SECTION 3 – SCREW FASTENINGS FASTENINGS SIMPLE TENSION INCLUDING TIGHTENING STRESSES DESIGN PROBLEMS
221.
A 50005000-lb. lb. g!" g!" b#$ %& %& '"#(%) '"#(%)) ) *%+, *%+, ! &+l &+l !& "#ll "#ll) ) B1113 B1113 / /b#l+ b#l+ #" #" & & % #(%g %+. W,!+ &%4 b#l+ &,#l) b &) ! % UNC +,"!)& !" &)6 b I UNF +,"!)& !" &)6 7 I +, 8-+,"!) &"%& %& &)6 E$'l!% +, b!&%& # /#" 7,#%7 # )&%g !7+#".
S#l+%# B11139 !& "#ll) s y = :5 ksi T!bl AT-; 5000 lb F e =
i5.<9 sd
=
F#" D ≥
s y <
3 4
( As )
1
2
D < 3 in :
in
sd = 0.4s y
sd = 0.4( 45,000) = 18,000ps
As =
F e 5000 = = 0.2778sq.in. sd 18,000
T!bl AT 1: !) T!bl 5.1
! ! UNC UNC T," T,"!) !)&& U& D =
3 4
in9 As = 0.334sq.in.
b UNF T,"!) T,"!)&& U& D =
3 4
in9 As = 0.373sq.in.
7 8-T," 8-T,"!) !) S"% S"%& & U&
D
=
1in9
P!g 1 # :0
As = 0.606sq.in.
SECTION 3 – SCREW FASTENINGS FASTENINGS 222. 222.
A #+# #+#"" *%g,% *%g,%g g 2 +#& +#& %& l%+ l%+) ) b/ ! *"# *"#g,+ g,+-% -%"# "# / b#l+ b#l+ *,%7 *,%7, , %& &7" &7"* *) ) %+# +, "!. D7%) '# ! )&%g !7+#" !) )+"% +, &%4 # +, /b#l+ % ! UNC +,"!)& !" &)9 b UNF +,"!)& !" &). N#+ F% +,"!)& !" #+ "7#)) #" b"%++l !+"%!l&.
S#l+%# T!bl T!bl AT-; AT-; W"#g,+ %"#9 s y = 25 ksi sd = 0.4sy = 0.4( 25)
As =
= 10ksi= 10,000psi
F e 2( 2000 ) = = 0.4 sq.in. sd 10,000
T!bl AT 1; ! ! UNC UNC T," T,"!) !)&& U& D =
7 8
in9 As = 0.462sq.in.
b UNF T,"!) T,"!)&& U& D = 22:.
7 8
in9 As = 0.509sq.in.
A *!ll b"!7=+9 F%g. 8-139 Text 9 %& l#!)) &# +,!+ +, +*# +#' b#l+& +,!+ !&+ %+ +# +, *!ll !" !7, &b>7+) &b>7+) +# ! +&%l l#!) # ;10 lb. T, b#l+& !" +# b 7#l) #"g) "# AISI C1020 &+l *%+, UNC +,"!)&9 Ngl7+%g +, 7+ # &,!"% &,!"%g g &+"&& &+"&&&9 &9 )+"% )+"% +, )%!+ )%!+" " # +,& +,& b#l+& b#l+& % +,/ +,/ !" *ll *ll +%g,+).
F%g" 8-13
P!g 2 # :0
SECTION 3 – SCREW FASTENINGS FASTENINGS 222. 222.
A #+# #+#"" *%g,% *%g,%g g 2 +#& +#& %& l%+ l%+) ) b/ ! *"# *"#g,+ g,+-% -%"# "# / b#l+ b#l+ *,%7 *,%7, , %& &7" &7"* *) ) %+# +, "!. D7%) '# ! )&%g !7+#" !) )+"% +, &%4 # +, /b#l+ % ! UNC +,"!)& !" &)9 b UNF +,"!)& !" &). N#+ F% +,"!)& !" #+ "7#)) #" b"%++l !+"%!l&.
S#l+%# T!bl T!bl AT-; AT-; W"#g,+ %"#9 s y = 25 ksi sd = 0.4sy = 0.4( 25)
As =
= 10ksi= 10,000psi
F e 2( 2000 ) = = 0.4 sq.in. sd 10,000
T!bl AT 1; ! ! UNC UNC T," T,"!) !)&& U& D =
7 8
in9 As = 0.462sq.in.
b UNF T,"!) T,"!)&& U& D = 22:.
7 8
in9 As = 0.509sq.in.
A *!ll b"!7=+9 F%g. 8-139 Text 9 %& l#!)) &# +,!+ +, +*# +#' b#l+& +,!+ !&+ %+ +# +, *!ll !" !7, &b>7+) &b>7+) +# ! +&%l l#!) # ;10 lb. T, b#l+& !" +# b 7#l) #"g) "# AISI C1020 &+l *%+, UNC +,"!)&9 Ngl7+%g +, 7+ # &,!"% &,!"%g g &+"&& &+"&&&9 &9 )+"% )+"% +, )%!+ )%!+" " # +,& +,& b#l+& b#l+& % +,/ +,/ !" *ll *ll +%g,+).
F%g" 8-13
P!g 2 # :0
SECTION 3 – SCREW FASTENINGS FASTENINGS
S#l+%#
7#l) #"g)9 AISI C1020
= << ksi T!bl AT-; F e = ;10 lb
s y
F e
=
s y
( As )
2
< <<9000
;10 = A s
3
<
D < 3 in : ( A s )
3
2
= 0.1<1 sq.in. 9 D < 3 in :
T!bl AT 1: 9 UNC T,"!)& U& D =
225.
? 1<
in 9 A s
= 0.1820 sq.in.
A 7#7+%# &% &%%l!" +# +# F% F%g. 5. 5.?9 Text 9 %& &b>7+) +# ! $+"!l l#!) F e # 1250 lb. T, b#l+ %& !) "# 7#l)-%%&,) AISI B1113 &+l *%+, UNC +,"!)&. ! D+"% +, )%!+" # +, b#l+ % %+ %& *ll +%g,+). b C#'+ +, %%+%!l +&%# !) 7#""&'#)%g !''"#$%!+ +%g,+%g +#"@ % si = 0.85s y i5.8. F%g" 5.?
P!g 3 # :0
SECTION 3 – SCREW FASTENINGS FASTENINGS
S#l+%# C#l)-%%&,) AISI B1113 T!bl A-;9 s y = ;2 ksi F e = 1250 lb
! F e
=
1250 = A s
s y
( As )
< ;29000
<
3
2
( A s )
3
2
= 0.221: sq.in. 9 D < 3 in :
T!bl AT 1: 9 UNC T,"!)& U& D =
5 8
in 9 A s
= 0.22<0 sq.in.
b si = 0.85 s y = 0.85( ;29000) = <19200 psi I%+%!l T&%# F i
= si A s = ( <19200) ( 0.22<0) = 139831 lb
T%g,+%g +#"@ T = CDF i
5 (139831) = 1;2? in − lb 8
T = 0.2 DF i = 0.2
22<. 22<.
T, T, 7/l% 7/l%) )" " ,! ,!) ) # ! 10 $ 18 18 %. %. F" F"# # 7# 7#'" '"& &&# &#"" %& %& !+ !++!7, +!7,) ) b/ b/ 10 &+) &+) b#l+& !) # SAE G"!) 5. T, 7/l%)" '"&&" %& 200 '&%. ! W,!+ &%4 b#l+& &,#l) b &)6 b W,!+ !''"#$%!+ +%g,+%g +#"@ &,#l) b )) +# %)7 ! +%g,+%g &+"&& si # 0.? +%& +, '"## &+"&&6
S#l+%# T!bl 5.2
P!g : # :0
SECTION 3 – SCREW FASTENINGS SAE G"!) 5 A&& s y = 88 ksi !
F e
F e
=
=
s y <
15;1 = A s
π (10) : = 15;1 lb 2
200
10
3
( As ) 2 9 D < 889000 <
( A s )
3
3 :
in
2
= 0.2255 sq.in. 9 D < 3 in :
T!bl AT 1: 9 UNC T,"!)& U& D =
5 8
in 9 A s
= 0.22<0 sq.in.
b T = CDF i C = 0.2
= 0.? s p s p = 85 ksi 9 T!bl 5.2 si = 0.?( 859000 ) = ;<9500 psi F i = si A s = ( ;<9500)( 0.22<0) = 1;928? lb si
T%g,+%g +#"@
5 (1;928?) = 21<1 in − lb 8
T = 0.2 DF i = 0.2
22;.
