solution manual of design of concrete structure, aurther h. nelson(13th edition); (rectangular beam...

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Md. Mohotasimur Rahman (Anik) Jr. Structural Design Engineer 017 17 879702 I mohotasim.anik@gmaiLcom SINClE1912 ASSOCIATED BUILDERS CORPORATION LTD.

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Page 1: Solution Manual of Design of Concrete Structure, Aurther H. Nelson(13th Edition); (Rectangular beam only)

Md. Mohotasimur Rahman (Anik)Jr. Structural Design Engineer

017 17 879702 I mohotasim.anik@gmaiLcom

SINClE1912

ASSOCIATED BUILDERS CORPORATION LTD.

Page 2: Solution Manual of Design of Concrete Structure, Aurther H. Nelson(13th Edition); (Rectangular beam only)

I

Ffei'-urc./ lI'MbS;~~ l).es~n..rJ &~

SO~«'Ilb d ~f~ ~ P~'(&'s€. ~ "~~n cJ&~~ed~ $Jy~'res -A-rltturrS-l.NiLsocn ~ D",,,;d ~'(""/~~"'~ W. Dt) lDo.1'l •

([

Et<tJAMpk 3. IA~~~cl~~ ~ ~ b« aL~$l~ b.zl(),~/h:z~5in _

~ ...l"25 hot. ~ i6 Ye&"njrrreuJ t.:}i&' ~ /'Io. .gbo-'l'S se ~I- A!> ~ £,':1 ;,;-.~ ~'l1e.yeJe ey~r .$(y~h.. J~ i6 40-00 ~I ~ 6.L ~ s.J..-EIv\~ ra ~<116. 4=1" psi. -tk <fe-Id F71~-j ~ !>~eel~ ,'[, "~t(!OD

psI I k 6tr~ -sk....m. ~ve.-:. cf f.u.. ?nP--te.-n<>.16 h.el"<}od ~ i FId ·,. 14. bekr,",,'N.. ~ "kehb ,~.•••b~ ~

CA ~~ ••t~, ~ I- M;: itS ~'p:Jt-io" _\Cl ~ 10" W

-.2,3"

2c I, 1'-1.1\~ - - -- - -

~'2')Sill'\.. ~. 2- 90- i?1"-q_C_--l3# 2> ; fts ~ 2.•~7·

Cil~ letz.6l0) 'YYl~y 'Co.hCl} 7L 7 £~ ? 23 X, (O{, Ip!:>; ~ .) =~~OSZ; c: 8EL .a'E)X1{OO \.:. If~,

1r~ CA'<'tl.. ('h-0~ = OH) rq2'.31 = 16'53' 1'.y,'L-

~ -= '2.SXlld -::-250 (')12-

- -:= 2..SO)<J lZ°C;- -t Q.x. 8'2.95"" ~£.3 _ -=:z 13'1 S"d 2..50-+ Z-~~.29S-1::2 bl-,3+.AJ 2-__ IOr<a.f3~+Z-X8'2~X~3-{3'ltjt-

t'2-. 12- ~::;

== l4"2D '4Lt (nit

~fyoid ~(ffi'\ kpfv1()/Ylyvl} ~ LcrtsL)" -h"tJ\

Page 3: Solution Manual of Design of Concrete Structure, Aurther H. Nelson(13th Edition); (Rectangular beam only)

f~plt. $"L

~""""pk S., t6 ~,,-Io(i'uteJ ./0 0.. r ~~ M•.~j·~&l~~-k. ~ -rde.vtANlf. p~of>d"Ji~ ~ sti ~ &

: • .,gh~ ,J @e'&!':.~e lao~ j; beY , jc.lo

c= ~ :J-

.'j~~&ox'Vllcm0x (t:;:::~~:= STLr'7<J f'~j

As it'-'- sft-clD ~ &sneW~ l4imn j-k<r iD (jOeode-r ~ n«.~t~ ~ ~'Ye. ) ~ I~ 41S psi. ~o~k u:Jill ~veJ.op cwd

bo~ p~"D1 ~ &rt~"rd-eG\)itl he lAY1~edive

M~.Jtu,J--0 I ~~ ~ ~NeJolA( ~~

~ LOx 2<1 £ - 8~2:J:/f-~~~'X)-:D

:=t> ?Z~3·TC)Z~-~T'2Jb -zD

--t> )( 27 '(,33 4

10:/1

f J. ?

r I -

, I 3 ~', fJ6YYUMt' ~ l'Yle'¥ft£A, I ::= -si< h~ -t- ~d

I 3 ~:= 3)q /OXlr'63?> +~(lJ2'37xc&3-1'b3~= 59 5')<70 ,in~

,". .s/Y~ ..f- &Ilc'(d~~~ }ky? J1Ct. z: ~';L

,,-J -=- (:50 )q12-.'X/DOlJ)" 7-633 z: 13B3 '23 psic:.t- 595 c:5• TO

Page 4: Solution Manual of Design of Concrete Structure, Aurther H. Nelson(13th Edition); (Rectangular beam only)

sfo~ J ~Jeel,Is?- 01 N<2 "2 g~ 90~lCOOXl2-~(23-1'b3~) C!..-J~ J 5:359'" 10 .

= 2.2..:2.. 18 0/1 psi.

~~J-'L

p:::=. fh = 2 ·37- -z: 0"0 I0.3bd \O~2~

11-= Es ;;:!. ~

Ee...

/0/1

f---

N·fj L / / /-1--:1

1ok-i'Cj ~+-~ N.fj.

kJ ~lO X ~ - 2~2.f3f,x ~:3- k.J)::z 0~ U :Z7~633

.: k =' T·-633h~ ::z 0 '3312'

. " -j -= /- ~ -:::: \_ 6·~l(s -zz 06 'iS~'3Lt

..sfoe»-:> d- ~c.DeJe. j ~~~;Z L:>q~O X (2-X((}l5t) 'L= 13<63'y3psic. KJbolL O'3318')QO'5.?8j'-1XI())QZ~

SI.-eS1; at .sted .1S? ~ 2 '30Xl2.~l()OD .2 222'£56'10 j~Jd 2:57~'~~'X22> ps

Page 5: Solution Manual of Design of Concrete Structure, Aurther H. Nelson(13th Edition); (Rectangular beam only)

E~~.3z:dq~ k-?'IU'mmJ 9Ile~1- M'n.J. ""Wdt.. ~ ~~~Flt.b $.\ ~ !J '2. ~i"l\ JeL ..

