o t r o u n d h
a n d a s a r e s u l t w e l e a r n e d s o m e t h i n g . O u r m e a s u r e s o f m e r i t a r e a l s o s e n s i t i v e t o r o u n d i n g .
W h e n t h e d e s i g n d e c i s i o n i s m a d e , r o u n d i n g t o t h e n e x t l a r g e r s t a n d a r d w e l d f i l l e t s i z e w i l l
d e c r e a s e t h e m e r i t .
b u d y n a s _ S M _ c h 0 9 . q x d 1 2 / 0 1 / 2 0 0 6 1 6 : 1 6 P a g e 2 5 0
F I R S T P A G E S
2 5 0 S o l u t i o n s M a n u a l " I n s t r u c t o r s S o l u t i o n M a n u a l t o A c c o m p a n y M e c h a n i c a l E n g i n e e r i n g D e s i g n
H a d t h e w e l d b e a d g o n e a r o u n d t h e c o r n e r s , t h e s i t u a t i o n w o u l d c h a n g e . H e r e i s a f o l -
l o w u p t a s k a n a l y z i n g a n a l t e r n a t i v e w e l d p a t t e r n .
b 1
d 1 d
b
9 - 1 7 F r o m T a b l e 9 - 2
F o r t h e b o x A = 1 . 4 1 4 h ( b + d )
S u b t r a c t i n g b 1 f r o m b a n d d 1 f r o m d
A = 1 . 4 1 4 h ( b - b 1 + d - d 1 )
3
d 2 d 1 b 1 d 2
I u = ( 3 b + d ) - -
6 6 2
1 1
3
= ( b - b 1 ) d 2 + d 3 - d 1
2 6
l e n g t h o f b e a d l = 2 ( b - b 1 + d - d 1 )
f o m = I u / h l
9 - 1 8 C o m p u t e r p r o g r a m s w i l l v a r y .
9 - 1 9 Äa l l = 1 2 8 0 0 p s i . U s e F i g . 9 - 1 7 ( a ) f o r g e n e r a l g e o m e t r y , b u t e m p l o y b e a d s a n d t h e n
b e a d s .
H o r i z o n t a l p a r a l l e l w e l d b e a d p a t t e r n
6 "
b = 6 i n
8 "
d = 8 i n
F r o m T a b l e 9 - 2 , c a t e g o r y 3
A = 1 . 4 1 4 h b = 1 . 4 1 4 ( h ) ( 6 ) = 8 . 4 8 h i n 2
x = b / 2 = 6 / 2 = 3 i n , y = d / 2 = 8 / 2 = 4 i n
¯ ¯
b d 2 6 ( 8 ) 2
I u = = = 1 9 2 i n 3
2 2
I = 0 . 7 0 7 h I u = 0 . 7 0 7 ( h ) ( 1 9 2 ) = 1 3 5 . 7 h i n 4
1 0 0 0 0 1 1 7 9
Ä = = p s i
8 . 4 8 h h
b u d y n a s _ S M _ c h 0 9 . q x d 1 2 / 0 1 / 2 0 0 6 1 6 : 1 6 P a g e 2 5 1
F I R S T P A G E S
C h a p t e r 9 2 5 1
M c 1 0 0 0 0 ( 1 0 ) ( 8 / 2 ) 2 9 4 8
Ä = = = p s i
I 1 3 5 . 7 h h
1 3 1 7 5
Äm a x = Ä 2 + Ä 2 = ( 1 1 7 9 2 + 2 9 4 8 2 ) 1 / 2 = p s i
h h
E q u a t e t h e m a x i m u m a n d a l l o w a b l e s h e a r s t r e s s e s .