T, A"%7! S+l Fl!g S+!)!") &'7%%& +,!+ 8 b#l+& !" +# b &) # l!g& #" :-%. '%' *," +, &+! #" *!+" '"&&" %& 1500 '&%. I+ %& !l&# &'7%%) +,!+9 % 7!l7l!+%g +, b#l+ l#!)9 +, #+&%) )%!+" # +, g!&=+9 *,%7, %& < 31< %.9 &,#l) b &). D+"% ! +, )%!+" # +, UNC b#l+& % +,/ !" *ll-+%g,+) !) !) # ASTM 35: BD T!bl 5-29 b +, !''"#$%!+ +#"@ +# +%g,+ +, +& % +, %%+%!l &+"&& %& ?0 # +, '"## &+"&&. T, S+!)!") &'7%%& +,!+ 1 1: –%. b#l+& *%+, 8 +,.%. b &) +,& b#l+& !" !l&# &b>7+) +# b)%g. H#* )#& /#" !&*" 7#'!"6
S#l+%# T!bl 5.29 ASTM 35: BD s p s y
= 120 ksi = 125 ksi 2
π 3 1500 < : 1< = 5<38 lb F e = 8
P!g 5 # :0
SECTION 3 – SCREW FASTENINGS
=
! F e
5<38 = A s
s y
( As )
3
< 1259000
<
9 D <
2
( A s )
3
3 :
in
2
= 0.:18: sq.in. 9
T!bl AT 1: 9 UNC T,"!)& U& D = D >
3 :
; 8
in 9 A s
= 0.:<20 sq.in.
in
& sd = 50,000 psi 5.<9 ASTM A35: BD F 5638 As = e = = 0.1128sq.in. sd 50,000 T!bl AT 1: 9 UNC T,"!)& U& D =
3 4
in9 A s
= 0.33: sq.in.
b T = 0.2 DF i si
= 0.? s p
si
= 0.?(1209000) = 1089000 psi
F i
= si A s = (1089000) ( 0.33:0) = 3<90;2 lb
T%g,+%g +#"@
3 ( 36,072) = 5411in− lb 4
T = 0.2DF i = 0.2
D < 1
1 :
in !& &'7%%) b/ +, &+!)!").
CHEC PROBLEMS 228.
A 7!' &7"*9 %.-10-UNC-29 *%+, ! ,$!g#!l ,!) +,!+ %& ?1< %. +,%7=9 7!""%& ! +&%l l#!) # 3000 lb. I +, !+"%!l %& AISI 10159 7#l) )"!*9 %) +, !7+#" # &!+/ b!&) # l+%!+ &+"g+,& # ! +, +,"!)) &,!=9 b +, ,!) !g!%&+ b%g &,!") #9 !) 7 +, b!"%g &"!7 )" +, ,!). ) I& +," !/ ) +# 7#&%)" +, &+"g+, # &+!)!") 7!'-&7"* ,!)& % )&%g6
S#l+%# F#" %. UNC9 T!bl AT 1:9 A s
= 0.33: sq.in.
H!)
P!g < # :0
SECTION 3 – SCREW FASTENINGS
A = 1
1 8
in.
F#" AISI 10159 7#l) )"!* su = ;; ksi 9 sus = 58 ksi
= F =
! s N =
A s
su
b s s = t =
s s
? 1<
=
N =
7
0.33:
;;9000
=
sd
3000
8?82
π Dt
in
π : 1< sus
θ
=
= 8.5;
F
3000 3 ?
s s
= 8?82 psi
=
= 22<: psi
589000 22<:
3<0
o
12
= 25.<
= 30 o
2
Area
sb
=
N =
)
1 1 1 A A 1 8 = <( 2 ) +! θ = <( 2 ) 2 2 2 2 2
F Area − Ab
su sb
=
=
3000 2
3 1.0?< − : :
;;9000 :58<
π
+! 30
= 1.0?< sq.in.
= :58< psi
= 1<.8
N# ) +# 7#&%)" +, &+"g+, # &+!)!") 7!'-&7"* ,!)& &%7 %+& !7+#" # &!+/ %& ("/ 7, ,%g," +,! #" +, +,"!)) &,!=.
P!g ; # :0
SECTION 3 – SCREW FASTENINGS
22?.
A b#l+9 1 18 %.-;-UNC-29 %& &b>7+) +# ! +&%l l#!) # 109000 lb. T, ,!) ,!& ! +,%7=&& # %. !) +, + ! +,%7=&& # 1 %. I +, !+"%!l %& SAE g"!) 2 T!bl 5.29 %) +, )&%g !7+#" !& b!&) # l+%!+ &+"&&& ! # +, +,"!)) &,!=9 b # +, ,!) !g!%&+ b%g &,!") #9 !) 7 # +, b!"%g &"!7 )" +, ,!). T, b#l+ ,!) %& %%&,). ) I& +," !/ ) +# 7#&%)" +, &+"g+, # &+!)!") b#l+ ,!)& % )&%g6
S#l+%# F#" SAE g"!) 2 T!bl 5.29 D
=1
1 8
= 55 ksi 9 sus = 0.;5su
su
F#" 1 18 %.-;-UNC-2 T!bl AT 1: A s
= 0.;<3 sq.in.
A = 1
11 1<
in
F = 109000 lb.
! s = N =
F A s
su sd
3
s s
:
=
N =
7
109000 0.;<3
559000
=
b s s = t =
=
13910<
= 13910< psi
= :.2
F π Dt
in
109000 = 3;;3 psi 1 3 π 1 8 :
sus
θ
s s
=
=
0.;5( 559000 )
3<0
3;;3 o
12
P!g 8 # :0
= 30 o
= 11
in
SECTION 3 – SCREW FASTENINGS
2
1 11 1 A A 1 1< +! θ = <( 2) Area = <( 2 ) 2 2 2 2 2 sb
=
N =
F Area − Ab
su sb
=
=
109000
2.:<<1 −
559000 <;?3
2
1 : 8
π
1
+! 30
= 2.:<<1 sq.in.
= <;?3 psi
= 8.1
) N# ) +# 7#&%)" +, &+"g+, # &+!)!") b#l+ ,!) % )&%g &%7 %+& !7+#" # &!+/ %& ,%g," +,! #" +, +,"!)) &,!=. 230.
A !$%!l #"7 %& !''l%) +# ! "gl!" + *,%7, # 7#"& +)& +# &,!" +, +,"!)& # +, &7"*. ! W,!+ %& +, "!+%# # +, #"7 7&&!"/ +# &,!" +, +,"!)& !ll +,"!)& %%+%!ll/ % %+%!+ 7#+!7+ +# +, #"7 7&&!"/ +# 'll +, b#l+ % +*#6 U& 7#!"& +,"!)&9 ! 1 -%. b#l+9 !) !&& +,!+ sus = 0.;5su . T, ,!) +,%7=&& %& 1 %. !) +, + +,%7=&& %& 1 51< %. b I& !%l" # +, +,"!) b/ &,!" l%=l/ % +,%& b#l+6
S#l+%# 1 - %. UNC A s
= 1.:05 sq.in.
! F s &,!" #"7 sus π Dt D = 1 t = 1 sus
1
2 5
in.
in. 1< = 0.;5su
1 5 = ( 0.;5 su )( π ) 1 1 = :.<388su 2 1< F = su A s = 1.:05su
F s
R!+%#
:.<388 su 1.:05 su
= 3 .3
b R!+%# 19 !%l" b/ &,!" %& #+ l%=l/ +# #77". 231.
F#" b#l+) &+"7+"!l >#%+&9 &'7%%7!+%#& &gg&+ +,!+ -%. b#l+& ,%g,&+"g+, !+"%!l b +%g,+) +# ! %%+%!l +&%# # F i = 129500 lb . W,!+
P!g ? # :0
SECTION 3 – SCREW FASTENINGS &,#l) b +, !''"#$%!+ +%g,+%g +#"@6 H#* )#& /#" !&*" 7#'!" *%+, T = ?0 ft − lb .9 *,%7, %& +, (!l % +, &'7%%7!+%#6 S#l+%#
1 (129500) = 1250 in − lb 2
T = 0.2 DF i = 0.2 T = ?0 ft − lb
232.
in − lb < 1250 in − lb #.=. = 1080
O +,#) # &+%!+%g +, %%+%!l +&%l &+"&& % ! +%g,+) b#l+ %& +# +" +, + +%l %+ %& &g9 b+ *%+, # &%g%%7!+ &+"&& % +, b#l+. T, +, + %& +") +,"#g, ! '")+"%) !gl +,!+ %)7& ! 7"+!% %+ &+"!% 7#""&'#)%g +# +, )&%") &+"&&. A - %. b#l+ # +, +/' &,#* % F%g. 5.:9 Text 9 %& +") )#* +%l9 #" '"!7+%7!l '"'#&&9 +, )%!+" # +, +%" &,!= %& +, %#" )%!+". T, !+"%!l %& AISI :1:09 OT 1200 #F. T, g"%' %& 5 %. !) +, 7+%( &+"!% lg+, %& &+%!+) +# b 5.3 %. I +, %%+%!l +&%l &+"&& !+ +, "##+ )%!+" %& +# b !b#+ ;5 # +, /%l) &+"g+,9 +,"#g, *,!+ !gl &,#l) +, + b +") !+" %+ %& >&+ &g6 T, +,"!)& !" UNC !) +, '!"+& b%g b#l+) !" !&&) +# b "%g%).
