Design of concrete structures arthur h nilson

Solutions Manual to Accompany DESIGN OF CONCRETE STRUCTURES The McGraw-Hill Companies,.. tm ra " A Division of The McGraw Hill Companies a ` Solutions Manual to Accompany DESIGN OF CO

Solutions Manual to Accompany

DESIGN

OF CONCRETE STRUCTURES

The McGraw-Hill Companies, Inc

New York St Louis San Francisco Auckland Bogota Caracas Lisbon London Madrid Mexico City Milan Montreal New Delhi San Juan Singapore Sydney Tokyo Toronto

tm ra "

A Division of The McGraw Hill Companies a `

Solutions Manual to Accompany DESIGN OF CONCRETE STRUCTURES Tvefth Edition Copyright © 1997 by The McGraw-Hill Companies, Inc All rights reserved

Printed in The United States of America The contents or parts thereof may be reproduced for use with

DESIGN OF CONCRETE STRUCTURES Twelfth Edition

by Arthur H Nilson provided such reproductions bear copyright notice, but may not

be reproduced in any form for any other purpose without permission of the publisher

ISBN 0-07-046587-8

1234567890 BKMBKM90987 http:/www.mhcollege.com

PREFACE

The set of problem solutions that follows is provided in response to numerous requests from college teachers using the textbook DESIGN OF CONCRETE STRUCTURES by Nilson (McGraw-Hill Inc, New York, 1997) I make these solutions available with some reservations, and would emphasize that there is seldom a single answer to any problem in engineering design Many valid answers may be given in response to a given set of requirements, and each may be "best" in some particular sense Material economy,

construction practicality and cost, geometric constraints, and esthetics must all be considered, as well as functional

requirements and safety The solutions given here, therefore, are for guidance only, and may provide the instructor with an idea of the probably length of class assignments

All problems are classroom-tested Special thanks are due to

my former students who performed most of the actual caiculations

Their solutions, condensed in most cases for this manual, have been carefully checked and are believed to be correct in all details If errors to appear, I would appreciate these being

‘brought to my attention

Ithaca, New York Arthur H Nilson January 1997

oo & No aT 6.00 in®

Zo Ags 320 wut A © 314 int

ee 6 el 24 COO , Coo “+ E.= 3Ee00, too psi

n= ¢g

Foe fy Go, 0o@ pst : For f.= do ,com pr t

(Q) “P2\2e0 (320 + 1¥6e) (A) P= 12eœ (32e + 7x€)

= 434, coo \L = 434,000 \b

(0) Sys 24 os0,000 oz Cb) Eu ZF 002, coe jecid

C= #3e© pe {.: Beco psi

P= 3300 ¥ 214 +€occo ve Ps Zeco + 214 + 4o,oon¥e

is AN 16° INCRE MCE IN Leds CAUSIA ST EBL MIELDING | AND A 3% INCREASE IN STRENGTH, Fo@ Wienke ATEEL PATIOS DIFFECENCES WOUlD BE

GREATER, ALTHeUGH CoLUMA COST is SAME,

}-

= 4&7 ovd \b = 4&faro Ib

2, = &v 2ơo # IZ.S© G: \Weeeo b

| (c\ P= Buon » 3e8 + Gea x «5 (C) Rs 34eœx5e§ +Áseøo ¥ Z.Se

(= 16€oœzo bb f% = uo eco (b

tor the Cat2 (Co een] Rr eputts for + “*éo®oc Zđầ

aud hoaoo pet an oe + stv ae

erttta Ce Le Gt age ` vs .sf ,\hlu»

ue Ate one 2 ACI ode , ga

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C25 lg0e 158 ¡Sea® SZ 42 $2 1

2010 262© Z4? #o@ae 304 1536 tô 2e o2S đieo l4 — 4Seeø 445 974 16 24 ©02o 33oo Is64 5 Jooo 511 ZlẢI 13 71