3 1 7 5
Äm a x = Äa l l = = 1 2 8 0 0
h
f r o m w h i c h h = 0 . 2 4 8 i n . I t f o l l o w s t h a t
I = 1 3 5 . 7 ( 0 . 2 4 8 ) = 3 3 . 6 5 i n 4
T h e v o l u m e o f t h e w e l d m e t a l i s
h 2 l 0 . 2 4 8 2 ( 6 + 6 )
v o l = = = 0 . 3 6 9 i n 3
2 2
T h e e f f e c t i v e n e s s , ( e f f ) H , i s
I 3 3 . 6 5
( e f f ) H = = = 9 1 . 2 i n
v o l 0 . 3 6 9
I u 1 9 2
( f o m ) H = = = 6 4 . 5 i n
h l 0 . 2 4 8 ( 6 + 6 )
V e r t i c a l p a r a l l e l w e l d b e a d s
6 "
b = 6 i n
8 "
d = 8 i n
F r o m T a b l e 9 - 2 , c a t e g o r y 2
A = 1 . 4 1 4 h d = 1 . 4 1 4 ( h ) ( 8 ) = 1 1 . 3 1 h i n 2
x = b / 2 = 6 / 2 = 3 i n , y = d / 2 = 8 / 2 = 4 i n
¯ ¯
d 3 8 3
I u = = = 8 5 . 3 3 i n 3
6 6
I = 0 . 7 0 7 h I u = 0 . 7 0 7 ( h ) ( 8 5 . 3 3 ) = 6 0 . 3 h
1 0 0 0 0 8 8 4
Ä = = p s i
1 1 . 3 1 h h
M c 1 0 0 0 0 ( 1 0 ) ( 8 / 2 ) 6 6 3 3
Ä = = = p s i
I 6 0 . 3 h h
1
Äm a x = Ä 2 + Ä 2 = ( 8 8 4 2 + 6 6 3 3 2 ) 1 / 2
h
6 6 9 2
= p s i
h
b u d y n a s _ S M _ c h 0 9 . q x d 1 2 / 0 1 / 2 0 0 6 1 6 : 1 6 P a g e 2 5 2
F I R S T P A G E S
2 5 2 S o l u t i o n s M a n u a l " I n s t r u c t o r s S o l u t i o n M a n u a l t o A c c o m p a n y M e c h a n i c a l E n g i n e e r i n g D e s i g n
E q u a t i n g Äm a x t o Äa l l g i v e s h = 0 . 5 2 3 i n . I t f o l l o w s t h a t
I = 6 0 . 3 ( 0 . 5 2 3 ) = 3 1 . 5 i n 4
h 2 l 0 . 5 2 3 2
v o l = = ( 8 + 8 ) = 2 . 1 9 i n 3
2 2
I 3 1 . 6
( e f f ) V = = = 1 4 . 4 i n
v o l 2 . 1 9
I u 8 5 . 3 3
( f o m ) V = = = 1 0 . 2 i n
h l 0 . 5 2 3 ( 8 + 8 )
T h e r a t i o o f ( e f f ) V / ( e f f ) H i s 1 4 . 4 / 9 1 . 2 = 0 . 1 5 8 . T h e r a t i o ( f o m ) V / ( f o m ) H i s
1 0 . 2 / 6 4 . 5 = 0 . 1 5 8 . T h i s i s n o t s u r p r i s i n g s i n c e
I I 0 . 7 0 7 h I u I u
e f f = = = = 1 . 4 1 4 = 1 . 4 1 4 f o m
v o l ( h 2 / 2 ) l ( h 2 / 2 ) l h l
T h e r a t i o s ( e f f ) V / ( e f f ) H a n d ( f o m ) V / ( f o m ) H g i v e t h e s a m e i n f o r m a t i o n .
9 - 2 0 B e c a u s e t h e l o a d i n g i s p u r e t o r s i o n , t h e r e i s n o p r i m a r y s h e a r . F r o m T a b l e 9 - 1 , c a t e g o r y 6 :
J u = 2 Àr 3 = 2 À( 1 ) 3 = 6 . 2 8 i n 3
J = 0 . 7 0 7 h J u = 0 . 7 0 7 ( 0 . 2 5 ) ( 6 . 2 8 )
= 1 . 1 1 i n 4
T r 2 0 ( 1 )
Ä = = = 1 8 . 0 k p s i A n s .
J 1 . 1 1
9 - 2 1 h = 0 . 3 7 5 i n , d = 8 i n , b = 1 i n
F r o m T a b l e 9 - 2 , c a t e g o r y 2 :
A = 1 . 4 1 4 ( 0 . 3 7 5 ) ( 8 ) = 4 . 2 4 i n 2
d 3 8 3
I u = = = 8 5 . 3 i n 3
6 6
I = 0 . 7 0 7 h I u = 0 . 7 0 7 ( 0 . 3 7 5 ) ( 8 5 . 3 ) = 2 2 . 6 i n 4
F 5
Ä = = = 1 . 1 8 k p s i
A 4 . 2 4
M = 5 ( 6 ) = 3 0 k i p · i n
c = ( 1 + 8 + 1 - 2 ) / 2 = 4 i n
M c 3 0 ( 4 )
Ä = = = 5 . 3 1 k p s i
I 2 2 . 6
Äm a x = Ä 2 + Ä 2 = 1 . 1 8 2 + 5 . 3 1 2
= 5 . 4 4 k p s i A n s .