S#l+%#
F#" %.9 UNC Dr A s
= 0.<2;3 in = 0.33: sq.in.
Th in. = 10
AISI :1:09 OT 1200 #F s y
= 115 ksi
s
= 0.;5(115) = 8<.25 ksi
δ
= sL E
L
= 5.3 in
'%+7,9 p =
θ
θ
= =
δ
p
1 10
( 3<0 )
sL pE
o
(3<0 ) o
P!g 10 # :0
in = 0.10 in
SECTION 3 – SCREW FASTENINGS
( 8<9250)( 5.3) (3<0o ) = 55o < ( 0.10) ( 30 ×10 )
θ =
233.
W, b#+, )& # ! b#l+ !" !77&&%bl #" %7"#+" !&"+&9 +, +#+!l l#g!+%# δ 7!&) b/ +%g,+%g 7! b )+"%) b/ !&"%g lg+,& b#" !) !+" +%g,+%g. I #")" +# ")7 +,%& +#+!l l#g!+%# +# %+ l#g!+%#9 +,7 +# &+"&&9 +, 7+%( &+"!% lg+, #" +, b#l+ &+ b =#*. F#" ! 1 J-% &+l b#l+9 +,"!)) #" %+& ll lg+,9 8-+,"!) &"%&9 +, 7+%( &+"!% lg+, ,!& b #) b/ $'"%+ +# b Le = 0.?;G + 1.1 in. 9 *," G %& +, g"%' b/ W.A. M7D#!l)9 N#"+, C!"#l%! S+!+ C#llg. L+ +, b#l+ !+"%!l b AISI 8;:29 OT 1000 #F. ! I+ %& )&%") +,!+ +, %%+%!l +&%l &+"&& b !b#+ 0.; s y . W,!+ +#+!l l#g!+%# &,#l) b #b+!%) #" ! g"%' lg+, # :.8 %.6 b I(&+%g!+ +, !''"#$%!+ +%g,+%g +#"@ #" +, &'7%%) 7#)%+%#. H#* 7#l) +,%& +#"@ b #b+!%)6
S#l+%# 1 J %.9 8-+,"!) &"%& T!bl 5.1 Dr = 1.0?<< in A s
= 1.000 sq.in.
Th in. = 8
AISI 8;:29 OT 1000 #F
= 1:; ksi
s y
! si = 0.;0 s y si
= 0.;0(1:;) = 102.? ksi = 1029?00 psi
δ
=
Le
si Le E
= 0.?;G + 1.1 in.
= :.8 in Le = 0.?;( :.8) + 1.1 in. = 5.;5< in G
δ
= s L = i
e
(1029?00)( 5.;5< ) 30 × 10
E
b θ = G
δ
p
=
<:TL
= 11.5 × 10<
p =
1 8
:
π Dr G
psi
in = 0.125 in
P!g 11 # :0
<
= 0.01?;5 in
SECTION 3 – SCREW FASTENINGS
θ
=
0.01?;5 0.125
=
<:T ( 5.;5< )
(
×
π (1.0?<< ) 11.5 10 :
<
)
T = 229:08 in − lb
ELASTIC CONSIDERATIONS 235.
T, b" C &,#* %& '!"+ # ! &*%(l 7#7+%# +,!+ %& +# b 7l!') b/ ! 1-%. b#l+ D +# +, b" B9 *,%7, ,!& l!"g )%&%#& % +, 'l! '"')%7l!" +# +, '!'". B#+, B !) C !" !l% !ll#/ 202:-T:9 HT !g). T, b#l+ %& !) # AISI C11139 7#l)-)"!* &+lK 7#&%)" +, +,"!)) &,!= +# b 2 %. l#gK %+ %& *ll +%g,+) *%+, ! +#"@ # 250 +lb.K UNC +,"!)&9 lb"%7!+). ! E&+%!+ +, %%+%!l +&%# b/ @!+%# 5.29 !&& l!&+%7 !7+%#9 !) 7#'+ +, b#l+ l#g!+%# !) +, +#+!l )#"!+%# # B !) C. L+ +, 7+%( &+"!% lg+, b 2 %. b A+" +%g,+%g ! $+"!l !$%!l #"7 F e # 5000 lb. %& !''l%) +# b" C. D+"% +, +#+!l #"!l &+"&&& % +, b#l+ !) % B !) C. 7 D+"% +, l#!) "@%") +# #' +, 7#7+%#. D"!* ! )%!g"! &%%l!" +# F%g. 5.<9 Text 9 l#7!+%g '#%+& A9 B9 D !) M.
P"#b. 2359 23< S#l+%# F#" !l% !ll#/9 202:-T: HT !g)9 E = 10.< × 10 < psi s y
= :; ksi
F#" AISI C11139 7#l)-)"!* &+l9 E = 30 ×10< psi s y
= ;2 ksi
! T = 0.2 DF i D = 1 in. T = 250 ft − lb = 3000 in − lb
F i
= 159000 lb
D#"!+%#& L = 2 in. T!bl AT 1:9 1-%. UNC B#l+9 A s = 0.<< sq.in.
P!g 12 # :0
SECTION 3 – SCREW FASTENINGS π
Ab =
:
(1) 2 = 0.;85 sq.in.
B#l+ δ i
F i L
=
(159000)( 2) = 0.0012; in ( 0.;85) ( 30 × 10 < )
=
Ab E i
Mb" B !) C F i L δ c
=
Ac
= π De2 − π D 2
Ac E c :
:
De N+ #" ,!) *%)+, !7"#&& l!+&
h 2
T!bl AT 1: A = 1
1
2 1 De = 1 2
in
+ 2 = 2 1 in. 2
2
Ac
= π De2 − π D 2
Ac
=
δ c
=
:
π
:
:
[( 2.5)
F i L Ac E c
2
=
− (1) 2 ] = :.123: sq.in.
(159000)( 2) = 0.000<8< in. ( :.123: ) (10.< ×10< )
b F e = 5000 lb
k δ b 0.000<8< F ∆ F b = F e b = = 5000 e 0.000<8< + 0.0012; k b + k c δ b + δ c ∆ F b = 1;5: lb B#l+ F t
= F i + ∆ F b = 159000 + 1;5: = 1<9;5: lb
sb
=
F t A s
=
1<9;5: 0.<0<
= 2?9132 psi
Mb" B !) C
k = F i − F e c k b + k c δ c F c = F i − F e + δ δ b c F c
F c
0.0012; = 119;5: lb = 159000 − 5000 0.0012; + 0.000<8<
sc
=
F c Ac
=
119;5: :.123:
= 2851 psi
7 F o #'%g l#!)
P!g 13 # :0
SECTION 3 – SCREW FASTENINGS
F o
δ + δ 0.0012; + 0.000<8< = 239102 lb 15 9 000 = F i i c = 0.0012; δ i
F%g. 5.<
23;.
A 1-%. &+l b#l+ %& &) +# 7l!' +*# !l% 201:-T<9 HT !g) 'l!+& +#g+," !& &,#* b/ F%g. 5.?9 Text . T, !l% 'l!+& ,!( ! +#+!l +,%7=&& # 2 %. !) ! @%(!l+ )%!+" # 2 %. T, b#l+ %& ,!+) +# ! +'"!+" # 200 #F9 +, %&"+) % +, !l% 'l!+&9 *,%7, !" !+ 80 #F9 !) +%g,+) &# !& +# ,!( ! +&%l +%g,+%g &+"&& # 30 =&% % +, +,"!)) &,!= *,%l &+l !+ 200 #F. W,!+ %& +, +&%l &+"&& % +, b#l+ !+" !&&bl/ ,!& 7##l) +# 80 #F6 T, )#"!+%#& !" l!&+%7. F%g" 5.?
S#l+%# F#" !l% 201:-T< E = 10.< × 10 < psi
sb
= 309000 psi
F i
π = sb Ab = ( 309000 ) (1) 2 = 2395<2 lb :
P!g 1: # :0
SECTION 3 – SCREW FASTENINGS < S+l b#l+. E b = 30 × 10 psi s b L ( 309000 )( 2)
δ i
=
δ c
=
Ac
= π De − π D
Ac
= π [( 2 ) − (1) ] = 2.35<2 sq.in.
E c
= 10.< × 10
δ c
=
E b
=
F i L Ac E c
30 × 10
<
= 0.002 in.
