Concrete Design Flowcharts Updated 3/10/17 LAP SPLICES (How do they work?) Servicability (cracking etc.)
Concrete Design General Provisions General Preliminary Design Information Applica Applicable ble Codes Codes ASCE/S ASCE/SEI EI 7-10 7-10 ACI ACI 318318-1 11 Othe Otherr ACI ACI stuf stuff f CRSI • • • •
Concrete Design General Provisions General Preliminary Design Information Genera Generall Prelimi Preliminar nary y Design Design Inform Informatio ation n Load Load Comb Combin inati ation onss from from ASCE ASCE/S /SEI EI 7-10 7-10 Load Load Fact Factor orss from from ACI ACI 318318-1 11 Ch.9 Ch.9 Floo Floorr Live Live Load Loadss ASCE ASCE 7-10 7-10 Unit Unit Weight eight of Conc Concre rete te
General General Design-Stren Design-Strength gth Consideratio Considerations ns ACI ACI 9.3 9.3 – Design Strength Tensi ension on cont contro rolle lled d sect section ion (ACI (ACI 10.3 10.3.4 .4)) Compression Compression cntrl cntrl section section (ACI 10.3.3) 10.3.3)
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Light Lightwe weig ight ht stru struct ctur ural al concr concrete ete = 90
•
∅ ∅0.70.565
Shear and Torsion Bearing on Concrete
Sand Sand ligh lightw twei eigh ghtt conc concre rete te = 115 Normal weight concrete = 145
4000
Heav Heavy y weig weight ht conc concre rete te = 200 200
Specif Specified ied Compre Compressi ssive ve Streng Strength th •
When When usin using g equa equati tion onss w/
•
E.g. E.g. 4ksi 4ksi conc concret retee
150
for for R.C. R.C.
it is common to use
ACI 9.3
∅∅0.0.∅7950.65 . 10.9.3
Concrete Design General Provisions Mechanical Properties of Concrete Mech Mechani anica call Prop Proper ertie tiess of Conc Concre rete te Compressive Compressive Stress-Stra Stress-Strain in Relationship Relationship Line Linear ar elas elasti ticc up to 0.65 0.65 Comp Compre ress ssiv ivee stren strength gth reac reache hed d @ appr approx ox.. 0.00 0.002 2 stra strain in des descend cendss past past 0.002 .002 to an ulti ultima mate te stra strain in of at leas leastt 0.00 0.003 3 •
• • •
•
33.. 57,000 40,000 1.1.010 010 Modul u s of Rup 7. 5 λ λ λ λ ∆ ∆ 0.000006 ξ Young’ oung’ss Modulu Moduluss ( •
ACI ACI 3-18 3-18-1 -11 1 Sect Sectio ion n 8.5. 8.5.1 1(
•
For high-s high-stren trength gth concre concrete te (
or
Pois Poisso son’ n’ss Rati Ration on usua usuall lly y 0.18 0.18 to 0.2 0.2 Tensile Strength Strength •
•
ACI ACI Eq. Eq. 9-10 9-10 =1.0 1.0 for for norm normal al wt., wt., = 0.85 0.85 for for sand and-ltw -ltwt, t, & =0.7 =0.75 5 for for ltwt ltwt.. Volum olumee Chan Change gess (Sec (Sectio tion n 3-6 3-6 of Wight/ ight/Ma MacG cGre rego gorr textb textboo ook k for for exam exampl ples es)) Temperature emperature Change Axial Axial Deform Deformatio ation n •
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Creep Stra Strain in incr increa ease se over over long long peri period odss ACI Shrink Shrinkage age (humidi (humidity ty depend dependent ent)) Comm Common on valu values es 0.00 0.0004 04 to 0.00 0.0008 08 in/i in/in. n. •
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Dura Durabi bili lity ty of Conc Concre rete te (Wma (Wmacc pg 90). 90).
Concrete Design General Provisions Mechanical Properties of Rebar Mech Mechan anic ical al Prop Proper erti ties es of Reba Rebarr (Wma (Wmacc pg 93) 93) ASTM ASTM A615 A615 – Std Std Spec Spec for for Defo Deform rmed ed & Plai Plain n Carb Carbon on-s -ste teel el Bars Bars for for Conc Concre rete te Rein Reinfo forc rcem emen entt (des (desig igna nate ted d w/ “S”) “S”) ASTM ASTM A706 A706 – Std Spec Spec for Low Low-All -Alloy oy Stee Steell Defo Deform rmed ed and and Plai Plain n Bar Bars for for Conc Conc.. Rein Reinf. f. (desi design gnat ated ed w/ “W”) “W”) ACI ACI 318318-1 11 Sect Sectio ion n 21.2 21.2.5 .5.1 .1 requ requir ires es A615 A615 w/ spec specia iall requ requir irem emen ents ts of A706 A706 for for seis seismi mic. c. ASTM ASTM A996 996 – Std Spec Spec for for Rail Rail-S -Ste teel el & Axlexle-St Stee eell Defo Deform rmed ed Bars Bars for for Conc Conc.. Rein Reinf. f. (des (desig igna nate ted d w/ “I, “I, R, or A”) A”) • •
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Mech Mechan anic ical al Prop Proper erti ties es of Reba Rebarr (Wma (Wmacc pg 93) 93) Welde elded d Wire ire Fabr Fabric ic Prestr Prestress essing ing Steel Steel • •
Concrete Design General Provisions
Concrete Design General Provisions Mechanical Properties of Rebar
Concrete Design General Provisions Mechanical Properties of Rebar
Design of Formwork Design of Formwork?? Genera Generall Prelimi Preliminar nary y Design Design Inform Informatio ation n Desi Design gn of Form Formwo work rk!! !!!! •
Flexural Concrete Beam Design Flexural Design of Singly Reinforced Beams
h
∅ ∅ 0.9
Genera Generall Flexura Flexurall Consid Considera eration tionss for tension tension-co -contr ntrolle olled d section sectionss ACI ACI 318318-1 11 Sect Sectio ions ns 10.2 10.2 & 10.3 10.3 give give gove govern rnin ing g prin princi cipl ples es of flex flexur uree Stra Strain in vari varies es line linear arly ly thro throug ugh h the the dept depth h of the the sect sectio ion n Comp Comple lete te bond bond btw btw steel teel & conc concre rete te (equ (equat atin ing g the the strai trains ns in adja adjace cent nt S&C) S&C) ACI 9.3 9.3 – Desig esign n Stre Streng ngth th Tensi ension on cont contro rolle lled d sect section ion (ACI (ACI 9.3. 9.3.2) 2) Compression controlled section (ACI 9.3.2) •
•
• •
∅∅ 0.0.795 . 10.9.3 ∅ 0.65 0. 8 5 β β 4000 β 0.85 4000 8000 β 0.85 0.0505 0.85β 4000 0.85β 0.65 ∑ 0 0.85 F :
Whitney Stress Block in Uniform compression stress
•
c
a=
β
0.85
•
jd
•
When
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When
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•
d
•
over
When
or
Usually Set Resulting Nominal Moment Strength is either Tension Tension or Compression multiplied by moment arm between the force couple (usually the tension force). •
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•
•
See pg 129 Textbook Textbook for irregular shaped section jd.