P = As ::2 2r

!!J7- -;:z O'Gf03bd 10 ((l 23

M'}\ = pJ~bd2-(/-O'59 P R'):::::0'0(03)<1 eo Xl (OX 26'L~ () -o·~:1')<lO'()to.?X ~ )

~ 2.971'2.-1 ~IP~I'n. = 2~'1--'(,,0 h'p~j-

tNkTL ~ ~ omeh.eb Mn I ~ ~~~~ cb ik ~J ~ I

~ ~ ~~ ~ 2.. '.31""'0 .z 4.01 ~ ;?L--'j~b J(/\. L- ()·lQ~LtX(O

E~~pl~ 2>,4~ ~"J~t. -n;e.~cj"'-~~ Sh-~ di:sln'~hCsn. ,~~ld ~ ~dJ.o ~We ~ ')te~ ~#- ~~ ~ ~lIioz.h~

6.'IIA~ l1:.d in E!Ca-wltk B. S.

f:. ' J~ ZL{.. Lt 0·()Q3r;mo..:;)t 2. 0 8~ r?, .~ ~V\ <t z.t a C) 'g5 a> xo -gS"" ?\ 60~-O'-OO-~--t 0-'00-4-

;:z o02.06

P As t2''h?:2 bd :2 {O~2.'?> = 0 '0103

P < f'm"''X ; lA71de.•• 'Oe..+eQd k:vvvL-

0. 2 ~ 2 2'39'1<.(.0 = 4'18 (,f

O'~S'jc:b 0 -gS~4 X IQ

.'. M ? ~ CoR- -Z)z 2"3t-~bc)~~3- ~~):2 £9t?:/~o2. Idp-t'n

-;z.. 2/1'1 .T'6 kt' P- fl--

Page 6: Solution Manual of Design of Concrete Structure, Aurther H. Nelson(13th Edition); (Rectangular beam only)

IEXo..~pl.L S.S- (:jIt .•.~+'W' b- ~ CA:liJ&. It..I'll. ~ ~w. ApJr-. 11'/:3 ~

11-lb -r:e4'n?a.d ~i~ FY No ..~· ~~'r.!S r" O)lL ~ .1J{t9~~~j~ --4 b"U)W lb bu. ~~rn.J~CA'1"oJ $k~jt"...~dWw.tb «/k... ~i~lAt)n ~l- ~ &N\ bt.lA~(i~J i~ ~~fj'JL,~l"..lA~ ~ br If,..... P,e..l &J... ? I""

jf ~ I

P.. =O'8/() f!J ss. ~~~ . I J £:.. lA +zt. \

~ o-sza X(y~/,\~~ O·DQ3eo OV03+D 'oot,

=-Q'L)2.06

P J5 ~ '-I -=- 0 '01<"]0? hd 12:~'1'5 L~-:!t::~ •••

f J As:: LI''Y1'L ~P L o .•30 0@M'L if.> ()..«\~oet;" e« ~(""''''~ ,

? AJJ :z 4xI X'C -;:z 5'SSu0... O'8c;J~b (j'~5;xJ4)<!.12-

1411 ~/JsJQ~-£.) ~4X('O'ArJ?'5- '31~)~.3L1'?4·18 1.<tf-in.

-;2-CJ{O"b JA'PJ+-NOlN I ~ ? cf!3, -:2 6.~%'~5 :;: 6 "91 4

1- -:2 i d·-c:. -;:z Cr{)o3 ~ /1'5""-(':2.1 -:z. (J>(JOLjb< ()'t/Jc:;t ~ c: /.. (/9'1

1J -;, C' 483 -t-15:Y3 Zc = O'4fS.3-tO'o046 )( 83'3 =0-'/366 'Z

Jvl.u ? (jJ M?t- '" o "/5bb2- X2-'J/'lt{, '" 2.5"2:2-/ ldp-j-

£~""'mple $.,Fi,..,.,o ~ t!.lr/E6 5e.Ji6YI. ~ t!Sl<!.ye.t-e .w.J 6-••..eo: ~ !5l--1 .•..~'r&ljttr 0. ~'\mplc:t !>lAppoYkl ~eJ.cJtA\A'lI' ~ w;ht. od. ~ ~

15jt- W- 1.1> 40 eAYY'~ 0.. eO"nlplA~ ~ ttR "2.1 I4pS/j-tIN\..t tA. :5e(vb .. Uve. I«,...l ~ !l"1f,lAps/jr. M~..l ~~~o..'e.. J't!.. ';:& 4 ~ ~d Jo ~eo /4J

~D =" 1·21 ~psfJ~Nl- =2.·15 ~'F':>fjf-W ? 1~2.Wl) -t-I-f, WL-

=1"2~t·2.1+I·~ ')<t2..-15=4~b4 Jq~1J-~~------~------~~''51

Page 7: Solution Manual of Design of Concrete Structure, Aurther H. Nelson(13th Edition); (Rectangular beam only)

As ~ ~ I~ 2,tw,~ Z,LAPfX:roJ-d I ~ ~l-. ~ 'cjH = 10;: 4'~152- ?!h';J'(.1 turjf- = !(,75'3i? kf-In.

L N':J be_liCJ ~ ~ ~~]f~ -=0'8<;" (h iYt-t :t~ = O'8'GX)O'<3S-~ 3-~ 0'603( vd Z:.u.+f ~ ~o o '~3--t D 'cm Lt

=(j<6Q..6£,

M Zt 7::? o·OO?I la 'YN-t~Y\~'YI CfJ -:z 0 .~ ~.J

I = D'SS"hI j~ Z ~'" "o'<gS-x D'''''S- X Lt >' c,.~;~soor;-tj tA.-t-f t bO

==O'6180b

f < fJ -rnc.!X., )0 /).~y-.e..+Qd ~(;J e. k7tOU M lA -= r:p IJ.7L

9> '(,1S-'~,?= tf'.tr wlj - p~ ) ~0" ;><IO'OI1$O(,)obO>qbol~~-()()I86b~)

gJ 101~ 2...%6'17 1 in".?> ~.d2- j bsE,H'/to~'::c235 '£I?I LI.} b= 10<]=* d'L; £35 '£111 LI::.p d ;;z... i5~.34')23q