b u d y n a s _ S M _ c h 0 9 . q x d 1 2 / 0 1 / 2 0 0 6 1 6 : 1 6 P a g e 2 5 3
F I R S T P A G E S
C h a p t e r 9 2 5 3
9 - 2 2 h = 0 . 6 c m , b = 6 c m , d = 1 2 c m .
T a b l e 9 - 3 , c a t e g o r y 5 :
6
A = 0 . 7 0 7 h ( b + 2 d )
B
= 0 . 7 0 7 ( 0 . 6 ) [ 6 + 2 ( 1 2 ) ] = 1 2 . 7 c m 2
4 . 8
d 2 1 2 2
G
y = = = 4 . 8 c m
¯
b + 2 d 6 + 2 ( 1 2 )
7 . 2
2 d 3
I u = - 2 d 2 y + ( b + 2 d ) y 2
¯ ¯
A 3
2 ( 1 2 ) 3
= - 2 ( 1 2 2 ) ( 4 . 8 ) + [ 6 + 2 ( 1 2 ) ] 4 . 8 2
3
= 4 6 1 c m 3
I = 0 . 7 0 7 h I u = 0 . 7 0 7 ( 0 . 6 ) ( 4 6 1 ) = 1 9 6 c m 4
F 7 . 5 ( 1 0 3 )
Ä = = = 5 . 9 1 M P a
A 1 2 . 7 ( 1 0 2 )
M = 7 . 5 ( 1 2 0 ) = 9 0 0 N · m
c A = 7 . 2 c m , c B = 4 . 8 c m
T h e c r i t i c a l l o c a t i o n i s a t A .
M c A 9 0 0 ( 7 . 2 )
ÄA = = = 3 3 . 1 M P a
I 1 9 6
Äm a x = Ä 2 + Ä 2 = ( 5 . 9 1 2 + 3 3 . 1 2 ) 1 / 2 = 3 3 . 6 M P a
Äa l l 1 2 0
n = = = 3 . 5 7 A n s .
Äm a x 3 3 . 6
9 - 2 3 T h e l a r g e s t p o s s i b l e w e l d s i z e i s 1 / 1 6 i n . T h i s i s a s m a l l w e l d a n d t h u s d i f f i c u l t t o a c c o m -
p l i s h . T h e b r a c k e t s l o a d - c a r r y i n g c a p a b i l i t y i s n o t k n o w n . T h e r e a r e g e o m e t r y p r o b l e m s
a s s o c i a t e d w i t h s h e e t m e t a l f o l d i n g , l o a d - p l a c e m e n t a n d l o c a t i o n o f t h e c e n t e r o f t w i s t .
T h i s i s n o t a v a i l a b l e t o u s . W e w i l l i d e n t i f y t h e s t r o n g e s t p o s s i b l e w e l d m e n t .
U s e a r e c t a n g u l a r , w e l d - a l l - a r o u n d p a t t e r n T a b l e 9 - 2 , c a t e g o r y 6 :
A = 1 . 4 1 4 h ( b + d )
= 1 . 4 1 4 ( 1 / 1 6 ) ( 1 + 7 . 5 )
= 0 . 7 5 1 i n 2
7 . 5 "
x = b / 2 = 0 . 5 i n
¯
d 7 . 5
y = = = 3 . 7 5 i n
¯
2 2
1 "
b u d y n a s _ S M _ c h 0 9 . q x d 1 2 / 0 1 / 2 0 0 6 1 6 : 1 6 P a g e 2 5 4
F I R S T P A G E S
2 5 4 S o l u t i o n s M a n u a l " I n s t r u c t o r s S o l u t i o n M a n u a l t o A c c o m p a n y M e c h a n i c a l E n g i n e e r i n g D e s i g n
d 2 7 . 5 2
I u = ( 3 b + d ) = [ 3 ( 1 ) + 7 . 5 ] = 9 8 . 4 i n 3
6 6
I = 0 . 7 0 7 h I u = 0 . 7 0 7 ( 1 / 1 6 ) ( 9 8 . 4 ) = 4 . 3 5 i n 4
M = ( 3 . 7 5 + 0 . 5 ) W = 4 . 2 5 W
V W
Ä = = = 1 . 3 3 2 W
A 0 . 7 5 1
M c 4 . 2 5 W ( 7 . 5 / 2 )
Ä = = = 3 . 6 6 4 W
I 4 . 3 5
Äm a x = Ä 2 + Ä 2 = W 1 . 3 3 2 2 + 3 . 6 6 4 2 = 3 . 9 0 W
M a t e r i a l p r o p e r t i e s : T h e a l l o w a b l e s t r e s s g i v e n i s l o w . L e t s d e m o n s t r a t e t h a t .