2030 = oo ray boces 6°] 2219 75) (U7

Mes EL abd®- Lee 425 8SSv24¥ 155° lel Hk

ASSUME £EtF-WT tư: Seo lb/ƒt

ur, = 1.4.( 500+ 500) tide izeo = 2440 Ib (#H

Liú¬ 3.44» cz*

M.= “3 = 7 = 2o¢ ft-k

Faom TABLE AS witH ff, 60,600 (Si

AND fi ooo psi : ds, = 0214

$1 = 40c0 pai

Sy * 60000 per

E, 3†©OOffc` * 2.s©x\0^ pe

a ™ HP, = 2v CỔ 2.2

wy = SER ISO = 200 ie} pe

Ud = UL, + We = 260+ 2450 * ZFIO Ib] cy

(Q) Fea qesre Al fet 542

Ay =545xIOxZ25Go34@G = Zito Pre

1Z000

Wy ® Bà ‹ si 2 4220 |b) or 432°f a = 1.59 £185 “NG,

TNE SECTION Bequiees ALAraGE Ag:

20.014 23.22 n>

—@) créceing Momenr (4) (A) Steenem

dạ" th vizv24” : \(28©Oud as Asty + 339.0000

Ñke ={CTÍc = 495212806 ô5% b 85 x4C0Ox I2

() ẢÀAYUAOAAL ELAST AACAAEL+T, i bes (N-DA, * 2.5 ne

FOR CRACKED secre | K* 0.384 j jr 84

Ant 0S y4 v ST = 2121” USE 2Mo.8+ tNo+T

Ar À ANDE AND MiDSPAN OF BC AND CB!

Use 2 lb.6+ ¡| No-7

AT MIDSPAN of AB ADD DE

Mut tes #t-& R= G2 = 01S Ag= 163 1%

(Ke 2No-7 + \he-c

2.Ð Wo span ConTNwows BEAM,

ARAWOIS & Most DEFINE LOCATION AND MUGNIURES OF CRITCAL Stemsses,

Foe MOMENTS | A-TE2ZNATE SPAN LINE LCD PESOUC(S (H CE(VAC

MOMENTS

9

Ma : 3 eB w_ 0° “\tl err @ x= z(E+8)0 = I0.2'

he FRM EERO SUPPORTS

Mia = (Us We) ee 2S ueerr CC C er sezmeer,

Desh S DEsGh LEFT SPAS Use SYMMRTEY To DESIGN BIGHT 2P,

Tey DMO, 4423.74 2! #2 zneeor<

p= it “ae * OOF © Prag or,

STAN, CQMTS TOR BAe baw 4d, + 202k 210" el

a= bo os" or! (eerste Z5 PONG STEEL wre

Tey 3-%S 12 -#q As? 5, 35," THE SUPPORT)

=~ |9O-

Foe BAL STEEL ATIC £5 E;|<,- 3 Gu ref kì

ÊL * 24000 | ee2- 2 (.cozet.c02i\{

FIND c Feom E@ (355) ,ADD ashe

e Feo £@.( 356) My Bee fi-k

(b) fee A¥10 = 5.06 ium er O24

344 ( ce'T) (cy Ass 6 Ne.ies 7.54 iw ẹ= ,o5S |

TOE SINCLY- CEINE BEAM WITH SF Pmey |

Nee ,Ô@2\4 #242 = ECR in”

ae fAef _ COR xEo _ 4X

WITH Œ* 6/A4x¿z£ ~ 4X AND ct STR?

ckecie Sex &S B,

TH fie als: Seco kes

Mụ= Ash, (d-S)= cate S (11.5- 254)= 310 fee

bMy= “219 ft-k « BUT Nere ¢> 159,

AEST Check © wird fis B,[é.- J'6.46,)| ‹

G.44|xeo = 4 zA *2Ác +73 voob *[eoo* ~e"

fou wich ct 445" a= 3&7"

My,= '?1€ H-t AND đcMụ= 22 f+-e

ete THAT SẰ©tort2M) (GÀ 1S oNLÝ %'% RELew

THE coeeetr NALOE F62 C) , AND IS COnsERVA

TNE THE SeloTioN OF db) 1S LdcondsEeCVUATIVNE

Rot one I% Hie FoR THIS CASE

Clec¿z wo = œ = ls = BAB Reo c S-IGin * Ew

= (A, Ace) + A= 3.38 + 783 = 6.2 iuX

le

>

CHEcc Suh ™ St Sp = OLES + 014 = ,®43

ACTURL Sy> O31 < Os, oe Leaf

ASS” ASSL NMED

¬l6-

wn it ot

Nore : Tals AGEA COULD BE EsOx£> v£ THE N¿ (@nt£e(= te

BY Anny 12 ACOOHIER FOR

4.> TC#es¿œ\ cy 2lESE VEHEOZEAEAL

Ve = (vad Fl » 2800p HE) by 4 $ 25VFE bod

MESITOVE ERQUATIAA WOULD NOT BRE MAE VF IS COUSsTIZOCTIED COST SAVINGS EXCEPT Ins S(TUATISNS

m : — @F (@#wrŒ£œwf CONGESTION

-Zl-

a | we DIETANGE “ Eoouexe NEE za, SIZ ke

x= 8.0 Similac Fievee For (b)