AsslA.-.vU't( 2'5'-71 &sne~"-1e ('.ova ~ ~ &v-bd ~ ~ k"s

- .'. h.. ";2{l5·.3Lt~g+~'5)i( = 17'849'8 ~ 18u

.$0 I J ;;z L~-2.•5 ::= \5-l3M~ i6"'1-5-2>S- [Q.d- S "'J

,N610 f3s"'" f1(~_;..)0'-D'9'~Q,0r ~5'5 _ ~:) . I ('J. =

=- 2 '3gGS" IYl~

=- '~2 ,"O'?<l2'2J3(;'? -:=> Lt '21 q

a. O'85J~b O·'<3S"IGLt:XIO

:Lb~?1 As::z 1b 15 ..3S- = 2--3\£,"'-n 2.-

'(J' (j'9X60;Q (15'5"- ~~'C)~2:2>Lb

CA :2 ? ~rOSo "35 ~'i .')< lo, U.se.. 2.:# I \ ~d Z-=ft l 0 bo..~.5

~ , } iD" 4

l>2# 11't> 2.#-/ D

Page 8: Solution Manual of Design of Concrete Structure, Aurther H. Nelson(13th Edition); (Rectangular beam only)

E~()...()V\pk- S'~

V6i'Cj ~ ~ &n<!.ydt! ~~ ab ~ eM>eJ. In-" k~<!.<m~ 5c:iv.h~~ cf f)a~pk 3.b ~ "l'e).'ora / d :z 11"S .~n.~-'h. "'~ I?t.) ~ ~ ~ -nvJ.n~ ~h-~k"J~ A.... .s~l iI\.'I'oo...

y~~ .40 "'e.$i~ Do. ~ 1..t<A.;f 121(10 i",-k'rS,,{I~ ~ O'3S pi 4-- Z ~ =0 ''8 Sxo"BS.><l Lt.><1 O'OO:i3 - 0'0206

,jj '"+Zt ~O O'(J03--t-O,oo~

10 ~0l~01 ~ ~ 0' '7 ) ~l-- 4:=Z O'(jQ5

.'.p .~0'8S01 :1~ ~£" ~ ~ (l'SS)<:O'30X~ Xl 0'003 - ~Cl'O\90b'-'cj 1.-\+0'005 60 O'OO3-+0'OOS

.. P < I!r , cS~ ()'Y\d e\() 'Oe\ n L-~ h.eo.NV\ ,'n\.o-X (ju"

.', I1s 72 phd = 0 'Ol80~)<t 10~ It'S- = 3'/bDS IYl'L-

., a. :2 ~~ ?- 3'bOS~ (;0 =- 5- 51 £1

o '8S:f le.. b O' 85><1 Lt )1110

· A }v\l\ L36D ;:::...l'b'3I')12-" s ~ Y":b &_ ~) 2 6'~ )<1<;:0,>q (rr-s-_ 5:Zt-)C.~c:k'~ ~ =- - l'b~?\bD -:2 2-' 81 b

U o'8s~4x to

; As -;2. \3<5l) = \ ,Ltc:J • 2-. , B9 ~w XJ (!":r's- 2-'~) IIfl

U&2.... 3':tt:' 1- bctJS'5

Ift-- to---4

----,- fEx~pk.-~·8Ddcym'hA.h"&n. ~ 5~a.l cn~ ~ Vll.Y1~bk.s~~ 'Y~~~

jaeb-. A',-e.I,u~.J e.m:xd« ••Jidl'lb {....."ut ~ ~ ~ ••.20jl-

~ !>i"""pk. £FCWI bt....... -10 't. l'n. a.v.d dJ..u,..;J~~ 12 in... 4'1A.c..

jcUm.)iO ~ ~ ?>\Abt~1F"pe'If#.t.b ~ c:ftem :W.-\ sa o' 7~ ktps/}r-~IAJL.G '·t:/~~'p"/Jf- I j~~~600 F"' ~ ~-'ftOD

p$" , De.k"fJ)"-'?\t. k ~7t ~~ Jat' ~ ~.,

Page 9: Solution Manual of Design of Concrete Structure, Aurther H. Nelson(13th Edition); (Rectangular beam only)

L _

20'

"= (j·02.43

kt- £t.::2 0 'OD 5 Jo 07t0-i11~71 (jJ -:2 0 ':30

'P '==O'<'6Sfb J/e:. ~l.-\ CS O'OOpI +(1 ZtA -+ Z ~ :2 6 ''Ss)Q 0 '25;X (.0 .X 0'003+ 0 'OO':J

~ 0·02121:3

fJ < f?YIo~ ) h-o l.Arld~'(oci+~ B~

l.J- 0. = z, iYI

2.t '> o'(JO,:) ib ~I-..5C1-J-isJ'ed .

," £t ::=: ZlA d'~ L _ o' 00 3 X 1.3'S-, . or;.20b =. I' Se:;X 6003 .:d:YOOLt~~ S'~06

~ rp == 0 'it'6'.?:> + '6Q'3 ~~ ;2 0' Lt <8'3 -t- <B.3' 3)<l 0 '06Lt 8:z 0 '2,16

N6lAJ ~L-\ ';2r:pMn 2 qJ~&- i=) ~O~'33X3'S4Xl"O~(lb'5- 4'I~t)7 , ' ;, ZI.3Lt'OJ li-t'p-1'n. I

-----~

Page 10: Solution Manual of Design of Concrete Structure, Aurther H. Nelson(13th Edition); (Rectangular beam only)

f~evl61A...b ~t- . ..se ~ oe;+~~, (f)

~J.;Cl ~ &>..b[",tT<lYlD:

CA..? 3'3/)<J '0 =- 4-4 <3 'I

O'gSXS><:I2-

r2 -= 4'4~ = 5'6 "r

0' 80

_" Mm ==' ,s''6{ ,)q('O (/3'5 - C;~S);7 251Lr k-\ps~in

6'()l) 3 (1.3"fj - 5 ·(,O ).". Zc ::0 , ~ or(W4Z~S·~O. t :C)'4~3 + 83,'3 ~O '(j04Z~ ""d '83S

, f.-1u..z cP Men ~ 0 'g35 ~ 2151Lt = Z/So lLt"PS -i''Y7 .

b-o ~ .3#-IO bO--fQ .

Ex~CW\fit. g. '2-A ~~:r""l...'r "'- /,w. #0. c...li,U~ ~ 12. i'n -.J ---'"':.~~ ~ <hu. ~btJ er .flu. ~tSY/ 'Y~~~~'cl 2.4f:n.

fu ttMbi.sn. 'r'eirt}w..'m6vt!- e~s~ a $i~ No./O b.tlr in.

~ 'Y6W5·~'lrt.hbicSl1.. 'pe,t+4.'t1lIMl- &-nt.rs~ ~ Jwo N.,.S

bo..YS \,10 FI..o.~ct.o1 £:5 il1·JOY! ~ ~PY~cJ)1 r~~~ . .u- JQ '" 'tro'tlO psi -...f j~~561R>PSi, "'~ •.tb ~ &..~O't.~t &.p...e.l~ ~ -k ~ ~ 2'~' J.' I !