F o r t h e A 3 6 s t r u c t u r a l s t e e l m e m b e r , S y = 3 6 k p s i a n d S u t = 5 8 k p s i . F o r t h e 1 0 2 0 C D
a t t a c h m e n t , u s e H R p r o p e r t i e s o f S y = 3 0 k p s i a n d S u t = 5 5 . T h e E 6 0 1 0 e l e c t r o d e h a s
s t r e n g t h s o f S y = 5 0 a n d S u t = 6 2 k p s i .
A l l o w a b l e s t r e s s e s :
A 3 6 : Äa l l = m i n [ 0 . 3 ( 5 8 ) , 0 . 4 ( 3 6 ) ]
= m i n ( 1 7 . 4 , 1 4 . 4 ) = 1 4 . 4 k p s i
1 0 2 0 : Äa l l = m i n [ 0 . 3 ( 5 5 ) , 0 . 4 ( 3 0 ) ]
Äa l l = m i n ( 1 6 . 5 , 1 2 ) = 1 2 k p s i
E 6 0 1 0 : Äa l l = m i n [ 0 . 3 ( 6 2 ) , 0 . 4 ( 5 0 ) ]
= m i n ( 1 8 . 6 , 2 0 ) = 1 8 . 6 k p s i
S i n c e T a b l e 9 - 6 g i v e s 1 8 . 0 k p s i a s t h e a l l o w a b l e s h e a r s t r e s s , u s e t h i s l o w e r v a l u e .
T h e r e f o r e , t h e a l l o w a b l e s h e a r s t r e s s i s
Äa l l = m i n ( 1 4 . 4 , 1 2 , 1 8 . 0 ) = 1 2 k p s i
H o w e v e r , t h e a l l o w a b l e s t r e s s i n t h e p r o b l e m s t a t e m e n t i s 0 . 9 k p s i w h i c h i s l o w f r o m t h e
w e l d m e n t p e r s p e c t i v e . T h e l o a d a s s o c i a t e d w i t h t h i s s t r e n g t h i s
Äm a x = Äa l l = 3 . 9 0 W = 9 0 0
9 0 0
W = = 2 3 1 l b f
3 . 9 0
I f t h e w e l d i n g c a n b e a c c o m p l i s h e d ( 1 / 1 6 l e g s i z e i s a s m a l l w e l d ) , t h e w e l d s t r e n g t h i s
1 2 0 0 0 p s i a n d t h e l o a d W = 3 0 4 7 l b f . C a n t h e b r a c k e t c a r r y s u c h a l o a d ?
T h e r e a r e g e o m e t r y p r o b l e m s a s s o c i a t e d w i t h s h e e t m e t a l f o l d i n g . L o a d p l a c e m e n t i s
i m p o r t a n t a n d t h e c e n t e r o f t w i s t h a s n o t b e e n i d e n t i f i e d . A l s o , t h e l o a d - c a r r y i n g c a p a b i l i t y
o f t h e t o p b e n d i s u n k n o w n .
T h e s e u n c e r t a i n t i e s m a y r e q u i r e t h e u s e o f a d i f f e r e n t w e l d p a t t e r n . O u r s o l u t i o n p r o -
v i d e s t h e b e s t w e l d m e n t a n d t h u s i n s i g h t f o r c o m p a r i n g a w e l d e d j o i n t t o o n e w h i c h e m -
p l o y s s c r e w f a s t e n e r s .