.
2
:
2
:
2
2
:
F i L
=
Ac E c
L′ = L − δ c
<
psi
( 2395<2 )( 2) = 0.00188; in ( 2.35<2 ) (10.< × 10< )
= 2 − 0.00188; = 1.??8113 in.
∆ L = α L′∆t
= 0.00000; in. ( in. − F ) #" &+l ∆ L = ( 0.00000;)(1.??8113)( 80 − 200) = −0.001<;8 in.
α
′ = δ i + ∆ L = 0.002 − 0.001<;8 = 0.000322 in. s′ L δ i′ = b δ i
E b
0.000322 =
′( ) < 30 ×10 sb 2
sb′ = :830 psi
238.
A 1 18-%. &+l b#l+ A '!&&& +,"#g, ! /ll#* b"!&& B3<-8 +b B !& &,#*. T, lg+, # +, +b %& 30 %. (%"+!ll/ +, +,"!)) b#l+ lg+,9 +, +,"!)& # +, b#l+ !" UNC9 !) +, +b& 7"#&&-&7+%#!l !"! %& 2 &@. %. A+" +, + %& &g %+ %& +%g,+) J +". ! W,!+ #"!l &+"&&& *%ll b '"#)7) % +, b#l+ !) % +, +b6 A&& +,!+ *!&,"&9 +9 !) ,!) !" "%g%). b W,!+ !" +, &+"&&& % ! !$%!l l#!) # 5 =%'& %& #* !''l%) +# +, b#l+& )6 C#'+ +, b#l+ l#!) +,!+ >&+ "&l+& % ! 4"# &+"&& % +, +b.
P"#b. 238
P!g 15 # :0
SECTION 3 – SCREW FASTENINGS S#l+%# F#" ll#* b"!&&9 B3<-89 E = 15 × 10< psi
S+l b#l+ E = 30 ×10< psi
T!bl AT 1:9 1 18 %.9 UNC Dr A s
= 0.?:?; in. = 0.;<3 sq.in.
Th in
=;
L = 30 in. θ
= δ i
p
p = θ
=
1 ; 1 :
in.
+"
δ i
1 1 1 = = in. : ; 28
δ i
=
1 28
F i L Ab E b
=
F i ( 30 ) 2
π 1 1 (30 ×10 ) : 8 <
F i
= 359500 lb
!
B#l+ sb
sc
F i A s
=
359500 0.;<3
= :<952; psi
= F i
Tb sc Ac
=
Ac
= 2 sq.in.
=
F i Ac
=
359500 2
= 1;9;50 psi
b F e = 5000 lb k c
=
Ac E c L
=
( 2 ) (15 × 10 < ) 30
= 190009000 lb
in
2
π 1 1 ( 30 × 10 ) : 8 = = ??:9000 lb <
A E k b = b b L
P!g 1< # :0
30
in
SECTION 3 – SCREW FASTENINGS B#l+&
k b F e k k + b c
F t = F i + F t
??:9000 = 359500 + ( 5000) = 389000 lb ??:9000 + 190009000
st
=
F t A s
=
389000 0.;<3
= :?9800 psi
Tb F c
k = F i − c F e k k + b c
F c
190009000 ( = 359500 − 5000) = 339000 lb ??:9000 + 190009000
sc
=
F c Ac
=
339000 2
= 1<9500 psi
F#" 4"# &+"&& % +, +b F o
k + k ??:9000 + 190009000 = b c ( 359500) = ;09;8; lb F i = 190009000 k c
ENDURANCE STRENGTH DESIGN PROBLEMS 23?.
A& &,#* )%!g"!!+%7!ll/9 ! b!"%g %& &''#"+) % ! '%ll#* bl#7= !++!7,) +# ! #(",!) b! b/ +*# 7!' &7"*&9 !7, # *,%7,9 %+ !/ b !&&)9 7!""%) ,!l +, +#+!l b!"%g l#!). T,%& l#!) !7+& ("+%7!ll/ )#**!")9 (!"/%g "# 0 +# 1500 lb. T, &7"*& !" +# b !) # AISI C11189 !& "#ll)9 !) +,/ !" +%g,+) +# g%( ! %%+%!l &+"&& # !b#+ si = 0.5s y . T, '%ll#* bl#7= %& !) # 7l!&&-20 7!&+ %"#. A&& +,!+ +, 7+%( lg+, # &7"* %& @!l +# +, +,%7=&& t 9 !& &,#*9 !) +,!+ +, ,!) !) b! !" "%g%) #("l/ 7#&"(!+%(6. T, @%(!l+ )%!+" # +, 7#'"&&%# !"! !/ b +!= !& +*%7 +, b#l+ )%!+". F#" ! )&%g !7+#" # 1.;59 )+"% +, &%4 # +, &7"* ! "# +, S#)"b"g l%9 b "# +, #)%%) G##)! l%. 7 W,!+ &%4 )# /# "7#) &%g6
P"#bl 23?
P!g 1; # :0
SECTION 3 – SCREW FASTENINGS
S#l+%# F#" AISI C11189 !& "#ll)
= :< ksi = ;5 ksi
s y
su
= 0.5s y si = 0.5( :< ) = 23 ksi = 239000 psi si
= si A s = 23 A s
F i
kip = 239000 A s lb
k ∆ F b = b F e k b + k c k b
= Ab E b
E b
= 30 × 10
Lb
= t
k c
=
Lb
<
psi &+l
Ac E c Lc
F#" 7!&+-%"# 7l!&& 20 Lc
= ?.< ×10< psi = t
Ac
= π De2 − π D 2
Ab
=
De
=
Ac
= π ( 2 D ) − π D = 3π D = 3 Ab
k b
= Ab E b
E c
:
π
D
2
: 2 D
2
:
2
2
:
:
Lb
k b
=
k c
=
Ab ( 30 ×10< ) t < 3 Ab ( ?.< × 10 )
k b k b
:
+ k c
t
=
30 × 10 30 × 10
∆ F b1 = 0
P!g 18 # :0
<
<
+ 3(?.< ×10 ) <
=
300 588
SECTION 3 – SCREW FASTENINGS
k 300 1500 ∆ F b = b = 383 lb F e = k b + k c 588 2 1 1 F m = F i + ( ∆ F b + ∆ F b ) = 239000 A s + ( 383 + 0 ) = 239000 A s + 1?2 lb 2
2
2
1
2
F a
= 1 ( ∆ F − ∆ F ) = 1 ( 383 − 0 ) = 1?2 lb
sn
= 0.5 su = 0.5( ;59000 psi) = 3;9500 psi
b2
2
b1
2
F#" !$%!l l#!)%g *%+, &%4 !7+#" sn
= ( 0.8)( 0.85)( 3;9500 psi ) = 259500
psi
N = 1.;5
sm
=
F m
sa
=
F a
=
A s A s
=
239000 A s
A s
+
1?2
A s
= 239000 +
1?2
A s
T!bl AT 129 K f = 1.8 ! S#)"b"g l% 1
N
=
1 1.;5
sm s y
+
K f sa sn
1?2 239000 + 1?2 (1.8) A s As = + :<9000
259500
= 0.2:82 sq.in.
A s
T!bl AT 1:9 UNC U& D =
3 :
in. 9 A s
= 0.33: sq.in.
b M#)%%& G##)! l% 1
N
=
1 1.;5
A s
sm su
+
K f sa sn
1?2 239000 + 1?2 (1.8) A s As = + ;59000
= 0.0<0? sq.in.
T!bl AT 1:9 UNC
P!g 1? # :0
259500
1?2
A s
SECTION 3 – SCREW FASTENINGS 3
U& D =
8
in. 9 A s
= 0.0;;5 sq.in.
7 R7#))9 D =
3 :
in. − NC
A 7#7+%# &%%l!" +# F%g. 5.?9 Text 9 %& &b>7+) +# ! $+"!l l#!) +,!+ (!"%) "# 0 +# 1250 lb. T, b#l+ %& 7#l) #"g) "# AISI B1113 &+lK UNC +,"!)&.T, !l% '!"+& C 3003 H1: ,!( ! +#+!l +,%7=&& # 1 %. !) ! $+"!l )%!+" # 2 D . I+ %& )&%") +,!+ +, 7#7+%# #+ #' #" ! $+"!l l#!) # 1.5 F e . D+"% ! +, %%+%!l +&%l l#!) # +, b#l+9 b +, b#l+ )%!+" #" N = 2 b!&) # +, S#)"b"g l%.
2:0.
F%g. 5.?
S#l+%#
k c lb k k + b c
! F i = !F e !
= 1 .5
k b
= Ab E b
Ab
=
E b
= 30 × 10
Lb
=1
k c
=
Ac
= π De2 − π D 2
Ac
= π ( 2 D ) − π D = 3π D = 3 Ab
Lb
π
:
D
1 2
2
<
psi
in.
