Copy of Axial and Flexure
Transcript of Copy of Axial and Flexure
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Design Aid
Solid Section - Only considers tension steel
Allowable
Fb
Thickness 7.625 inches Bending is about axis parallel to width Fa
Width 16 inches fa
d .!1 inches r 2.2"11#! in
f$% 15"" psi h&r !#.5"16 '(
)eight 15.5 feet *eduction ".656+ '(
Allowable Stress YES
, 2.+7 kips e 1.2525 in
- .2! kipft
Fs 2# ksi
n 21.5
Strength
,u 2.2 kips Strength Design-u .71 kipft a ".7#++#1 in
f/ 6" ksi 0s ".1++2# in2
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Stress Design
5"" psi
2!.!7 psi
2#.##26 psi OK
o%pression 3-4all 6.15 kipft (
racked 'o Tension 3-4all ".!! kipft 'o ood
Tension in 8teel 0s -35.784 in2
o%p controls
o%p ontrols Tension ontrols
a 1.16+ in a ".!+ in
kbal "."+5 -p ".!#716 kipft
kd .+#1"! in 0s ".55552 in2
k 1."##"# xi ".6##"610s 5.7!# in2 a2 ".55#6 in
9ifference ".1656
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Flag
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Aial !oad-"ending #o$ent %nteraction Diagra$
Allowable Stress Design
Solid Section
Bending is about axis parallel to width
Thickness 7.625 inches
Width 7.625 inches
d .!1 inches heck of :oad ase
d$ .! inches , 3kips4 - 3kipft4
)eight 12 feet "."1 " OK
f$% 15" psi "."1 " OK
Fs 2# ksi "."1 " OK
n 21.5
0s ".2 in2
0s " in2
0$s " in2
r 2.2"11#! in
h&r 65.#2"#1
*eduction ".7!16#1
Fa 26.!"+ psi
Fb #5" psi
kd , - % -ar% T -ar% 1
3in4 3kips4 3kipft4 3kips4 3in4 3kips4 3in4 3kips4
7 12.""+! 1.#!"22 12.""+! 1.#7+167 " ".""25 "
0xial 15.77 "
7.625 1."!16# 1.!5!2 1."!16# 1.27"! " ".""25 "6.71755+ 11.52#!1 1.511"12 11.52#!1 1.571# " ".""25 "
6.15"!57 1".55256 1.5#+657 1".55256 1.76221# " ".""25 "
5.667"#2 +.72251+ 1.55!#27 +.72251+ 1.+2#!6 " ".""25 "
5.2"2#! !.+71#5 1.5#71!2 !.+71#5 2."6+"!# " ".""25 "
#.!25+ !.27!56 1.52"521 !.27!56 2.2"#"7 " ".""25 "
#.###2!! 7.62#71 1.#!11#+ 7.62#71 2.1"71 " ".""25 "
#."!1!7 7.""2+57 1.#"!66 7.""2+57 2.#51!77 " ".""25 "
0 0.20
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2.#57+1! .152#6 1."516" #.216!65 2.++1+# 1."6##2+ ".""25 "
2.16"1#2 2.22!"+# ".+5#7# .7"5++# ."+2#5 1.#77+ ".""25 "
1.!6+16! 1.1+76"2 ".!51+"5 .2"67+1 .1!+### 2.""+1!+ ".""25 "1.5!#6! " ".7#+5 2.71!1!1 .2!#77 2.71!1!1 ".""25 "
9oubl/ reinforced bea%
rho ".""6!!#
rho$ "
k ".#15!#5
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-ar% 2 -ar%
3in4 3kips4 3in4
".""25 " "."125
2+ 15.77 :oad ase
".""25 " "."125 " 1."!16# ##".""25 " "."125 1 1 11.52#!1 ;B;##
".""25 " "."125 2 2 1".55256 ;B;#5
".""25 " "."125 +.72251+ 1.1+76"1+
".""25 " "."125 # # !.+71#5 "
".""25 " "."125 5 5 !.27!56 a
".""25 " "."125 6 6 7.62#71 b