b u d y n a s _ S M _ c h 0 9 . q x d 1 2 / 0 1 / 2 0 0 6 1 6 : 1 6 P a g e 2 5 5
F I R S T P A G E S
C h a p t e r 9 2 5 5
9 - 2 4
y
x
F
F B
R x
A
6 0
A
R y B
A
F = 1 0 0 l b f , Äa l l = 3 k p s i
F B = 1 0 0 ( 1 6 / 3 ) = 5 3 3 . 3 l b f
x
F B = - 5 3 3 . 3 c o s 6 0 æ% = - 2 6 6 . 7 l b f
y
F B = - 5 3 3 . 3 c o s 3 0 æ% = - 4 6 2 l b f
y
I t f o l l o w s t h a t R A = 5 6 2 l b f a n d R x = 2 6 6 . 7 l b f , R A = 6 2 2 l b f
A
M = 1 0 0 ( 1 6 ) = 1 6 0 0 l b f · i n
1 0 0
4 6 2
2 6 6 . 7
1 6
3
2 6 6 . 7
5 6 2
T h e O D o f t h e t u b e s i s 1 i n . F r o m T a b l e 9 - 1 , c a t e g o r y 6 :
A = 1 . 4 1 4 ( Àh r ) ( 2 )
= 2 ( 1 . 4 1 4 ) ( Àh ) ( 1 / 2 ) = 4 . 4 4 h i n 2
J u = 2 Àr 3 = 2 À( 1 / 2 ) 3 = 0 . 7 8 5 i n 3
J = 2 ( 0 . 7 0 7 ) h J u = 1 . 4 1 4 ( 0 . 7 8 5 ) h = 1 . 1 1 h i n 4
V 6 2 2 1 4 0
Ä = = =
A 4 . 4 4 h h
T c M c 1 6 0 0 ( 0 . 5 ) 7 2 0 . 7
Ä = = = =
J J 1 . 1 1 h h
T h e s h e a r s t r e s s e s , Ä a n d Ä , a r e a d d i t i v e a l g e b r a i c a l l y
1 8 6 1
Äm a x = ( 1 4 0 + 7 2 0 . 7 ) = p s i
h h
8 6 1
Äm a x = Äa l l = = 3 0 0 0
h
8 6 1
h = = 0 . 2 8 7 ’! 5 / 1 6 "
3 0 0 0
D e c i s i o n : U s e 5 / 1 6 i n f i l l e t w e l d s A n s .
b u d y n a s _ S M _ c h 0 9 . q x d 1 2 / 0 1 / 2 0 0 6 1 6 : 1 6 P a g e 2 5 6
F I R S T P A G E S
2 5 6 S o l u t i o n s M a n u a l " I n s t r u c t o r s S o l u t i o n M a n u a l t o A c c o m p a n y M e c h a n i c a l E n g i n e e r i n g D e s i g n
9 - 2 5
y
g g
1 " 3 "
G
4 8
x
1 " 3 "
4 8
B g g
9 " 7 "
F o r t h e p a t t e r n i n b e n d i n g s h o w n , f i n d t h e c e n t r o i d G o f t h e w e l d g r o u p .
6 ( 0 . 7 0 7 ) ( 1 / 4 ) ( 3 ) + 6 ( 0 . 7 0 7 ) ( 3 / 8 ) ( 1 3 )
x =
¯
6 ( 0 . 7 0 7 ) ( 1 / 4 ) + 6 ( 0 . 7 0 7 ) ( 3 / 8 )
= 9 i n
I 1 / 4 = 2 I G + A 2
x
¯
0 . 7 0 7 ( 1 / 4 ) ( 6 3 )
= 2 + 0 . 7 0 7 ( 1 / 4 ) ( 6 ) ( 6 2 )
1 2
= 8 2 . 7 i n 4
0 . 7 0 7 ( 3 / 8 ) ( 6 3 )
I 3 / 8 = 2 + 0 . 7 0 7 ( 3 / 8 ) ( 6 ) ( 4 2 )
1 2
= 6 0 . 4 i n 4
I = I 1 / 4 + I 3 / 8 = 8 2 . 7 + 6 0 . 4 = 1 4 3 . 1 i n 4
T h e c r i t i c a l l o c a t i o n i s a t B . F r o m E q . ( 9 - 3 ) ,
F
Ä = = 0 . 1 8 9 F
2 [ 6 ( 0 . 7 0 7 ) ( 3 / 8 + 1 / 4 ) ]
M c ( 8 F ) ( 9 )
Ä = = = 0 . 5 0 3 F
I 1 4 3 . 1
Äm a x = Ä 2 + Ä 2 = F 0 . 1 8 9 2 + 0 . 5 0 3 2 = 0 . 5 3 7 F
M a t e r i a l s :
A 3 6 M e m b e r : S y = 3 6 k p s i
1 0 1 5 H R A t t a c h m e n t : S y = 2 7 . 5 k p s i
E 6 0 1 0 E l e c t r o d e : S y = 5 0 k p s i
Äa l l = 0 . 5 7 7 m i n ( 3 6 , 2 7 . 5 , 5 0 ) = 1 5 . 9 k p s i
Äa l l / n 1 5 . 9 / 2
F = = = 1 4 . 8 k i p A n s .