Ac E c Lc
: De = 2 D
:
2
:
P!g 20 # :0
2
:
2
:
SECTION 3 – SCREW FASTENINGS E c
= 10 × 10 < psi 3003-H1: !l%
Lc
=1
=
k b
1
in.
2
Ab ( 30 ×10< )
1 1 2 < 3 Ab (10 × 10 ) = 1 1 2
k c
k c k b
+ k c
=
(
3 10 ×10 30 ×10
<
<
)
+ 3(10 ×10< )
= 0.5
F e = 1250 lb
k c lb k k + b c
F i = !F e F i
= (1.5)(1250) ( 0.5) = ?3;.5 lb
b F#" AISI B1113 &+l9 7#l) #"g)
s y
= 83 ksi = ;2 ksi
sn
= 0.5 su = 0.5( 83) = :1.5 ksi = :19500
su
psi
F#" !$%!l l#!)%g *%+, &%4 !7+#" sn
= ( 0.8)( 0.85)( :19500 psi) = 289220
psi
k ∆ F b = b F e k k + b c ∆ F b1 = 0 < k b 30 ×10 ∆ F b 2 = = (1250) = <25 lb F e < < + × + ( × ) k k 30 10 3 10 10 b c
F m
1 1 = F i + ( ∆ F b 2 + ∆ F b1 ) = ?3;.5 + ( <25 + 0) = 1250 lb 2
2
1
1
2
2
F a
= ( ∆ F b 2 − ∆ F b1 ) = ( <25 − 0) = 312.5 lb
sm
=
F m
sa
=
F a
A s A s
=
1250
=
312.5
A s A s
P!g 21 # :0
SECTION 3 – SCREW FASTENINGS
S#)"b"g l%9 K f = 1.8 T!bl AT 12 1
=
N 1 2
=
A s
sm s y
+
K f sa sn
1250 ;29000 A s
+
(1.8) ( 312.5) 289220A s
= 0.0;:5? sq.in.
T!bl AT 1:9 UNC U& D = 2:3.
3 8
in. 9 A s
= 0.0;;5 sq.in.
T,%& '"#bl 7#7"& +, F"# 7#'"&&#" # 22< &%49 10 $ 18 %.K 10 &+)&9 UNCK !) # C11189 !& "#ll)K 200 '&% g!& '"&&". T, %%+%!l +&%# % +, b#l+&9 !&&) +# b @!ll/ l#!))9 %& &7, +,!+ ! 7/l%)" '"&&" # 300 '&% %& "@%") #" +, >#%+ +# b # +, #'%g. T, b#l+) '!"+& !" 7!&+ &+l !) #" +, %"&+ 7!l7l!+%#&9 %+ *%ll b &!+%&!7+#"%l/ +# !&& +, @%(!l+ )%!+" # +, 7#'"&&) '!"+& +# b +*%7 +, b#l+ &%4. ! F#" N = 2 # +, S#)"b"g 7"%+"%#9 *,!+ b#l+ &%4 %& "@%")6 b C#'+ +, +#"@ "@%") #" +, &'7%%) %%+%!l +&%#.
S#l+%# 2
π (10) = 235< lb. F o = 300 : 10 k c F i = F o k k + b c k b
= Ab E b
Ab
=
E b
= 30 × 10 < psi
Lb
= L
k c
=
Ac
= π De2 − π D 2
Ac
= π ( 2 D ) − π D = 3π D = 3 Ab
Lb
π
:
D
2
Ac E c Lc
: De = 2 D
:
2
:
C!&+ S+l9 E c Lc
= L
P!g 22 # :0
2
2
:
= 30 × 10
:
<
psi
SECTION 3 – SCREW FASTENINGS
=
k b
=
k c
Ab ( 30 ×10< )
(
L
3 Ab 30 × 10
<
) = 3k
b
L
k c 3k b ( ) 235< = = 1;<; lb 3 k k k k + + b b c b
F i = F o
! ∆ F b
k = b F e k k + b c
∆ F b1 = 0
k k b π (10) ( 200) = b = 3?3 lb F e = k + 3k : k k + 10 b b c b 2
∆ F b
2
F m
= F i + 1 ( ∆ F b 2 + ∆ F b1 ) = 1;<; + 1 ( 3?3 + 0) = 1?<: lb
F a
= 1 ( ∆ F − ∆ F ) = 1 ( 3?3 − 0) = 1?< lb
sm
=
sa
=
2
b2
2 F m
=
A s F a A s
2
=
b1
2
1?<:
A s
1?<
A s
F#" C11189 !& "#ll)
= ;5 ksi s y = :< ksi sn = 0.5 su = 0.5( ;5) = 3;.5 ksi = 3;9500 psi su
F#" !$%!l l#!)%g *%+, &%4 !7+#"
= ( 0.8)( 0.85)( 3;9500 psi) = 259500 psi
sn
= 1.8 T!bl AT 12
K f
1
=
N 1 2
=
A s
sm s y
+
K f sa sn
1?<: :<9000 A s
+ (1.8) (1?< ) 259500 A s
= 0.1131 sq.in.
T!bl AT 1:9 UNC U& D =
1 2
in. 9 A s
b T = 0.2 DF i
P!g 23 # :0
= 0.1:1? sq.in.
SECTION 3 – SCREW FASTENINGS
1 (1;<;) = 1;<.; in − lb. 2
T = 0.2
2:5.
A 7!&+-%"# 7l!&& 35 D%&l-g% 7/l%)" ,!) %& ,l) # 8 &+) b#l+& *%+, UNC +,"!)&. T,& b#l+& !" !) # AISI 31:0 &+l9 OT 1000 #F F%g. AF2. A&& +,!+ +, 7#'"&&) !+"%!l ,!& ! @%(!l+ )%!+" +*%7 +, b#l+ &%4. T, !$% 7/l%)" '"&&" %& ;50 '&% !) +, b#" # +, g% %& 8 %. L+ +, %%+%!l b#l+ l#!) b &7, +,!+ ! 7/l%)" '"&&" # 1500 '&% b"%g& +, >#%+ +# +, '#%+ # #'%g. F#" ! )&%g !7+#" # 29 )+"% +, b#l+ )%!+" ! &%g +, S#)"b"g @!+%#9 b &%g +, G##)! @!+%#. 7 W,!+ !''"#$%!+ +#"@ *%ll b "@%") +# %)7 +, )&%") %%+%!l &+"&&6 ) D+"% +, "!+%# # +, %%+%!l &+"&& +# +, /%l) &+"g+,. C#&%)"%g +, l&&#& # $'"%7 i5.89 *,!+ %%+%!l &+"&& *#l) /# "7#)6 U&%g +,%& (!l9 *,!+ !7+#" # &!+/ %& 7#'+) "# +, S#)"b"g @!+%#6
S#l+%# 2 π ( 8 ) = ?:25 lb. F o = 1500 : 8 k c F i = F o k b + k c
k b
= Ab E b
Ab
=
E b
= 30 × 10 < psi
Lb
= L
k c
=
Ac
= π De2 − π D 2
Ac
= π ( 2 D ) − π D = 3π D = 3 Ab
Lb
π
:
D
2
Ac E c Lc
: De = 2 D
E c Lc
:
2
2
:
:
= 1:.5 ×10 = L
<
k b
=
k c
=
L < 3 Ab (1:.5 × 10 )
P!g 2: # :0
:
psi 9 #" 7!&+-%"# 7l!&& 35
Ab ( 30 ×10< )
L
2
SECTION 3 – SCREW FASTENINGS
k F = F k + k c
i
o
b
c
< 3(1:.5 × 10 ) ?:25 ( ) = 30 ×10< + 3(1:.5 ×10< ) = 55;8 lb
k ∆ F b = b F e k k + b c ∆ F b1 = 0
k ∆ F 2 = k + k b
b
b
c
< π ( 8) 2 ( ;50) 30 ×10 = 1?23 lb F = 30 ×10< + 3(1:.5 ×10< ) : 8 e
F m
= F i + 1 ( ∆ F b 2 + ∆ F b1 ) = 55;8 + 1 (1?23 + 0) = <5:0 lb
F a
= 1 ( ∆ F − ∆ F ) = 1 (1?23 − 0 ) = ?<2 lb
sm
=
m F
sa
=
F a
2
b2
2
A s A s
2
=
<5:0
=
?<2
b1
2
A s A s
! F#" AISI 31:0 &+l9 OT 1000 #F
= 153 ksi = 13: ksi = 0.5 su = 0.5(153) = ;<.5 ksi = ;<9500 psi
su s y
sn
F#" !$%!l l#!)%g *%+, &%4 !7+#"
= ( 0.8)( 0.85)( ;<9500 psi ) = 529000 T!bl AT 129 K f = 3.3 ,!")) sn
S#)"b"g E@!+%# 1
=
N 1 2
=
A s
sm s y
+
K f sa sn
<5:0 13:9000 A s
+ ( 3.3) ( ?<2 ) 529000 A s
= 0.21?; sq.in.