~ 1'Yl~o~.f--.1 n:1'4 X 12-)xJ fjs::> l{ "" - :2~ dJ (.,J - ~) 0'38 XbO ~ (I.:?'5 - ~'~7-)

__ As--=::ch~_ 2> 'IQT «l 'D~ ;;;z I.rl.,

O'3S-j~1a O'~S)OS~I2-"

WR-'# 10 ho...~s ,~ As =3'8l 1?1L-.

21'SD t:, tt 10

4 A.s=~'1 'b2..,';-

Page 11: Solution Manual of Design of Concrete Structure, Aurther H. Nelson(13th Edition); (Rectangular beam only)

j~astmOpS >Lt6l5D psi; ~ ::zO'~S- ~'D5 J~-LttmJ?O~S- 0'05 5630'-4mm {"L6lJO :::z 0'80 cr L~

1 !) le. 2v. 5 (5'6ac3 .. , Irnw...r;x ~O'3;.0 /r, Z +~, :=O'~SXJO"80/<J-)q -= 0'02.4;:;

I JJ £A. ~ GO (J'603+O'oo4

fY ') f""",,~; baJ,~ Yci+&d beLJMA.

fn = lo'ss /b J~ ~ ~ ) /Cl L' . I JCj d 2,< -"(1 +P=~''3Sl<lC,g~2-Xl 2.'S >q 0'003 ~+O'6055 =00245/P

, /J_ bO 2...4 o'OO:!;-()'6V2.o7- <-.......so, ~mpYO>Dt'an kx..1'(5 ~ill 21-i'eJd'~?rl ~ L:L&

fJ ,..., to / . ~ J~ .0'n0.)<.. - (~-t- P ~ 0'024:3 -rO'(Jl/)S =:z (JD:8S / P

, 0... ~ (As -Asr)~ ~ (7'b2-I'C,-g)>o,C = 7'1/ inO'gS J~10 d'8S (q S ~ (2-

t!..- = ~ 7 '2 T d /{ ..." c:;2 "8 Cl( ~0, ()'8 - U J I'YL

Z ? f (d '-L ) = 0'00:3:;x/24 - 8'~!J) ::7 0'00511. t-\ e C 8 '8') J

tMA.d C(J:2 0' 30

, A. M u ? rJ M71 .

,,1f\s'JI ld-,JJ~:,-As)Jr(d- 1)2 O·~A /. Sh (,0 ~ (24 - 2''0 + 0 ''))<. (T .,'2. - I-5'3) "C.6 X (!.4- "i.'-)~ ~ 5 00 ~'ps-h-t

E~plt. ~.t8A Y~IA"," ~ W 'bUAl>t- e.."(~ a. .sewl~ iA'vL (pJ

tf 2:41 ~ps/Jt-~ (J.. ~~f~ ~ ~ ~ '·05 ~~rrdt-&1 6N\ (eg jt- ~'J1\pk 5p4Nl to U~~eJ f91 ~Yd5~ ~ti'~ jrr~-r~ke..~Yat ~eA~ 40 10 In. wtJk dMd ZOl'n. ~~l~Jf ~::2 '0, (j?fO p~i ~ j~24600 psi ,,~ J~l "'YeA. W)1A..t.b~k

I 104

pYl)Vid~ ? I I

1N:2 )'LWd +I'~ WL ::zlr2.X\ I'OS+ I~b~£'47-

:::? 5-21 klp/jf-Ivt ::z L0 L?3 z> 5'21 ~ «- 211 ~F~~~ 2;82. k,ps-i\,

Page 12: Solution Manual of Design of Concrete Structure, Aurther H. Nelson(13th Edition); (Rectangular beam only)

~ I

f!.. ~ 0'8S Ib. J~ __~ ;:z O'~c;'X:O'S5x Lt 0'C03 o(

.~,?( r J(1 ZC-( -t z.t 60 .XlD '0031-0'004 = 0 '026 b

-1" ~?1b1'Y1 ~ ? 0 ~~~ Z{? ()ODe:;

.'.f ? 0'85 ~O'8S")<\ .!L X 6'00.3 ::z oovso«(;'O 0 ~OOs+O'OO5 b

.' fJ-s::z f /od ::2 o '()I ~O6)<\ 10 ~~O - 4) = 2' 89 I~ 'L

/\? A-sc6 2- '23:1 !<lbO 5 I •LA ~J:2 -=- • 1?1...

O'gSu ~ to O'gS~ Lt)q 10

.'. "-1,,;," ~ kJcJ (;1-1::.) " 0'9)4. 2 '2l~ ~60 )<J~b - "5~)" 20':)')'00? tt',n" Nu, < f-..I lA ., On-,lotJ DeJ.'-nJn~",-d ba.wt.

.: Mu ::: 25:?2--J.j.u. :a25'32-2J:Jc;f)'60l -=4S<2'~3 ~'p-I''n..2- I

.:1~k. oet+e(.n<M~~./o &mp-r<!Won '6"ef:y,Jm'(u.~/-

As Mu. 2- 432 .~~2- ~ q'f:r& _cl) 2 Cl'~ 1':;"°)006'4-'2'5) 2 0 'SH ,'.,'2-

&mp~~8tn Cr~1n~~~1-:I ~·t62.-2'S- I' ~-d/i~.::z. 0 '603 ~ t0ka<:: 2L.:2.2V\ ---~ b~d2- I 7 ~

::z. O'OO/?c:J ~:;2- ~ :z 5#1/ 2.b'(}2-/ fJ I /0 ''flt;"

, (I I- , J ~ 7 t=s ~ ;:? 6 '00 {15"" )q 2,} 1600 := SO' ~ iG!>t

_~s: = 432'~'J3 =- 6"b<g 1'172-·

6"3' X 56~~)c C(;4~2r?) .

" '1obJ -t8vcbo' k. 'Oetjr Q~ = CD 'ST1 -t 2'53'3}-. :3'467- f>n1-

~ 4~ Ie-o.~~ i'h J~k.~ ~ QiI=-b bt)..fQ.!>I"rn (!o'OnpD~'<m

~.NiJW RD~J R.amL~A_~~ t'/n.. +~&. ~ :4 4~i::;:4'00 l'rnL

) ~~~~v;Jd Ru~~~t t'-n ~'6"ahldn 2znu. z.£XO'4-~..70~8~ \?,L

},o, Run..t~~ u. py,jViJd t:n .Jew.i~C<mz k./o ptAlfe. ~

ih Lt -O\8~ ~ Z~ =. 3'2.6t- 1?'l'L > 2'"8c:J I11-L

~ {:.t ~cl la»: ~A.eekd .