0 . 5 3 7 0 . 5 3 7
9 - 2 6 F i g u r e P 9 - 2 6 b i s a f r e e - b o d y d i a g r a m o f t h e b r a c k e t . F o r c e s a n d m o m e n t s t h a t a c t o n t h e
w e l d s a r e e q u a l , b u t o f o p p o s i t e s e n s e .
( a ) M = 1 2 0 0 ( 0 . 3 6 6 ) = 4 3 9 l b f · i n A n s .
( b ) F y = 1 2 0 0 s i n 3 0 æ% = 6 0 0 l b f A n s .
( c ) F x = 1 2 0 0 c o s 3 0 æ% = 1 0 3 9 l b f A n s .
b u d y n a s _ S M _ c h 0 9 . q x d 1 2 / 0 1 / 2 0 0 6 1 6 : 1 6 P a g e 2 5 7
F I R S T P A G E S
C h a p t e r 9 2 5 7
( d ) F r o m T a b l e 9 - 2 , c a t e g o r y 6 :
A = 1 . 4 1 4 ( 0 . 2 5 ) ( 0 . 2 5 + 2 . 5 ) = 0 . 9 7 2 i n 2
d 2 2 . 5 2
I u = ( 3 b + d ) = [ 3 ( 0 . 2 5 ) + 2 . 5 ] = 3 . 3 9 i n 3
6 6
T h e s e c o n d a r e a m o m e n t a b o u t a n a x i s t h r o u g h G a n d p a r a l l e l t o z i s
I = 0 . 7 0 7 h I u = 0 . 7 0 7 ( 0 . 2 5 ) ( 3 . 3 9 ) = 0 . 5 9 9 i n 4 A n s .
( e ) R e f e r t o F i g . P . 9 - 2 6 b . T h e s h e a r s t r e s s d u e t o F y i s
F y 6 0 0
Ä1 = = = 6 1 7 p s i
A 0 . 9 7 2
T h e s h e a r s t r e s s a l o n g t h e t h r o a t d u e t o F x i s
F x 1 0 3 9
Ä2 = = = 1 0 6 9 p s i
A 0 . 9 7 2
T h e r e s u l t a n t o f Ä1 a n d Ä2 i s i n t h e t h r o a t p l a n e
1 / 2
2 2
Ä = Ä1 + Ä2 = ( 6 1 7 2 + 1 0 6 9 2 ) 1 / 2 = 1 2 3 4 p s i
T h e b e n d i n g o f t h e t h r o a t g i v e s
M c 4 3 9 ( 1 . 2 5 )
Ä = = = 9 1 6 p s i
I 0 . 5 9 9
T h e m a x i m u m s h e a r s t r e s s i s
Äm a x = ( Ä 2 + Ä 2 ) 1 / 2 = ( 1 2 3 4 2 + 9 1 6 2 ) 1 / 2 = 1 5 3 7 p s i A n s .
( f ) M a t e r i a l s :
1 0 1 8 H R M e m b e r : S y = 3 2 k p s i , S u t = 5 8 k p s i ( T a b l e A - 2 0 )
E 6 0 1 0 E l e c t r o d e : S y = 5 0 k p s i ( T a b l e 9 - 3 )
S s y 0 . 5 7 7 S y 0 . 5 7 7 ( 3 2 )
n = = = = 1 2 . 0 A n s .
Äm a x Äm a x 1 . 5 3 7
( g ) B e n d i n g i n t h e a t t a c h m e n t n e a r t h e b a s e . T h e c r o s s - s e c t i o n a l a r e a i s a p p r o x i m a t e l y
e q u a l t o b h .
.