".""25 " "."125 7 7 7.""2+57 -fail
0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
Moment (kip-ft)
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".""25 " "."125 12 #2 .152#6
".""25 " "."125 1 # 2.22!"+#
".""25 " "."125 1# ## 1.1+76"2".""25 " "."125 #5 "
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:oad ase 2 :oad ase
## ##;;## ;B;## ;;## ;B;## ;;##
;;#5 ;B;#5 ;;#5 ;B;#5 ;;#5
".!51+"5 1.1+76"2 ".!51+"5 1.1+76"2 ".!51+"5
".7#+5 " ".7#+5 " ".7#+5
"."+"6"6 a "."+"6"6 a "."+"6"6
".7#+5 b ".7#+5 b ".7#+5
".7##"1 1 -fail ".7##"1 1 -fail ".7##"1
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Aial !oad-"ending #o$ent %nteraction Diagra$
Strength Design
Solid Section
Bending is about axis parallel to width
Thickness 7.625 inches
Width 7.625 inches
d .!1 inches heck of :oad ase
d$ .! inches ,u 3kips4 -u 3kipft4
)eight 12 feet "."1 " OK
f$% 15" psi "."1 " OK
e% ".""25 "."1 " OK
f/ 6" ksi
0s ".2 in2
0s " in2
0$s " in2
r 2.2"11#! in
h&r 65.#2"#1
*eduction ".7!16#1
kd % -ar% T -ar% 1
3in4 3kips4 3kipft4 3kips4 3in4 3kips4 3in4 3kips4
1.25 .!!5 2."#6 2.6#!5+2 !.25 .125 12 ".""25 "
0xial 5.!12 " 5.!127.625 #5.21"15 2.!7272! 5.!12 5".25 ".7625 " ".""25 "
6.751! #"."#"+6 .7"7!!5 1.2+767 ##.#!++5 1.11122! " ".""25 "
6.2"!725 6.!1277 #."77"#5 2!.77#! #".+""! 1.2+"1 " ".""25 "
5.7#+"2 #."567# #.2++#+1 26.62"16 7.!#"! 1.51#++ " ".""25 "
5.2#255 1.56!57 #.#26+61 2#.675 5."761+ 1.6!27+! " ".""25 "
#.+52!+ 2+.2622 #.#!2+#+ 22.!726# 2.516+ 1.!!!# " ".""25 "
#.56+1#7 27."+1+ #.#!1""! 21.17575 ".1"15# 1.+!#!#1 " ".""25 "
φ,n φ-n *educed φ,
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1.!21#+# " 2.77262 " 12 ."!+" 12 ".""25 "
a 6.5!!
b 12
c "
'0 1.!21#+#
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-ar% 2 -ar%
3in4 3kips4 3in4
".""25 " "."125
2+ 5.!12 :oad ase".""25 " "."125 " 5.!12 ##
".""25 " "."125 1 1 1.2+767 ;9;##
".""25 " "."125 2 2 2!.77#! ;9;#5
".""25 " "."125 26.62"16 1.6"6"2
".""25 " "."125 # # 2#.675 "
".""25 " "."125 5 5 22.!726# a
" ""25 " " "125 6 6 21 17575 b
1 1.5 2 2.5 3 3.5 4 4.5 5
Moment (kip-ft)
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".""25 " "."125 #5 "
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1 :oad ase 2 :oad ase
## ##
;;## ;9;## ;;## ;9;## ;;##
;;#5 ;9;#5 ;;#5 ;9;#5 ;;#5
."76+17 1.6"6"2 ."76+17 1.6"6"2 ."76+17
2.77262 " 2.77262 " 2.77262
".22177 a ".22177 a ".22177
2 77262 b 2 77262 b 2 77262
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Aial !oad-"ending #o$ent %nteraction Diagra$
Strength Design
&artially 'ro(ted Section) Steel in center o* wall
Thickness 7.625 inches heck of :oad ase
:ength #! inches ,u 3k&ft4 -u 3kft&ft4
Web :ength ! inches 25 1
Face 8hell 1.25 inches 15 1