HưLE BIT MORE oF THE

Wy" eV, = 53-189 = 34.) « BEAN Y© 8E LNEEIHEGSD

12L“

NV, 2 85x 24000 ‘Wale +100

Now SNPS ARE ZU\ĐED enero

He BHTIZS Let PALE OF THE CEA, THE FEQUIREMENT> FOS THE LEFT HAF WANE NeT CHANGES VERY Mvdr,

Just A WE BIT Omavnee ArucE lo

Hoo PEQUIZED TO PAN MINIMUM

-2>-

Ale see PeoBiem A4 Foe EAE EHNELOFE

| 1É TWÉ Af9QL ZfI€fvvP 22ldan

veg HULU UU eT B.'s CAN BE FOEMLLATED ID Mm

ssE—=———-— | WANS FOE EASE IP ConsTevenen)

NOQiETY OF NOMREE GF TyFES OCF %P4<4q2 TO A MINIM,

4 sung DESIGN Toe MEMBERS SuBIECT Oo AuaL Eoeces

CompreseiNe Foecrs Ny = \5O~ Acccc tO PROBLEMA 4.2

(HỒ Meme ACLOTATE Ðuoenexs:

AD

"[Ewzo» Feece t = 75." APCED TH PEOBLEM 4.Z

(a) MOE ALLOCATE EG oaTior’

Ve 2 O weB SEL ISTO TALE TOTAL 24A,

TRHETE 15 O BE HO CONCRETE CONTA BUTOA

-27-

ASSUMING b= Ilo TO STAT,

BIS | assume ais’ As 3xư0(2A-+ = (Z4a

h #132 CHECAO 6 = ILZ4 xO = 13.2" Close BHO,

Xà" #es (\a fSeo+zseex S oF) Wee 505 «

ANS THE LAWUT eA N, 16 Seco » 1%n1Z4 +1000 = (eo Bl Ke 90 ot!

SWEAS REINFOZCEWMESST: (4 + Z.\2 tiêm (N Vệ) 538 -.85.505_ | pc eases

Heer Z& LU *4 eneeses

But Lv uns 1-2 bips(ff ;M¿: 23215; Bo ee tác

Grud Ay prouded = 3.12 tư”

He

a Vedueed 1, = loo x 38° = 4e" : NG by 3"

(lo) alist +o nearest face = 259°

roduged 2," 4o x ST * 9e” <(4&6-%) okey

Couelubes (b) wove mole ta (a) wf

iudicale2 heaw is legal”

— 2® =

——

$.2 uy, = 14 Sd + Tx Les * 259 kít

Mut 8° 2-54 ¥25.I5== zig IK

Mu 21S ~1ze22 © 42% C= ot§S bbed> {y le * l&“” used As= 3.55 G8

Betual ci (Feiut <= €.†e ~ 1.33 + $.3T |

Freres Sepcad 4 L&-1e/ t ple

jt —- at z 4<

ST Pa, Z8.1S/ ey 4°

(b) Fon Hie la: $= 60° (Take Awd

Tor lo cut lean hoduce 6 L, = 60% 355 _ Sé

3-14 4.67!