Page 13: Solution Manual of Design of Concrete Structure, Aurther H. Nelson(13th Edition); (Rectangular beam only)

~ _ M S' ~·2(.1X bO, ;z 5 '~bS-(Y8f>J~h 6'85'X 4)4.10

ti -;;t t\ ::z S[1[5' ? 6' ';f~fo, O'gS .

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Page 14: Solution Manual of Design of Concrete Structure, Aurther H. Nelson(13th Edition); (Rectangular beam only)

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Page 15: Solution Manual of Design of Concrete Structure, Aurther H. Nelson(13th Edition); (Rectangular beam only)

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Page 16: Solution Manual of Design of Concrete Structure, Aurther H. Nelson(13th Edition); (Rectangular beam only)

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Page 17: Solution Manual of Design of Concrete Structure, Aurther H. Nelson(13th Edition); (Rectangular beam only)
Page 18: Solution Manual of Design of Concrete Structure, Aurther H. Nelson(13th Edition); (Rectangular beam only)

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Page 19: Solution Manual of Design of Concrete Structure, Aurther H. Nelson(13th Edition); (Rectangular beam only)

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Page 20: Solution Manual of Design of Concrete Structure, Aurther H. Nelson(13th Edition); (Rectangular beam only)

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Page 21: Solution Manual of Design of Concrete Structure, Aurther H. Nelson(13th Edition); (Rectangular beam only)

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Page 22: Solution Manual of Design of Concrete Structure, Aurther H. Nelson(13th Edition); (Rectangular beam only)

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Page 23: Solution Manual of Design of Concrete Structure, Aurther H. Nelson(13th Edition); (Rectangular beam only)

,I"~ ~~1i- lLt ~~Xr~ tV~- _. .z l4L-t)<)0 -rso 2 0~.3~

tN -= !'2.DL-tI·t, LL = 1'2 ~O'.3S-+l"b><JI·5 22.·~2.. 14p/J--M ~ 2·B~2."t<: 202,04 kif~ft- .M", 2 ~f'Jc!WL(I-O"5,)P J-)

of> 2LJ3'04 X.1'2... = 0 -3 xo: 010 2> ~ Gb )q bd'L><J ~ - 6 "S::r:><la '010::')0 e,O)~ bJ'2....=-4<B 1<::}'3'4 ~ cd3 = 12.'2-:;r9Ib8 b ~ \IIU Lt

I- -l

'~d 2: ,~., 33 '" ~ la -:;;z '2·~~ -t

So ~e~J1B .s ~ 6 ib O~. cl. 11' Ir, IJs =fW = O·OI03Xi/4 X2/ .= 3'02-82- /'7f)1--.

~clvlck 4~ 2 194¥'~

•• ~:2 kb ~ '-t~O#1'1)4 ~O 'z 3 ':18 t( Lr.41 $3 -4'~

.~ O'85"'j~.h 6'8S"?<l4~/Lt

•. Mu., = 1J k~ 0-1) "'(Y~".3·I(,x.bO>q(n- 3{'lI) z .s24~·gb6 lJf>-fn.

==- 270 -32-. > "--l Lt.

@kJk'O' P -:z p~ ZO'02..()b j ~ ~-l -:2 CYOO4 ~~K ~~ ~ ~ ().(j[)~

~ ~ '2 CY't83 -t<B.3'.3 ~t. = O~4cg;,+ 1S3"3 X0l100Lt '= O~1?lb2-

~J- ~~ 0~ = 56V .tb/JrIN ':2 1'2. D L + 1.(, LL = 1'-2,:>Q O· 5' + I·G Xi "s- "'"'3

, 'L,(vi ';;? ~~Q.4 2 2.16 ~'p-jt-,S J

.: /vi", ~ SZ'p.fu bdL6-o'S~p -t) 60 )~ Qlb)q I Z :2 0 '21 b2. x 0'02.06 ><:(;0xdO::l~Li>'6 '-O'S'J ~O·()'2.0b:><J-zt

~ ~3 =- 4;Z13'2.? I,),)S ~ d .~{b.~bb I{ :: la -;;2.11·11~ //

~t-- 6 = 12- ~ d -::2 l8 ; kz £1

, .s.e.1L 10-e..loL 1- .:;? 12.)q 2.1 XCY If;'Q '= 0 '2b2 T?, ';j (1' -. 14Lt

IN '2 !'2.DL + I'~ LL ~ "2.. )q 0 1'2b2.5' + 1'6 x I"~ = Q "715 tu.p/Il-2-

.: M~ 2-::t~X24 -= 19S·48 ~'F-j{-

~n, ~"'2~tJahl-(~-O'59fdt)'Z) \9 5'Leg XIL:z 0 'CZIC,2.. ~O'D2..0bXlbD ~hJ~~-O·53~O'6z.a-b ><l~)::p~ 3 -;z 42£S' 01- ~ -::Zl~S 1~ cl. ;2 l Go • 2.-1 r" ~~ b ~ t c) . 8 t 1/

It

Page 24: Solution Manual of Design of Concrete Structure, Aurther H. Nelson(13th Edition); (Rectangular beam only)

~~'re.d~lZ sono F'', (b\ "2 <"'&5 - S~4.00tJ ~O'E) 5 = 0 '8'0

.: f~ ~0'2,'0 (b, ~ '2"~ = 0 ''S''~0'80 >q .,'>0 x. 0,~;~~'1' 0'OZ-4'b

P 20 'f::,O p~ = 0"6 0 xO'024S = 0'0/458

ML.\<;2.~f~bJ'2.~ -O'S9p ~ )-==P147X[2... =09><lO'0/458 ~'£O'l<l.MQ-O'5')~O·Ot~8Je... ~SQ.)