T!bl AT 1:9 UNC U& D =
5 8
in. 9 A s
= 0.22< sq.in.
b G##)! E@!+%# 1
N
=
sm su
+
K f sa sn
P!g 25 # :0
psi
SECTION 3 – SCREW FASTENINGS 1 2
=
A s
<5:0 1539000 A s
+ ( 3.3) ( ?<2 ) 529000 A s
= 0.20;< sq.in.
T!bl AT 1:9 UNC 5
U& D =
8
= 0.22< sq.in.
in. 9 A s
7 T = 0.2 DF i
5 ( 55;8) =
T = 0.2
) si
=
R!+%# i5.8 si
F i A s si
=
s y
55;8
=
0.22<
= 2:9<81 psi
2:9<81 13:9000
= 0.18:
= 0.85 s y = 0.85(13:9000) = 1139?00
psi
F!7+#" # &!+/ F i
= si A s = (1139?00)( 0.22<) = 259;:2 lb 1
F m
= 259;:2 + (1?23) = 2<9;0: lb
F a
= 1 (1?23) = ?<2 lb
sm
=
sa
=
2
2
F m A s
F a A s
= =
2<9;0: 0.22< ?<2
0.22<
= 118915? psi
= :25; psi
S#)"b"g E@!+%# 1
N 1
N
= =
sm s y
+
K f sa sn
118915? 13:9000
+
( 3.3)( :25;) 529000
N = 0.8;
2:<.
A 309000-lb. b#)/ %& +# b #+) # ! &,!=" (%b"!+#". T, &,!=" *%ll $"+ ! ,!"#%7 #"7 # F = 309000 &% 2π t f lb. # +, b#)/ *," f 7'& %& +, "@7/ !) t &7. %& +, +%. T, "@7/ 7! b (!"%) "# 5 +# 109000 7'&. T, ,!"#%7 #"7 *%ll $"+ ! +&%l l#!) # +, b#l+& +,!+ !++!7, +, b#)/ +# +, &,!=" *, F %& '#&%+%(. D+"% +, %% b" # -%.-UNF b#l+& +,!+ &+ b &) #" N = 2 b!&) # S#)"b"g l%. T, !+"%!l # +, b#l+& %& +# b AISI 8<309 WT 1100 #FK +, !+"%!l # +, b#)/ +,!+ %& +# b (%b"!+) %& !l% !ll#/9 201:-T< !) +, >#%+ %&
P!g 2< # :0
SECTION 3 – SCREW FASTENINGS #+ +# #' #" ! $+"!l #"7 +,!+ %& 1.25 +%& +, !$% #"7 $"+) b/ +, &,!=". I+ !/ b !&&) +,!+ +, @%(!l+ )%!+" # +, !+"%!l % 7#'"&&%# %& +*%7 +, b#l+ )%!+".
S#l+%#
=0 F e !$ = 309000 lb F e %
k c k k + b c
F i = !F e !
= 1.25
k b
= Ab E b
Ab
=
E b
= 30 × 10 < psi
Lb
= L
k c
=
Ac
= π De2 − π D 2
Ac
= π ( 2 D ) − π D = 3π D = 3 Ab
Lb
π
:
D
2
Ac E c Lc
: De = 2 D
E c Lc
k b
k c
:
2
2
:
:
= 10.< ×10 = L
<
=
Ab E b
=
Ac E c
Lb
Lc
=
2
:
psi 9 Al% 201:-T<
Ab ( 30 × 10< )
=
P!g 2; # :0
L 3 Ab (10.< × 10
L
<
)
SECTION 3 – SCREW FASTENINGS
k c + k k b c
F i = !F e
< 3(10.< ×10 ) F i = (1.25)( 309000) = 1?92?< lb < < ( ) 30 10 3 10 . < 10 × + ×
k ∆ F b = b F e k k + b c ∆ F b1 = 0
k 30 × 10 F ∆ F b = b = e k b + k c 30 ×10 + 3(10.< ×10 <
2
<
<
( 309000) = 1:95<3 lb )
= F i + 1 ( ∆ F b 2 + ∆ F b1 ) = 1?92?< + 1 (1:95<3 + 0 ) = 2<95;8 lb
F m
2
2
1
1
2
2
F a
= ( ∆ F b 2 − ∆ F b1 ) = (1:95<3 − 0) = ;282 lb
sm
=
F m
s a
=
F a
nA s nA s
F#" -%.-UNF T!bl AT 1: A s
= 0.1:1? sq.in.
sm
=
F m
sa
=
F a
nA s nA s
= =
2<95;8 0.1:1?n ;282 0.1:1?n
=
18;9300
=
519318
n n
F#" AISI 8<309 WT 1100 #F
= 3.3 = 13; ksi = 125 ksi = 0.5 su = 0.5(13; ) = <8.5 ksi = <89500 psi
K f su s y
sn
F#" !$%!l l#!)%g *%+, &%4 !7+#" sn
= ( 0.8)( 0.85)( <89500 psi) = :<9580
S#)"b"g E@!+%#9 N = 2 1
N
=
sm s y
+
K f sa sn
P!g 28 # :0
psi
SECTION 3 – SCREW FASTENINGS 1
=
2
n
18;9300 1259000n
+
( 3.3)( 519318) :<9580n
= 10.3
M%% b" # b#l+& 10 b#l+& 2:8.
T, !$% $+"!l l#!) # +, 7!' b#l+& # ! !+##+%( 7#7+%g "#) )9 %'#&) b/ %"+%! #"7& !+ +#' )!) 7+"9 %& +!= +# b :000 lb.K +, %% l#!) %& 4"# !+ b#++# )!) 7+". T, !+"%!l %& AISI :1:09 OT 1100#F @!l%/%g #" SAE g"!) 5K !&& +,!+ sn′ = 0.:5su . T, g"%' #" +,"#g, b#l+& %& 1.5 %. F#" )&%g '"'#&)9 l+ !7, b#l+ +!= ,!l +, l#!)9 !) & ! @%(!l+ De
=1
3 8
in. #" +, 7#7+) '!"+&. T, +,"!)&
$+) ! gl%g%bl !#+ %+# +, g"%'. F#" +, %%+%!l 7#'+!+%#9 & ! #'%g l#!) F o = 1.;5 F e . C#&%)"%g +, !" % *,%7, +, b#l+ %& l#!))9 * )7%) +,!+ ! )&%g !7+#" # 1.: S#)"b"g &,#l) b @%+ !)@!+. ! D#& ! 51<-2: UNF &!+%&/ +,%& &%+!+%#6 I #+9 *,!+ &%4 )# /# "7#)6 b E$'"%7 &gg&+& +,!+9 % &%+!+%#& &7, !& +,%&9 ! %%+%!l &+"&& # +, #")" &gg&+) % i5.89 Text 9 %& g##) %&"!7 !g!%&+ !+%g !%l". D7%) '# &7, ! si !) "7#'+) N . H#* )#& %+ 7,!g6 W#l) /# b 7#7") !b#+ +, &!+/ % +,%& 7!&6 C#&%)" +, (!"%!+%# # si !& ! 7#&@7& # +, & # +#"@ *"7, !) !l&# +, &+"&& "l!$!+%# *%+, +% ) +# &!+%g !) #+," !7+#"&9 !) )%&7&&. C#'+ +, "@%") +%g,+%g +#"@ #" !7, si . S#l+%# F o
= 1.;5 F e = 1 .;5( :000) = ;000 lb
k c + k k b c
F i = F e
k b
= Ab E b
Ab
=
E b
= 30 × 10 < psi
Lb
= 1.5 in.
k c
= Ac E c
Ac
= π De2 − π D 2
Lb
π
:
D
2
Lc
:
:
2
1 3 − π D 2 = 1.:85 − π D 2 = 1.:85 − A b : 8 : :
π
Ac
=
E c
= 10.< ×10< psi 9 Al% 201:-T<
P!g 2? # :0
SECTION 3 – SCREW FASTENINGS
= 1.5 in. ≈ Ab
Lc A s
k b
k c
=
Ab E b
=
Ac E c
=
Lb
=
Lc
Ab ( 30 × 10< ) 1.5
(1.:85 − As ) ( 30 ×10< ) 1.5
1.:85 − A s = ;000 − :;1: A s 1.:85
F i = ;000
k ∆ F b = b F e k b + k c ∆ F b1 = 0
k A s ∆ F b 2 = b ( :9000) = 2
1 = F i + 1 ( ∆ F b + ∆ F b ) = ;000 − :;1: A s + ( 2
F a
= ( ∆ F b 2 − ∆ F b1 ) = ( 2
2
2
1
2
1
1
2
2
T!bl 5.2 s y
= 120 ksi = 88 ksi
sn′
= 0.:5 su = 0.:5(120) = 5: ksi = 5:9000
sm
=
F m
sa
=
F a
su
K f
A s A s
=
;000
A s
psi
− 33<;
= 13:;
= 3.3 ,!"))9 T!bl AT 12
S#)"b"g E@!+%#9 N = 1.: 1
N
=
1 1.:
A s
sm s y
=
+
K f sa sn
;000 889000 A s
−
33<; 889000
+
( 3.3)(13:;) 5:9000
= 0.118; sq.in.