loee (2s TS - ax s3i\4, = 1.se` > 4.67 okay

For Fie ceoutivud (eer

au.© Lov l ( pepe =sh tre Providing ax least <

é\.= 3.45) ee coÙbcL Can < (£e.€ + 3.4) = [b.0'

ae Ca Cuk loan be The” cow tax^e St

pla une)ed

2+ ( 5tS-£ Use extra 42 LÍ ft r+7 uta

al istanree = wan = 2° est CLG Fe te ee sys hg

arnt k& tá Leo otee|

But la Ưng Cal cular, Gouge - able (tests + ©£ jr eee \ aus on dường

4t<a2( Glace Ure! Luo wlat

\É only Cue lee +o loc ben bt , au

as gy 5 rf G2 Ao petitrers ott

(c\ akeove tuduca& cone 2, Could uh

hạ Acowdaked wf the Fic “wee ohh

FEDICTION FOS SPITAL FRINTORZENEST

cog #9 BACS: CLEAR SP=(lo -4-3)b 215 >d_

CLEA CINE = 2">dy,

ASSUME PR FEZ £3 STIARvPS

1 FEoM TABLE ay 2 /d,= 62

Oj= 6£*L= 6#

AND WE HAVE OnLy 4o-~ 2 = 38"

So NEED To UGE 4©” Hoot

a \220 x | +V4000 7 \† Ho A>VEVA©tÀ 4Ðe©

34°-?2®` se or!

TÖỤT 0E ÀLSO HEED LẠATEEAL, 2(EEL, AZ/6PANH To ÀT;

MAK SPAIN ^ 2k LG©Ô = 3`

4s

«ASSUME =o & BAECS ACE FULLY STEBSSED

BY ÀØ22v EỘ (SẢa:

4k g= 3.14 in: °° sOlO% \ bMys ‘ ¥S37 * lá v£C ((864 = 2e4""

2Nb-$ 2 157 3 et ceoSL ; M,=.97 292 ide at fizme = 18

áNo.* 5.06 ee od > OM, © Fe Mee ldercfece = Ae

ZNe.to = 2.5% 3 9° 00F% > PMs Fr U6 (441% [12000 = 242

2x = 1#

ƒeS f8Á£$:; EvreMPD Te zz"< 5 PAST TH PoinT

FfoM CeArt AS VITH CUTOFE oF a 4% To

THhee@eticAL PT = .2Šv 24: G6! FROM SOCT

ACTUAL = "12 ¬ tt s So” Fff£©M SOPT

œrtug 2 Ne.% CA€@fØ(® €" INTO SOPT

NE@ Ô0À(5Š\v EZTERBĐD ¿1c ¢ PASr TH, PowWwT

FEM CRAPH A® WITH CoTOFF oF đa.” 44%

THeogeTiCAL PT © CF x 2d* 2.16! Feom SoPT, AcTuUAL 2.6412 €22= 48" FeoM SUPT

Bor 24,5 46 AND (¡= 4&¥ 135 SZ" ComTects

CARRY BEMAIN(DE 2 No Io d=2"' ind,= 15"

PAST 10 Bot Ne Less THAN [l6= 18"; 22 codTHers

-25 -

CHECK Fo@ Nob 2, Zo" < 4%" ot

AMGo , SINCE Ke & BAECS ALE CUT CFF IN TERDSION

ZONE, WiLL NEED ExTeA ST( PReUPS CALCULATIONS

HÔDOtCÀATC 4 2:35 NEEHED, EGOALLY SPACED

ovee zd = 16.6"

TINÀL CoMMEWT" :( BecAuse @F LExcrkY

CALCOLATIONS | CoNPLCATED STEEL PLACENENT , NEe) FoR EyTeA sTIeR LES , AND SMA(Œ_

DIFFERENCE 1A) TeTAL ER oF STEGL MST

EXGIDEECS VĐoOoLb CARRY ALL Pos BÀ£S €” iuro

SuPpeeT FE, AND CUT oF ALC NEG BARS

OC FOE BEW CF TROBE 61

63 _Bepesel of peomens (ol

Forme Z-*\l cave

VÀ * †40 B,=120 AZO,

(a> ur * 0.076 x \.2ZO x 22.3 /2.5%30 = \B oe © a>

THS 1S >A, = CO O)Z2 By MBE (2\ so No Geom o

35, ( zZ= By \2.5x 30 “152 wae «© >I sy Y\ Lew

(&) wore À, 7=O A+7ZO @ Syes,

À,„ "5lÂn — vÀ*34o Aé "WBSxie 20.46"