)eight 12 ft 6 1
f$% 15" psie% ".""25
f/ 6" ksi
0s ".2 in2 ,u 3kips4 -u 3kipft4
1"" # OK
0 161 in2 6" # OK
< 12#.5!#6 in# 2# # OK
r 2.!6!155
h&r 5".2"6!2
*eduction ".!71#"77
kd % fs -ar% % web -ar%
3in4 3kips4 3kipft4 3kips4 3in4 3kips4 3in4
1.25 5.!56 12.!7+ 1.2#51+ 51.!# .125 " "
0xial 116.#!!1 " 116.#!!1
7.625 +6."6 15.+2!5 !.6!##15 6#.! .1!75 #1.+"# ".175
6.#157222 !!.5"!7#! 17."5##"1 77.1272"1 6#.! .1!75 .5#"5 ".621511
5.65++5!! !.!"+##1 17.#52+1# 7."21+ 6#.! .1!75 2!.216"1 ".+251!#
5."15"2 7+.7+7#57 17.6"5!6! 6+.56116 6#.! .1!75 2.!6!#1 1.1!1#+"7
#.#27715 76.175+5 17.5+57+2 66.7+!2 6#.! .1!75 1+.!+2! 1.#1#+"7
.!+"+5 72.!1!156 17.#6"+ 6.#5#2++ 6#.! .1!75 16.1"+"62 1.6"2626
.!5"!"5 6!."1"1# 17.22557 5+.26#557 6#.! .1!75 12.5+7675 1.!#67+
2.+"1+75 62.55!"1# 16.!+!56# 5#.515 6#.! .1!75 +.25!##1 2."2671"6
2.#+2121+ 56.#266# 16.#+6#+ #+.17"6"7 6#.! .1!75 6."5+!#7 2.211!151
1.++5#6 5".2"17 16."25"+ #.7#5!61 6#.! .1!75 2.+7+" 2.+""!66
1 5625 #7 52 15 #+125 #1 #"+2+2 6# ! 1!75 " "
φ,n φ-n *educed φ,n
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".2!+51!5 " .27"! " 12 .6+675+ " "
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T
3kips4
12
26 116.#!!1 :oad ase 1
" 27 !.6!##15 26
" 1 2! 77.1272"1 ;9;26 ;;26
" 2 2+ 7."21+ ;9;27 ;;27
" " 6+.56116 116.#!!1 "
" # 1 66.7+!2 !.6!##15 15.+2!5
" 5 2 6.#5#2++ a ".#!5#1#5
1.!"!51 6 5+.26#557 b 56.5#5"11
#.5#+56 7 # 5#.515 -fail !.""56#1
!.165675 ! 5 #+.17"6"7
12 + 6 #.7#5!61
12 7 #1 #"+2+2
4 6 8 10 12 14 16 18 20
Moment (kip-ft)
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12 #2 "
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:oad ase 2 :oad ase
2 +
;9;2 ;;2 ;9;+ ;;+
;9; ;; ;9;#" ;;#"
6.#5#2++ 17.#6"+ 2#.!#5575 11.1"+5!
5+.26#557 17.22557 16.56717 !.67675
a "."566#!5 a ".2+75#5
b 1.!66"! b .!11"!
1 -fail 17.26521+ 1 -fail 1".!611+2
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Slender Wall Design Criteria
Fully Grouted Walls
Input
Dead Load 350 lb/ft h/t 41.51351
Live Load 300 lb/ft Stress 24.12! psi
"ind Load 20 psf 0.05f#$ 250 psi
%ei&ht 16 ft 0.2f#$ 1000 psi
f#$ 5 'si (ethod )*
f+ 60 'si
,$ 3500 'si rho 0.00603
-hi'ness 4.625 in
"all "ei&ht 46 psf
Steel 0.186 in2/ft
eentriit+ 5.312 infr 103 psi
Servie lti$ate
d 2.3125 in ll. Defl. 1.344 in )*
I& !8.!3164 in4/ft t. Defl. 1.066303 in
n 8.28514 Servie )*
' 0.282336
Ir 5.35!!6 in4/ft
(r 4.40646! 'ipin/ft
Servieabilit+ Stren&th
D" D0.5L0.5" 1.2D1.6 1.2D1.6"0.5L
f 350 55 lb/ft 420 50 lb/ft
18 !43 lb/ft 861.6 1011.6 lb/ft
nra'ed nra'ed
left 0.!!203 0.!8!542 0.!!0445 0.!8881
ri&ht 8.60!6 .282 'ipin/ft 13.40352 13.801!2 'ipin/ft
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Aial !oad-"ending #o$ent %nteraction Diagra$