A 1 = b h = 0 . 2 5 ( 2 . 5 ) = 0 . 6 2 5 i n 2
F x 1 0 3 9
Äx y = = = 1 6 6 2 p s i
A 1 0 . 6 2 5
I b d 2 0 . 2 5 ( 2 . 5 ) 2
= = = 0 . 2 6 0 i n 3
c 6 6
A t l o c a t i o n A
F y M
Ãy = +
A 1 I / c
6 0 0 4 3 9
Ãy = + = 2 6 4 8 p s i
0 . 6 2 5 0 . 2 6 0
b u d y n a s _ S M _ c h 0 9 . q x d 1 2 / 0 1 / 2 0 0 6 1 6 : 1 6 P a g e 2 5 8
F I R S T P A G E S
2 5 8 S o l u t i o n s M a n u a l " I n s t r u c t o r s S o l u t i o n M a n u a l t o A c c o m p a n y M e c h a n i c a l E n g i n e e r i n g D e s i g n
T h e v o n M i s e s s t r e s s à i s
1 / 2
2 2
à = Ãy + 3 Äx y = [ 2 6 4 8 2 + 3 ( 1 6 6 2 ) 2 ] 1 / 2 = 3 9 1 2 p s i
T h u s , t h e f a c t o r o f s a f e t y i s ,
S y 3 2
n = = = 8 . 1 8 A n s .
à 3 . 9 1 2
T h e c l i p o n t h e m o o r i n g l i n e b e a r s a g a i n s t t h e s i d e o f t h e 1 / 2 - i n h o l e . I f t h e c l i p f i l l s
t h e h o l e
F - 1 2 0 0
à = = = - 9 6 0 0 p s i
t d 0 . 2 5 ( 0 . 5 0 )
S y 3 2 ( 1 0 3 )
n = - = - = 3 . 3 3 A n s .
à - 9 6 0 0
F u r t h e r i n v e s t i g a t i o n o f t h i s s i t u a t i o n r e q u i r e s m o r e d e t a i l t h a n i s i n c l u d e d i n t h e t a s k
s t a t e m e n t .
( h ) I n s h e a r f a t i g u e , t h e w e a k e s t c o n s t i t u e n t o f t h e w e l d m e l t i s 1 0 1 8 w i t h S u t = 5 8 k p s i
S e = 0 . 5 S u t = 0 . 5 ( 5 8 ) = 2 9 k p s i
T a b l e 7 - 4 :
k a = 1 4 . 4 ( 5 8 ) - 0 . 7 1 8 = 0 . 7 8 0
F o r t h e s i z e f a c t o r e s t i m a t e , w e f i r s t e m p l o y E q . ( 7 - 2 4 ) f o r t h e e q u i v a l e n t d i a m e t e r .
"
d e = 0 . 8 0 8 0 . 7 0 7 h b = 0 . 8 0 8 0 . 7 0 7 ( 2 . 5 ) ( 0 . 2 5 ) = 0 . 5 3 7 i n
E q . ( 7 - 1 9 ) i s u s e d n e x t t o f i n d k b
- 0 . 1 0 7 - 0 . 1 0 7
d e 0 . 5 3 7
k b = = = 0 . 9 4 0
0 . 3 0 0 . 3 0
T h e l o a d f a c t o r f o r s h e a r k c , i s
k c = 0 . 5 9
T h e e n d u r a n c e s t r e n g t h i n s h e a r i s
S s e = 0 . 7 8 0 ( 0 . 9 4 0 ) ( 0 . 5 9 ) ( 2 9 ) = 1 2 . 5 k p s i
F r o m T a b l e 9 - 5 , t h e s h e a r s t r e s s - c o n c e n t r a t i o n f a c t o r i s K = 2 . 7 . T h e l o a d i n g i s
f s
r e p e a t e d l y - a p p l i e d .
Äm a x 1 . 5 3 7
Äa = Äm = K = 2 . 7 = 2 . 0 7 k p s i
f s
2 2
T a b l e 7 - 1 0 : G e r b e r f a c t o r o f s a f e t y n , a d j u s t e d f o r s h e a r , w i t h S s u = 0 . 6 7 S u t
f
ñø üø
2 òø 2
ýø
1 0 . 6 7 ( 5 8 ) 2 . 0 7 2 ( 2 . 0 7 ) ( 1 2 . 5 )
n f = - 1 + 1 + = 5 . 5 2 A n s .