T!bl A+1:9 * D =
P!g 30 # :0
; 1<
in 9 A s
= 0.118; sq.in.
SECTION 3 – SCREW FASTENINGS
"a# 51<-2: A s
UNF
*%ll
#+
&!+%&/
+, &%+!+%#.
I&+!) &
D =
; 1<
in 9
= 0.118; sq.in.
"b# i5.89 Text
= 0.85 s y = 0.85( 88) = ;:.8 ksi = ;:9800 psi )( 0.118; ) = 88;? lb F i = si A s = ( ;:9800
si
F m
1 + ( 2
F a
= ( ∆ F b 2 − ∆ F b1 ) = ( 2
sm
=
F m
sa
=
F a
1
=
sm
N 1
2
2
1
1
2
2
A s A s s y
=
88;?
A s
+ 13:;
= 13:; +
K f sa sn
88;? + 13:; ( 3.3)(13:; ) 0.118; + =
N 889000 N = 1.0< 9 %+ )7"!&&
5:9000
N > 1 9 +,"#"9 &!.
C#&%)"%g (!"%!+%# # si 9 si +)& +# $7)& +, l%%+%g &+"&& +,"#" ")7& +, !7+#" # &!+/. W,%l &+"&& "l!$!+%# +)& +# ")7 +, l%%+%g &+"&& !''"#!7,%g +, si !) 7!&%g l#*" )&%g !7+#". 7 F i = ;000 − :;1: A s T = 0.2 DF i
= ;000 − :;1:( 0.118; ) = <::0 lb
; = 0.2 ( <::0) = 5<: in − lb 1<
88;? lb !+ F i =
T = 0 .2 DF i
; = 0.2 ( 88;? ) = ;;; in − lb 1<
CHEC PROBLEMS 2:?.
A 1-%. &+l b#l+ A #"!l%4) AISI 113;9 7#l)-"#ll) +,"!)& '!&&& +,"#g, ! /ll#* b"!&& +b B B3<-89 ,!") !& &,#*. T, +b lg+, %& 30 %.9 %+& 7"#&&-&7+%#!l !"! %& 2 &@. %. !) +, UNC b#l+ +,"!)& $+) ! gl%g%bl !#+ bl#* +, +. T, &+l *!&,"& !" J %. +,%7= !) !" !&&) #+ +# b) 7l!"!7& !" $!gg"!+). T, + %& +") J +". ! I ! $+"!l +&%l !$%!l l#!)9 (!"/%g "# 0 +# 5 =%'&9 %& "'!+)l/ !''l%) +#
P!g 31 # :0
SECTION 3 – SCREW FASTENINGS +, b#l+9 *,!+ %& +, !7+#" # &!+/ # +, b#l+ b/ +, S#)"b"g 7"%+"%#6 b W,!+ %& +, $+"!l l#!) # +, b#l+ !+ +, %&+!+ +,!+ +, l#!) # +, +b b7#& 4"#.
P"#bl 2:?9 250 S#l+%# F#" 1-%. UNC
= 0.<0< sq.in. Dr = 0.8:<< in. A s
Th in. = 8
=
p δ
=
p δ
=
1
Th in
=
1 8
in.
1 :
1 = 1 in. : 8 32
1
1 = 30 + 2 = 30.5 in. : E b = 30 × 10 < psi F i ( 30.5) 1
Lb
δ
=
32
=
π
: F i
(1) 2 ( 30 ×10< )
= 2:91:1 lb
k ∆ F b = F e b k b + k c π
Ab E b
k b
=
k c
= Ac E c
Ac Lc
Lb
=
:
Lc
= 2 sq.in. = 30 in.
P!g 32 # :0
(1) 2 ( 30 × 10 < ) 30.5
= ;;29525
SECTION 3 – SCREW FASTENINGS
= 15×10<
E c
k c
psi ll#* B"!&&
2(15 × 10
=
<
30
) = 190009000
! ∆ F b1 = 0 ;;29525 ∆ F b 2 = ( 5000) = 21;? lb ;;29525 + 190009000
F m
= F i + 1 ( ∆ F b + ∆ F b ) = 2:91:1 + 1 ( 21;? + 0) = 259230 lb
F a
= 1 ( ∆ F b 2 − ∆ F b1 ) = 1 ( 21;? − 0 ) = 10?0 lb
sm
=
F m
sa
=
F a
2
2
1
2
A s A s
2
2
259230
=
0.<0<
=
10?0
0.<0<
= 38922; psi
= 1;?? psi
F#" #"!l%4) AISI 113;9 7#l)-"#ll) +,"!) s y
= ?8 ksi = 58 ksi
sn
= 0.5 su = 0.5( ?8) = :? ksi = :?9000
su
psi
= 1.: T!bl AT 12
K f
F#" !$%!l l#!)%g9 sn = 0.8( :?9000) = 3?9200 psi 1
N 1
N
= =
sm s y
+
K f sa sn
38922; 589000
+
(1.:)(1;??) 3?9200
N = 1.38
k c + k k b c
b F i = F o
190009000 ;;29525 + 190009000
2:91:1 = F o
F o
= :29;?0 lb
250.
A -%. %-+,"!) b#l+9 !) # AISI 111;9 7#l) )"!*9 *%+, "#ll) +,"!)&9 '!&&& +,"#g, ! /ll#* b"!&& +b !) +*# &+l *!&,"&9 !& &,#*. T, +b %& : %. l#g9 ;8 %. %+"!l )%!+"9 1 J-%. $+"!l )%!+". T, *!&,"& !" !7, J-%. +,%7=. T, +,"!)) '!"+ # +, b#l+ %& 3 %. l#g. A&& +,!+ +," %& # &+"+7,%g # +, b#l+ %&%) +, + % %)%g %+& k . T, lb"%7!+) b#l+ %& +%g,+) b/ ! +#"@ # 1800 %-lb. T, $+"!l l#!)9
P!g 33 # :0
SECTION 3 – SCREW FASTENINGS (!"/%g "# 0 +# : =%'&9 %& !$%!ll/ !''l%) +# +, *!&,"& ! %)%%+ b" # +%&. ! C#'+ +, !7+#" # &!+/ # +, b#l+ b/ +, S#)"b"g 7"%+"%#. I& +," !/ )!g" # !%l" # +, b#l+6 b W,!+ 'll &+ b $"+) b/ +, *!&,"& +# "#( !ll l#!) "# +, b"!&& +b6 S#l+%# T = 0.2 DF i 1800
3 = 0.2 F i :
= 129000 lb
F i
k ∆ F b = F e b k b + k c 1
1
=
k b
k b1
+
1
k b 2
Ab E b
k b1
=
Lb1
= 3 in. π 3 = = 0.::18 sq.in. : :
Lb1 2
Ab
= 30 × 10 < psi
E b
( 0.::18) ( 30 × 10 < )
k b1
=
k b 2
= A s E b
3
= :9:189000
Lb 2 F#" -%. UNF T!bl AT 1:
= 0.3;3 sq.in. 1 Lb 2 = : + 2 − 3 = 1.5 in. 2 ( 0.3;3) (30 × 10 < ) A s
k b 2
=
1
=
k b 1
k b
=
= ;9:<09000
1.5 1
k b1
+
1
k b 2
1 :9:189000
+
1 ;9:<09000
k b
= 29;;:9;33
k c
=
Ac
1 2 ; 2 = 1 − = 0.<25? sq.in. : : 8
Ac E c Lc π
P!g 3: # :0
SECTION 3 – SCREW FASTENINGS E c Lc
k c
= 15×10< psi = : in. ( 0.<25? ) (15 × 10 < )
=
:
= 293:; 9125
∆ F b1 = 0 29;;:9;33 ∆ F b 2 = ( :000) = 21<; lb 29;;:9;33 + 293:;9125
F m
= F i + 1 ( ∆ F b + ∆ F b ) = 129000 + 1 ( 21<; + 0) = 13908: lb 2
2
1
1
1
2
2
2
F a
= ( ∆ F b 2 − ∆ F b1 ) = ( 21<; − 0 ) = 108: lb
s m
=
sa
=
F m
=
A s
F a A s
=
13908: 0.3;3
108:
0.3;3
= 3590;8 psi
= 2?0< psi
F#" AISI 1119 7#l) )"!*9 "#ll) +,"!)&
= :0 ksi s y = <8 ksi K f = 1.: sn = 0.8( :0 ) = 32 ksi = 329000 psi 9 !$%!l l#!)%g sn
! 1
N
1
N
=
=
sm s y
+
3590;8 <89000
K f sa sn
+
( 1.:)( 2?0<) 329000
N = 1.5<
k c k k + b c
b F i = F o
293:;9125 29;;:9;33 + 293:;9125
129000 = F o
F o
= 2<918< lb
251.