;;t> b&1... :: 2498 "41 i~~ -=t> ~ 2> "24372-· £.2- m~ [d::2 1-15 hJ "!J

l(

-1e>-ke. cd ~ 1'=('-5 iI~.J h '=' to '\ ~ h ~ 11-S- +2.'5 z 2-.0

~) As~'pkQ·;;z O~OI45g~17·5' 'fJ 1[)7 ~·551C)

a -= ~ = Q'5SI5~bD ~.3·bOces:j~to 6·8'5" X. t; ~ lD

4s ::> kt-\ "" ~2..~IL . __;I- '''.3 0CPhf?- ~) O~9?qbC))q Cr5- ~o)M 11-.30 xco

t:t.~ = ~r·g.3~0"8;J~ la 6'155'XlS 'X 10

4s ~ 92~l2- = \'2'2?2J, ? ~ J.J i?- i:) >(\'9 )QC-Cl;>o01'5" - 1~s :)

~~ ? 1~2.S3)ct bO ~ 't:J'-ttA'" O'8~J~b O'8S"~S)QlO

.~. ~ 2-1F 13 1e",1'('

A ~ I05;><l t2- 2 \"Lt~C~ ~ffJ~-1:) -2 O''))<JbO)o Cf'S- 3'0:2 A.d"':1 :z \' 4$3b xGG ~ 2 '0313

0.. Cn3S'j~ 10 cy<g5~ s~ fD

id:, 7 ~ -z 1()<5 1'-12- ~ -6"'8) = 1"41!?fJl:J 8- 1=) 0 '9~{;6~ (1't'~5'- ~-

t\ ~ _ Ikcht :z \'ltlE~bO ~2.·aolD .~~J~b 0'85 IQ 5 (cl. lO

'. iJJ:lQ. ,3{!::'f k:M.

As -:? Mu. _ \3Lt /<Il2- '. = I·~~{.tCff:J(~- 1)- O'~O~bC)qQ1'5'- 31°)

~ = Ih:6 -= \'89£1-/"..£0 = 2~bg0-8sj~b o· sS-,;>q'G ?QIO

f1 M.v-. 1.34X t2- - :;2 1°734? 9'~&- ~) ~ LY~~O)q~1'C; - 2:b~)

Page 25: Solution Manual of Design of Concrete Structure, Aurther H. Nelson(13th Edition); (Rectangular beam only)

0. '2 AsJr '-J. ~o ~ t 'g~ ~ z"s~O''8SjL b CV'E5'~5 ~ to

~ 11F-G~ ~ e~b ~

~ ~ Mu.. -;z i4t~l2-. ?-' 2..~OgOph, &.- i:..) ()":'J ,,£D l«r1" 5 - 31:)fL ,. 2 '080~ bO

O--?- ~ 7 = 2. '~3bO'8sJ~b oss ~S,Xl 10

11\ Mu. I~ 1- ;>q I2., "J'Ikl-S? 11 - "2 :z 2u9..7-~Jd&-1)O·~X'0)<1~1'5.-?-~j -J

0.,:::> ~ ~ 2 ·D'Yf /4.("(J ;z 2-' 8'1 So "8S;J~~ 0''6 1:;) ~ 5 r- \0

(Jb.L 11t-1- ~ ~ e~~ .top

r I ~ 7 ~~ (b)

J LIr ,

2.

r-rr

I'fcd

••• ~ ••1- '-'-

I/:fl:. 8z: 1'1'5 ~_ 201

/

.s.~e,J\~ CD - cD

- M~- 92 k'tr jr-+ M~Io:' (0 S \£.iF -J\ .+~ bL - 92 ~if-J-t- M e.J ::.9'2. bp-Jt y

+-MdL' ?\0 !tlf'-jt- Me:;:. Cj2 ~ P - Ji -

d

~e!t'Ot1l @ -r2J- t I b z. (lfl kip-J\--'- Md:2- 4'1 kie- t--

·m1-

Se~Ji~ ® -tZ,) - M~ '2 134 } ,'p-Jf-

e

Page 26: Solution Manual of Design of Concrete Structure, Aurther H. Nelson(13th Edition); (Rectangular beam only)

P~oblan-~'8~~

A -Mo -sf"""'- e.nJ-rn-wsw, &nex~ ~ I-., .to k ~~J6 Jb.12L '"Il>'IAb5n "'c:t w>••Il.\ .!>FI><!rI..Q .2.SJt- 6n ~ {-ClY5. fJ ~1rVI'<c..

t..'vz. ~ ~ \"5 k.4'F/JI- if.> Jo ~ ~'Y-r-{~ r~ ~C:LJ.,J,'o-z J-o

k ~J-~;fJ- ~ ~ ~ ,Pr ~~i- ~~~loJye."nSI.~ ~a.J,~ l~ ~ b. ~d I U)\~ h.. ~ 26 I ~ '1f~n~~~

lh ~ be. vo-....-{~ ~~d.l~ ~ ~Cfe.ltu-b, Fi~~ ~

y~~y~J ~e...YLJ~ ~~~t~ o.rn~ "'~~~<!.Q.~l-,*-alA (!Xi~e-.( ~<h~. MlE=w? NQ.2>(No. (0) 6~"Y~'

.£'nehJ..ck 6~ • ..h-csw"r\. ~ ~&o..ker ~'TiJ;e...1 C!.'To~ S4e!,Q,.b..

/44. J~;z4d2rO ~ ~ Jc! ~ (.0, (WO ps.\.

k~~elf~Jk ~ ~ :2 ~CX) )i~fA) ::::- '.2- XlO'5 +\'G ~ ,.s-

-:;z :3 ldr JJf--L~~+~ ~ 2-.-~ . +N 2 '3(.;:)L ~ 5'~3)Q2.S"2 131' 23 /4' ~kL

12.$ 12-8 r<fI L 'L,

- J---\ ::<> csi: = .3 ~2S ? 23L,<>31~

P ~ C)Oc35 (b d~, ~4. '8 8 ~r-fr, '}l-toX I b z C--\ -t- Z. t::

? O'8~ ~O '8S~ --=r...-?<l 0 '003 "!2 0 'GLObt' b 0 () 'tro3tO rDO 4

fJ = 6 '35 f; ~. z~I ~~ z~-t-~~

:z O·g~XJO·'b~/Q~)Q O~()n~ 2 ootz«eo O·()1)3+0'O 05

fJ <~~,~ke k ~['imtA'1n ')no~t- ~ ~k~'n"i~ Ad U

#J.lA ":L 1> /0.-n -2 CP;Ob bJ.'!. (1- 0'S9 f7 #-)!e. £0)~ 234·31f)~L2.. ~ O'~~O'OL8/~"C>?cJ h~L.;>QC~c)·5~/(J(j"OI~/X ~

~ bo\ 'L. -=<> 342b":!:>c:J m0 (d ::;> 52 6]

=t> cd :=- I~ ':J:J l(

~ Ja~ d 72-0L! ~ b 9100• 2x:) h:2 QO+2..'S -:z 22'54

Page 27: Solution Manual of Design of Concrete Structure, Aurther H. Nelson(13th Edition); (Rectangular beam only)

bo se1 w~dtJ- = 1~:~2'S-:>q O'LSO :;!' 0'2..34 ~'pj{-

~' . frJ ~ \. Z D L + l·G L L '2 I '2 ~ 0' 2.34 + I'~~ I~5" ~ Q' b 8 ~"F-fr,. M 9lA)L~ 9 ~Q:b8,>q zt;L .