óø þø
2 2 . 0 7 1 2 . 5 0 . 6 7 ( 5 8 ) ( 2 . 0 7 )
A t t a c h m e n t m e t a l s h o u l d b e c h e c k e d f o r b e n d i n g f a t i g u e .
b u d y n a s _ S M _ c h 0 9 . q x d 1 2 / 0 1 / 2 0 0 6 1 6 : 1 6 P a g e 2 5 9
F I R S T P A G E S
C h a p t e r 9 2 5 9
9 - 2 7 U s e b = d = 4 i n . S i n c e h = 5 / 8 i n , t h e p r i m a r y s h e a r i s
F
Ä = = 0 . 2 8 3 F
1 . 4 1 4 ( 5 / 8 ) ( 4 )
T h e s e c o n d a r y s h e a r c a l c u l a t i o n s , f o r a m o m e n t a r m o f 1 4 i n g i v e
4 [ 3 ( 4 2 ) + 4 2 ]
J u = = 4 2 . 6 7 i n 3
6
J = 0 . 7 0 7 h J u = 0 . 7 0 7 ( 5 / 8 ) 4 2 . 6 7 = 1 8 . 9 i n 4
M r y 1 4 F ( 2 )
Äx = Äy = = = 1 . 4 8 F
J 1 8 . 9
T h u s , t h e m a x i m u m s h e a r a n d a l l o w a b l e l o a d a r e :
Äm a x = F 1 . 4 8 2 + ( 0 . 2 8 3 + 1 . 4 8 ) 2 = 2 . 3 0 F
Äa l l 2 0
F = = = 8 . 7 0 k i p A n s .
2 . 3 0 2 . 3 0
F r o m P r o b . 9 - 5 b , Äa l l = 1 1 k p s i
Äa l l 1 1
F a l l = = = 4 . 7 8 k i p
2 . 3 0 2 . 3 0
T h e a l l o w a b l e l o a d h a s t h u s i n c r e a s e d b y a f a c t o r o f 1 . 8 A n s .
9 - 2 8 P u r c h a s e t h e h o o k h a v i n g t h e d e s i g n s h o w n i n F i g . P 9 - 2 8 b . R e f e r r i n g t o t e x t F i g . 9 - 3 2 a ,
t h i s d e s i g n r e d u c e s p e e l s t r e s s e s .
9 - 2 9 ( a )
l / 2
1 P É c o s h ( Éx )
Ä = d x
¯
l 4 b s i n h ( Él / 2 )
- l / 2
l / 2
= A 1 c o s h ( Éx ) d x
- l / 2
l / 2
A 1
= s i n h ( Éx )
É - l / 2
A 1
= [ s i n h ( Él / 2 ) - s i n h ( - Él / 2 ) ]
É
A 1
= [ s i n h ( Él / 2 ) - ( - s i n h ( Él / 2 ) ) ]
É
2 A 1 s i n h ( Él / 2 )
=
É
P É
= [ 2 s i n h ( Él / 2 ) ]
4 b l s i n h ( Él / 2 )
P
Ä = A n s .
¯
2 b l
b u d y n a s _ S M _ c h 0 9 . q x d 1 2 / 0 1 / 2 0 0 6 1 6 : 1 6 P a g e 2 6 0
F I R S T P A G E S
2 6 0 S o l u t i o n s M a n u a l " I n s t r u c t o r s S o l u t i o n M a n u a l t o A c c o m p a n y M e c h a n i c a l E n g i n e e r i n g D e s i g n
P É c o s h ( Él / 2 ) P É
( b ) Ä( l / 2 ) = = A n s .
4 b s i n h ( Él / 2 ) 4 b t a n h ( Él / 2 )
( c )
Ä( l / 2 ) P É 2 b l
K = =
Ä 4 b s i n h ( Él / 2 ) P
¯
Él / 2
K = A n s .
t a n h ( Él / 2 )
F o r c o m p u t e r p r o g r a m m i n g , i t c a n b e u s e f u l t o e x p r e s s t h e h y p e r b o l i c t a n g e n t i n t e r m s
o f e x p o n e n t i a l s :
Él e x p ( Él / 2 ) - e x p ( - Él / 2 )
K = A n s .
2 e x p ( Él / 2 ) + e x p ( - Él / 2 )
9 - 3 0 T h i s i s a c o m p u t e r p r o g r a m m i n g e x e r c i s e . A l l p r o g r a m s w i l l v a r y .
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