A 7#'l%g b#l+ i5.139 Text %& &) +# 7#7+ +*# '!"+& !) # 7!&+-%"#9 7l!&& 35. T, )%!+" # +, 7#!"&-+,"!) b#l+ %& -%.K %+& g"%' %& 2 %.9 *,%7, %& !l&# !"l/ +, +,"!)) lg+,. T, b#l+ +%g,+) +# ,!( ! %%+%!l +&%# # :000 lb. T, '!"+& &''#"+ ! $+"!l l#!) F e +,!+ +)& +# &'!"!+ +, !) %+ (!"%& "# 4"# +# 5000 lb. W,!+ %& +, !7+#" # &!+/9 S#)"b"g6
S#l+%# :000 lb F i =
P!g 35 # :0
SECTION 3 – SCREW FASTENINGS
k ∆ F b = F e b k b + k c k b
= Ab E b
Ab
1 = = 0.1?<35 sq.in. +,"!)) lg+, : 2
E b
= 30 × 10 < psi
Lb
= 2 in. ( 0.1?<35) ( 30 × 10 < )
k b
Lb
2
π
=
2
= 29?:59250
T!bl AT 1:9 UNC D =
1
A =
3
in. 2 A s = 0.1:1? sq.in.
De
in.
:
= A + h
2
h = 2 in.
De
=
k c
=
3 :
2
+
2
=1
3 :
in.
Ac E c Lc π
π
=
E c
= 1:.5 ×10< psi 9 C!&+ %"#9 7l!&& 35 = 2 in. ( 2.20? ) (1:.5 × 10 < )
Lc
k c
:
−
3 2 1 2 = 1 − = 2.20? sq.in. : : 2 π
Ac
2
De
:
=
D
2
= 1<90159250
2
∆ F b1 = 0 29?:59250 ∆ F b 2 = ( 5000) = ;;; lb 29?:59250 + 1<90159250
F m
= F i + 1 ( ∆ F b 2 + ∆ F b1 ) = :000 + 1 ( ;;; + 0) = :38? lb
F a
= 1 ( ∆ F b − ∆ F b ) = 1 ( ;;; − 0) = 38? lb
sm
=
F m
sa
=
F a
2
2
2
A s A s
2
= =
1
:38? 0.1:1?
38? 0.1:1?
P!g 3< # :0
2
= 309?30 psi
= 2;:1 psi
SECTION 3 – SCREW FASTENINGS
F#" ASTM 35: BC T!bl 5.29 D =
1 2
in.
= 125 ksi s y = 10? ksi sn = 0.5 su su
F#" !$%!l l#!)%g s n = ( 0.8 )( 0.5 ) (125 ) K f
= 50 ksi = 509000
psi
= 1.8
S#)"b"g L% 1
N 1
N
=
sm s y
=
+
K f sa sn
309?30 10?9000
+
(1.8)( 2;:1) 509000
N = 2.<
252.
T, 7!' # +, ) # ! 7#7+%g "#) !+##+%( g% %& ,l) # b/ +*# 51<-%. b#l+& +,!+ !" #"g) %+g"!ll/ *%+, +, !% 7#7+%g "#). T,& b#l+& ,!( UNF +,"!)& *%+, ! 58-%. # ! +,"!)) lg+, # (%"+!ll/ 58 %. T, +& !" +# b +%g,+) *%+, ! +#"@ # 20 +-lb. !) +, !$% $+"!l l#!) # # b#l+ %& $'7+) +# b 2330 lb. L+ +, @%(!l+ )%!+" # +, 7#7+) '!"+& b %. ! E&+%!+ +, !$% #"7 # +, b#l+. b C#'+ +, #'%g l#!). I& +,%& &!+%&!7+#"/6 7 I +, b#l+ !+"%!l %& AISI :1:09 OT 1000 #F9 *,!+ %& +, !7+#" # &!+/ b!&) # +, S#)"b"g 7"%+"%#6
S#l+%# T = 20 ft − lb = 2:0 in − lb
T = 0.2 DF i
5 F i 1<
2:0 = 0.2
38:0 lb F i =
k ∆ F b = F e b k b + k c k b
= Ab E b
Ab
=
E b
= 30 × 10 < psi
Lb
=
Lb
2
5 = 0.0;<; sq.in. +,"!)) lg+, : 1<
π
5 8
in.
P!g 3; # :0
SECTION 3 – SCREW FASTENINGS
k b
=(
k c
=
0.0;<; ) ( 30 × 10
5 8 Lc
π
=
E c
= 30 × 10
Lc
=
=
) = 39<819<00
Ac E c
Ac
k c
<
:
−
2
De
5 8
π
: <
D
2
3 2 5 2 = − = 0.3<51 sq.in. : : 1< π
psi 9 C!&+ %"#9 7l!&& 35
in.
( 0.3<51) (30 × 10 < )
5 8
= 1;952:9800
39<819<00 :05 lb ∆ F b = ( 2330) = 39<819<00 + 1;952:9800
! F !$
= F i + ∆ F b = 38:0 + :05 = :2:5 lb
k c k k + b c
b F i = F o
F o
1;952:9800 = F o 39<819<00 + 1;952:980 = :<:; lb < F !$
7
F m
F a
=
38:0
= F + i
∆ F b 2
=
∆ F
b
2 :05 2
= 38:0 +
:05 2
= :0:2 lb
= 202 lb
F#" AISI :1:09 OT 1000 #F su s y
= 1;0 ksi = 155 ksi
T!bl AT 129 K f = 2.< sn
= 0.5 su
F#" !$%!l l#!)%g sn
= ( 0.8)( 0.5)(1;0) = <8 ksi = <89000 psi
S#)"b"g L% 1
N
=
sm s y
+
K f sa sn
F#" 51<-%.-UNF9 T!bl AT 1:9 A s
P!g 38 # :0
= 0.0580 sq.in.
SECTION 3 – SCREW FASTENINGS
sm
=
F m
sa
=
F a
1
=
sm
N 1
N
=
A s
=
A s s y
0.0580 202 0.0580
= +
:0:2
=
= 38:3 psi
K f sa sn
+
( 2.<) ( 3:83) <89000
N = 1.;2
SET SCREWS 25:.
A <-%. 'll/ %& !&+) +# ! 1 J %. &,!+ b/ ! &+ &7"*. I ! + +!g+%!l #"7 # ;5 lb9 %& !''l%) +# +, &"!7 # +, 'll/9 *,!+ &%4 &7"* &,#l) b &) *, +, l#!) %& &+!)/6
S#l+%#
< = 3<5 lb 1.25
T!g+%!l #"7 ( ;5 lb)
A&& +!g+%!l #"7 ,#l)%g #"7 T!bl 5.39 & S7"* &%4 89 H#l)%g #"7 385 lb. 255.
A 77+"%7 %& +# b 7#7+) +# ! 3-%. &,!+ b/ ! &+&7"*. T, 7+" # +, 77+"%7 %& 1 J %. "# +, 7+" # +, &,!+ *, ! +&%l #"7 # 1000 lb. %& !''l%) +# +, 77+"%7 "#) '"')%7l!" +# +, l% # 7+"&. W,!+ &%4 &+ &7"* &,#l) b &) #" ! )&%g !7+#" # <6
S#l+%#
1.25 = 833 lb 3 2
T!g+%!l #"7 (1000 lb )
H#l)%g #"7 ( <)( 833) = 5000 lb T!bl 5.39 & S7"* &%4 %. 25<.
A l(" 1< %. l#g %& +# b !&+) +# ! 2-%. &,!+. A l#!) # :0 lb. %& +# b !''l%) #"!l +# +, l(" !+ %+& ). W,!+ &%4 # &+ &7"* &,#l) b &) #" ! )&%g !7+#" # 56
S#l+%# T#"@ (1<)( :0) = <:0 in − lb T!g+%!l #"7
2( <:0 ) 2
= <:0 lb
H#l)%g #"7 ( 5)( <:0) = 3200 lb T!bl 5.39 & S7"* &%4 ?1< %.
P!g 3? # :0