. ' -+ 2. 12 ~::> t2-8 ::2 117·:ti- kip-it-; 11 / C0LL:. L

• , - ~ ~ ~ ;z Z't,8 ~Q.: "2- 2-6::>- .315 6'p- j{-~t o:» Lt 4

} As?- M~ ~ 1I1'17-;>q 12- S2 /'4;-" 1J:J(J.~t) o~~~bC) ~ (£0 - t)

CA ~ /bJj /'45 ~b(j _{)''6sjC:... la tz: O'g5~4X to -=.:2 2. ·'?s

~ Mu... 11::t'T.i'(qt'L~ 1<iJ (],l--'L) 2 O'31G{,O>O (2.0- 2.~ = I' 3'77-

CA ~ Ids<h :z I ~g3t- ~Q,O ::2. 2- ~4b7-()'g;j~ b 6 BS' ~~)q io»: 14", =20-;J'51"~(L 22-'44:2'3

2 ifi1C~-~) O'~.I<;~ (O~CJ- ~)

0- " Ascb e: 2. '-'Lt ~ 'l! >060 ~ Lt •~2-() '~Sj ~ 10 0 "'B5 )q Lt ~ Co

A-s Mu.. 20l)'31-S'~{L ." 'cp1J 0- £.) 2 ()'~«J60 f<J 6-0- "I L) 7- 2«)"3

tss I . 2:c.a~)<l Coo(}... ::2- <:r:1:z ::2 ~. c. c

o<cgsJ~ La LJ ~s r4 )G lO

"~ Q1J:. b -t- l ~ -=1- 6-eJY l~ ~~\/~ ~ ~ 1-..1P'g+ 2-#- 3' 107

NQt1VIL 'LOLR. .

...--~ ~<j' I~ 2 +?_-:u:--cy b :2 10

/

Page 28: Solution Manual of Design of Concrete Structure, Aurther H. Nelson(13th Edition); (Rectangular beam only)
Page 29: Solution Manual of Design of Concrete Structure, Aurther H. Nelson(13th Edition); (Rectangular beam only)

I2'5 if

'--+---i--~ 1I J)f.fi

••18

Page 30: Solution Manual of Design of Concrete Structure, Aurther H. Nelson(13th Edition); (Rectangular beam only)

t; A. ~ Lt '2>-7) () <l-tso3 I~ 2 u ~5 ~ 85',;>q Go ';q '1(,<15" 'xiIY(fJ:, _ (j'(J02!J6 -r (')7J{J'f'?; = o 'D 302-

~:~ f<t:.. ~ {k<or1f~'m ,hfeel t0tfi ~+d~~d~U"..-e f /'>.,~~ eke -10 f1, ,.2>0 ~ J2JJ ~ CO ks;0... = & - ['58)>0(,0 , e:J

o '85";q4)<JIL -:z s S-O/J ~ 6'50.L :2 -7 :?1'/,r?

/hi o '~S-. I &d; f"6S<-2..'"5'Z.S"2 ~'" e. =- O~603 . 1-~r; ::z () ~602D19

.J~"2 F-SZ~' :2 2..CJaooXO"()D201C) -:2 t;~·551

A.5/= A-.4s/~-f~b-/"58 =4'458

t).. -;2 111&:1 = 4r45~ ~(,C = 6~SC;O~8S]~h 0'85?q~ »iz:

e : 0.. ._ ~ 'S5 ::> 1"71/1>, ~ 6' SS

1:.. I -::z:2 ~-d I=-O '062> ':It? 1·-2'5' =- 0.002..02-~ lA e. '7f '1- ,

J~1= ESzs' = 2.::)CSOO ;>q 6 *()OZ62. = 58"20 4i

7. '2 L, dt -~ "2 O·(]03 /1.'1r;-7-7f ':2 O·DO!;5~ ~ ~ 1·11

C!J -:z 0 '4?5~ -t-833.2 t :2 0 '~g31-g3 '31\ 0 -6035" :;;! 0<1?4 '3

M~ ~~[I1s,.h0-1)TAsJ/Gv-oI')]= (Y7-745 G'4"&/<J(,(l~~6'7> - 6i9 TtS8)<SS-SO~~b'r5- :2'5)~ 2:/B/~" cg£:'<=j) ktp-I'n= 2>I CC> "0 r ~~p-ft-

P..-o~~ ~.UJ

A ~~jl1..lAy ~erd-e. ~ ~ f1Jid~ b ?2.41~. 16 ~~Ld 'Cl~1reh;kL~fY"tJ ern~j.Q.YA.J,dn.s ~ -lA ~(~~m ~bJ cl~~ tt&lb/~

J~~><W;,(.e.•.!rr~ 0.. ~1.FeJav.~ ~ ~ ~ s: LeaDj--k,PSb.b.tY' IN. fo-lIIlky.J ~'.y.}r-~')rIA,J.J« ~ ~l.«, tA$t~

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Page 31: Solution Manual of Design of Concrete Structure, Aurther H. Nelson(13th Edition); (Rectangular beam only)

~t"/.J ~Iw. ~.f1 :o4?l,Oi'JCl ~. -.J.J~~~ t»i •.s..~t'f~,+Q7"\I•..J Ja praV~ & ~ ~~ ~ ~ A

~~ <f :11SU-Y" J?Al ~ I i'>,.!J......J.C1 ptcJvi~Oy) In- N().4

(NfJ ~12> ) , 6J.iY'r~ . b? 22(LIJ-- - - I

P ,,0·35 J3 ~ ~ :;,"~I J(1 4-t-~l:-

. ~O "b5Xl() '~5~ 3-Xl . O'OO~Go 0 OO~<t-O'ons-

~O·O/~o.b

~,?- fbcP ~ 0 'm~()£ ;><l2~~ 13 a: S"b3 ,"«12-

CA. ~ £1,d:t -z S"b?:>)q£O -z'

()~8~~ 10 lJ 'S~,><J~)q Q.~ 4 14~?- ~:z Lt'!1 '2- 4 'S7-

(h, 6~?Nu, 2cpk,JcJ p- ~)zo"9:>J 5'(,~)<JbO)<J(r!>- L,~ }-S33Z,'?4<?J kf'f'-;'"

= 2-71'8r:> ~p~}-IJ.", 1 < /-.It\, = 4GO kip -J- --f> D...J;b ,em}e.J ~

.'. ~ ~ fv\4 -M~I '2-450 - £11'~7 zL2..2-°1( ~'p-j{-~ ( L LZ.-of 4-'87- -3s <:;J:LfA e. ~0 r-6C~;>O. q_ 'Sf =- a~()0 (15

J~I == E52-5' :z VOOO 'X 0 -6{)I15' :z 33'.sS- b;. " th! :;2. Mu..2.. 12.2:' I ( (\ (2-fJJ~&'--d

') ""6':') /<l =:c:3) =- c, 'S'8 ;.,,'--

A~ ::2 lds/X )$' 12 418'6)( 3~'.35' -=z2."llr?-zL~ Jd £0

IJs ":;2 ~, + /ls2.:2. (5'(;,3 + 2.~r0~ 93"54 /n1-

~,decl ~ -;z 1-~I'1.r zr <3'89 mL.P'fQ'Jl'U As':2 4~{'2r .2. 5~08 L~1-.