BEAN DOES HET SOME Roun}

IN AODITION | Wp WoeLm Pectosiy

BE APPLIED EARLY AND Gà» 400002

BE BASEP orf 1, *6AO per Ôổlô,

bà vẽ 46O \Z1O Wh FT |

bày oy 21220 Ì SleeT -TEPIN*(ZZO lv er

wrth ALK Lea oN PLAZE

obo BEF ECNOMS

TWO 2A) COWfNWO00%%S “BEAN /

NAMM FosTiNe MOMENT she we

MAKUAON DEFLECTION “igs wit

(® A\ = LOS me? DL OnLy

Mt 2 34 mr-v 4

1 " i(©)(z2”= 8875 8

= oO 2 3S Fr-k

tk» (WW) ( zee)

AT EXTERIOR suPPOET NEO Ah ?My “Te*Ty

AT Mi oman Mg 34 Mp2 Atg “Teh

br remem suPpoET Mg"b4S Mer “Ny” Le “Tg

iy exTemce cureecr MytO ÁN Tee

AT Mute PAL Ny 95-2 Mer My“ Te 6g

TWE TOTAL DEFLERTIOR 8 ©0163 THÍS 15

Aunesr BQual +o Ad\ ie cant, aur

pote NOT NEAT Yate WIL 1S Meee

APPROPRIATE OVE +O PIPES E72

TRE EARLY APPLICATION OF POLL UNE LD INCREASED CRACKIN Ì DECRERSED me

SUPPNESS FOS ALL SYSSE@LErT LOAPS,

6-7 Ame BEAM AS PECK G6 (@ same as cca), A,= o1% im DEAD LD OnLy

4

(6) uy= œạ+/22uy * 14@€@ 4F Ms €2Ð f1

MỶ= 46.2 tr-w Minera: XP F874 w* Tee 3242 Ma = 356 FT-&

it der) ous = 6-37 in

(C) With FULL DE+LE IN PLACE I,m SAME AS

foe P£on 6< lb yị TỰ * 4314

4

_ 2.8 * (Z2 v t2) - THEN dieu ° (6eX4eso)(4572)0 2) 2°95 IN

ANt> For LAST o.® LL :

A, + dy yÐL c¿L de pee eee = 45-15 Z2 1N,

A;

A cy (A

GQ) REDoOCED Te TAL NEFL MOE Toe SUSTAINED LoAcd

6:8 UNCRACKEED ELASTIC SecTION :

nee (n-ÐÂ;s 2€ iụ*

th Ec 3&ooceo # \|.2 ‘Goce le

CRAcKet ELASTIC SECTION:

< % GEAY

| CRACKED SECTION | MATErZIALG INBLASTIC *

TAteE €, = , Golo, oes » OFZ cots

AND fed EACH , FISD nie BAKED ON C= T

To ORTAIN TOCC CUO\)E M |

FINALLY Mụ=ẽ As€, Cal - $) « 442 ink

B =60% tụ ` 4$ = ,ooo4sử ‘ “ " % lo ae

-44-

- ĐÁ vấu = O.o338<07; +5 )+o.es Ss (-ÈXà

L Font Si©€y©c 14 72 2ZÁc= G.exxys 5S)

USE Va Crosia smears f//ST gr

Te = 2¥IQ- = 26 {t- k AT FA OF SPF 3 FRou spr ACE, ZcCccc.o%A 2y 7

= > (U9 bt)- 23.59 ft-le Ar SATE Tan US€ TH

Z < Ar bh" rend $£4~7 LSMAAUAS M0577

d Chen, FACE of S.77- ⁄2£ Csn£A ro by od = PY S%2 2 s/

seat FReAt THE 20/7 wane Tes 26 6H

Acp = Z2anrS = S3cew 92h CC} ccco£€ G- Êx/3 = _ LBS! Kren,

Stout & “+c+l Coe Sse pt AT Leds

3 €V£.cy SAA BAS ro 55⁄2 THA X/⁄24cx~© < L462 Acre Ag

+z2y 8% bd CEL Ry Mu foadble )

ts ECE URAL Oni PIESS 1&5 zeke _

C.Aeese O = SS° Lead @ Pace oc

Ác» =:iOoy2O = Ze0.x°/ 26/2“ 2 2 (10122) = 60” GO, 6&» ‘

OSS Ụ KEÉzo xeœ*?

Auk > 6.5 x/b5 = SOT sna *

a: ONS KIS 7 = Govt

SnRLUuSS Q@//24a KOR

TORS &3 OnLy