Strength Design Shear +alls
Solid Section
Bending is about axis parallel to thickness
:ength 15.62 inches heck of :oad ase
Thickness 15.62 inches ,u 3kips4 -u 3kipft4
f$% 15" psi 26.+ 1 OK
e% ".""25 15" 7 OK
f/ 6" ksi 1+ #5 ,o 'ood
=nter up to 1" la/ers of steel -ar%
0s 3in24 d 3in4 3> or '4 3in4
".1 7 > ".!1".2 6.5 1.1
".1 ! > ".1+
".1 11.5 .6+
".1 12 #.1+
7.!1
7.!1
7.!1
7.!1
7.!1
:a/er 1 :a/er 2 :a/er :a/er # :a/er 5 :a/er 6 :a/er 7 :a/er ! :a/er + :a/er 1"
kd % -ar% F F F F F F F F F F
3in4 3kips4 3kipft4 3kips4 3in4 3kips4 3kips4 3kips4 3kips4 3kips4 3kips4 3kips4 3kips4 3kips4 3kips4
6 2!.1+5#2 #.6"!1 !".+7#"! 5.#1 .7#5! 1.2"! 7.#+1667 1!.6 1!.6 " " " " "
0xial 216."2#2 " ".1 " ".1 " " " " " " " 2+ 216."2#2
15.62 21".7527 25.2+276 21".!"25 1.562 12.#"2+! " 1".+6#12 " " " " " " " " 21".7527
1.62+"5 1!.727 ."656! 1!.+2 2.5!!2 1".+16# " +.2!25!7 " " " " " " " 1 1 1!.727
12.!56+ 166.+5+ 6.2!1"! 167.152 2.!55726 +.772!7 " 7.+5!2#2 " " " " " " " 2 2 166.+5+
11.2#1! 1#+.6!52 !.5##75 152.!275 .2!"2! !.5!2161 " 6.5+7#7 ".#!+#+ 1.#12+5 " " " " " 1#+.6!52
1".65!# 11.6!7 #".6"5! 1+.!+#1 .6666# 7.2+77#6 " 5.12+567 2.#5+"61 .5#15 " " " " " # # 11.6!7
+.#7757 11.!57 #2."67!+ 127.+"62 #."1!+72 5.!752! " .5"!+2 #.7+5+6! 5.+!1662 " " " " " 5 5 11.!57
!.6#1#1+ +5.75" #.116"5 116.621! #.5#2 #.26+"7! " 1.66!22 7.##72! !.75151 " " " " " 6 6 +5.75"
7.!#626 76.+5++ #.!!!++ 1"5.!+"6 #.671#+5 2.#2#"52 " ".##"6+ 1".#65!# 11.!+!"5 " " " " " 7 7 76.+5++
7."!#5+ 57."7# ##.517!2 +5.611# #.+7616 ".26!61 " 2.+"#"16 1#.""7# 15.5+52 " " " " " ! ! 57."7#
6.51"# 6.7672 ##.672! !5.71161 5.26+5!# 2.2+65 ".#""!+ 5.!52 1!.221"+ 1!.6 " " " " " + + 6.7672
5.6#15+2 1+.71#1 #2.2+22# 76.171 5.556 5.#116 2.2"6276 +.+5## 1!.6 1!.6 " " " " " 1" #" 1+.71#1
#.+5152 1.!"#62 +.#"26# 66.!#615 5.!2!7+ +.2!76"5 #.52!2!+ 1.!2512 1!.6 1!.6 " " " " " 11 #1 1.!"#62
#.2!262 17.77!52 6."!6"6 57.!"55 6."+66+5 1#.2551! 7.5"#25! 1!.6 1!.6 1!.6 " " " " " 12 #2 17.77!52
.62++# .1!!62 2.6152 #!.+!!#2 6.5!"27 1!.6 11.#6#66 1!.6 1!.6 1!.6 " " " " " 1 # .1!!62
2.++1526 #1.#2#5+ 2!.+772 #".726! 6.61!+ 1!.6 12 1!.6 1!.6 1!.6 " " " " " 1# ## #1.#2#5+2.66667 #+."1#2 25.!+7 1.++7! 6.!6 1!.6 12 1!.6 1!.6 1!.6 " " " " " #5 #+."1#2
φ,n φ-n
0 5 10 15 20 25 30 35 40 45 500
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Moment (kip-ft)
A x i a l ( k i p
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:oad ase 1 :oad ase 2 :oad ase
+ 2 #"
;B;+ ;;+ ;B;2 ;;2 ;B;#" ;;#";B;#" ;;#" ;B; ;; ;B;#1 ;;#1
57."7# ##.517!2 1!.727 ."656! 6.7672 ##.672!
6.7672 ##.672! 166.+5+ 6.2!1"! 1+.71#1 #2.2+22#
a ".""75"1 a ".1!5#67 a ".1#"17
b ##.+#566 b 67.1#1+! b +.#7"
-fail ##.7#!+ 1 -fail +.21+! 1 -fail #2.1!76# "