Pwvi de.d IJ ? Prs - As I L. ~l j

.,;;> 8"~ - 5"O~~ 33".9>S"bO

/0 t1 \ h. a I{,U

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Page 32: Solution Manual of Design of Concrete Structure, Aurther H. Nelson(13th Edition); (Rectangular beam only)

~cN ';::'6' () (.1- .,. .cC;) <:2 • b~ 2 D"8<;j~h 0'8<;M'-I)o24 44f!.-::2- tA ":2 Lt' 4 b 2. S 'ZLt 7-

(1.:;, lJ .8'S"I e. -- d' 5'Z47--'3:2..s :2 ~£-.\. e. ""2 (J"(}05 5' fit r- ~ O· 00 (2.<St;

J~(:2 P52.s/-:2eOOV~O'OOI2.:85:::> 37-~2bc;) ~

Z :2 Z ~~~ 'Z 6 "C50~ L~ - 5' 241- -;;z.. O·60¥t.t c-, C!- E;.2.4?-

CI"2 Cl' 4S3 + Zl3":? f" t: ;Z . O· Lt'8:?> t- 83:3,. <Y6114<'( = ()"349S

fJtA" ~ LIlslt r? -r)-t-Ids~Js'GJ -dJ],",Cl'SLA':> [~'O"r"'(',OXl~S- 4i'') t- 5 '0'30 237'l('l? X Q S -iVJ~103~'{'2- kl'p~~

? 41 ( .s? U1F-jt-F\rob~9n 30 11A ~ •.•.b..... ~ ~ik. wiJ.JJ", b" 24 ;"',JoJ..! d...ph-. h., 14 ,.,.

~ .aj?~<..ckt>h-..J.a d..a.-!~k. ~u.l d "'"1l·5"i,..•. It:. eclt",&Jw..O~ """",tcnAV:, ~,h.. ~f..r~~~ j~..l,(I(li) ~i ~ st(.O,oro~. ~~l.t.. ~"'rnjrre...~~ ~~~ ~ ~ No. tl bonr~pkb ,,"'Re ()<.b: !O ~$ I'YI coce: y6M.l. &-n. P"'(h~idYI 7:e.tjr •.•.

..~\.... ~,.l-i D <cf -/wo No. to ~r-("6 l6 plp.ea.J .J..,t$~u..&' .••2·S-" ~ th.... ~pr~dYI r .e..1e.J .••Je ~ ~" •.I~ ~.:r "\Yll.Ar ~ k ~ &.~~Jl.t.e.J..'Cl k~f1l'"~t.1VI ¥e..+e...~~® ~'TIJ.'C1 .r- ~&w-p~'on "'L<.~f"e.a...~l-~ ~~ M t~~~

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Page 33: Solution Manual of Design of Concrete Structure, Aurther H. Nelson(13th Edition); (Rectangular beam only)

A~-:2 2.~}'5£ "i-3~I~21-:2 6 .c:7'3A-5 ( ~ 2.)<j{'2 7- -z, 2..' Sl.l

-{ .d:.l~-2.'S

P iJ3 b'"') 3 /7\' () /I'S-::z bot ""7 2ft ~lt '5 z uO..!0 -;;

f~ /1,( 4< ~S4/od .24?<lII'5 7. O()o92-

~O -;2 s1i z~I ~~ d ~C;/b, :(j z<.-t -t-4 .

::;2 0 'SC;Xl 0 'g'S""(Q 4 ~ ()'~;> = O,()2.Db~e crtm; -t 6 '004

f ;>f~~ ~ f)~bb )-ci<nY&.d ~-f 1~ d( ~ IPo :z O'<6S" /b ~ - -+-? "..0 '8S""XO·g5,X~ X 2'"C;; () -003-d I JcJ d 4-ZcJ 60 /I'S ;q 0 '(J?)!J -cixJ266

-t- 6" 61)92

':2 O· 642..6

r<: -f?~po~~~ ~ wttt -rJ- cffdiLl: /f~391a; I

As, -:>- fJ-s - A-5' t "~'')?r !l·5t.r/'o' ~Z ="3'23")

()..r ~LJ:J ? S'2q9~'O =--3~3~c "30J~ I<;; 0 '8~~4~2/1

(!.. ~ ~ .-;2. _S'ZYZ5 ~ 4.5~/3;{ I ~'-gS"

~!/2~ ,~-.J ~6"6C>3~4'5b- 2.r~ = CY()OI2;5Si'\ ~ Lt '56

J~'::z E$-f.5( ~Q.')QOl) ~o~tm13C;5 --:z 39'£9 h~1- :2 Z .,.J-~ ?-6~063 X IITri -4"0(;"2 O'OO45f, ~CJ'Mb

e: ~ (!.. ~#S6,be) ~ ",()'tr'83+ '6;.3, Zt 20'L{2S5.-r'B~· 3?1C '6Ot66 = 0 '2(,n

Ivt')z "" AsAa ~ - "t) :2 0 '2?'J ~ ce»d1''7 - 5'~ J_.30253 '{j?; 'i'''' ,;"2. 2<;'2 '3!r k.f;jl-

NtA ? ~14~2-0 'g£2.rgXJ2S2-"34 :2 21:;-'7-z.. k<f~Jr-(9 ~ Jht p~~; jsl ~11

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Page 34: Solution Manual of Design of Concrete Structure, Aurther H. Nelson(13th Edition); (Rectangular beam only)

1 'i ?- 2; d - ~ z 0 ' OL)~ ,t 1~ - 3 A 2? -= 0 .00 b '/ c1>- 60S-,. t ~ C: 3~23.', C/ -2 O~'76

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