a
N.A.
d
ε
•
•
c
ε 0.003 0.85 .
Common Common Terms a = equi equiva vale lent nt dept depth h of comp compre ress ssio ion n zone zone = stee steell area rea in tens tensio ion n = stee steell area area in comp compre ress ssio ion n width h of comp compre ress ssio ion n zone zone b = widt = effe effect ctiv ivee widt width h for for flan flange ge sect sectio ion n = width of beam c = dist distan ance ce from from comp compre ress ssio ion n edge edge to N.A N.A d = dist. from extreme comp fiber to centroid of longitudina longitudinall tension tension reinforceme reinforcement. nt. = dist. from extreme comp fiber to centroid of longitudina longitudinall compressio compression n reinforcemen reinforcement. t. = dist. from extreme comp fiber to centroid of fart farthe hest st laye layerr of tens tensio ion n stee steell = spec specif ifie ied d comp comp.. stre streng ngth th of conc concre rete te • • • •
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Constr Cons truc ucti tion on Co Cons nsid ider er Spacing •
Flexural Concrete Beam Design ∅ Ɛ Flexural Design of Doubly Reinforced Beams
h
c N.A.
• • •
•
•
Ɛ Ɛ 0.85 ββ0.0.8585 0.85 Ɛ 60 0.85 ββ 0.0.8585 ∅ Ɛ Ɛ ƐƐ 0.0.00050 ∅ ∅ 0.90.65 Ɛ 0.005 Ɛ 0.00 Ɛ 0.0.005005 ∅ 0.65 Ɛ 0.0.002002
Analy Analysi siss of Nomin Nominal al Momen Momentt Stre Streng ngth th •
• •
•
Stra Strain in in the the comp compre ress ssio ion n rein reinfo forc rcem emen entt = =
2 Unknowns (c & This This res results ults in an iter iterat ativ ivee solu soluti tion on for for neut neutra rall axis axis dept depth h “c”. “c”. Nominal Moment Strength follows per the flowchart on the right. Sele Selecti ction on of
)
• •
•
•
**If
,
will be also
207
207
•
Mini Minimu mum m Tensi ension on Rein Reinfo forc rcem emen entt and and Ties for for Comp Compre ress ssive ive Reinf Reinfor orcem cemen entt Mi T si Rein Reinfo fo Sa fo si ly info info ed be
+
a
d
Flex Flexur ural al Analy Analysi siss of Doub Doubly ly Reinf Reinfor orce ced d Recta Rectang ngul ular ar Beam Beam (pg (pg 142 142 Textb extboo ook) k)
General General Flexur Flexural al Consid Considerat eration ionss Reas Reason onss to Prov Provid idee Comp Compre ress ssion ion Rein Reinfo forc rceme ement nt (144 (144 Textbo extbook ok)) Reduced Reduced sustai sustained ned-lo -load ad deflect deflection ionss Creep Creep transf transfers ers to over over time time Increas Increased ed ductil ductility ity Redu Reduce cess “a” Similar Similar triangl triangles es increa increases ses tension tension steel. steel. Fail Failur uree mode mode from from Comp Comp.. to Tensi ension on brittle failure = bad When is incr increas eased ed,, comp compre ress ssio ion n str str. incr increa ease sess allo allows ws tens tensio ion n stee steell to yiel yield d Eases Eases Fabric Fabricatio ation n allow allow stirru stirrup p anchora anchorage ge
εε 0.003 0.85 .
ε
Flowchart for Flexural Analysis of Doubly‐Reinforced Concrete Sections
Ɛ Ɛ ⁄ ⁄ Ɛ Ɛ Ɛ 60 0.0.8585 0.85β o ≅ ? o Ɛ Ɛ Ɛ
Decrease c
1. Assume
2. Select Value for “c” Typ.
Increase c
start w/
3.
4.
5.
6.
7. T
8. Is
N
9.
N
Flexural Concrete Beam Design Flexural Analysis Analysis of Flanged Sections
h
Flange Flanged d Sectio Sections ns Effec Effecti tive ve Flan Flange ge Width idth (ACI (ACI 8.12 8.12)) •
Slab extending on both sides
•
Slab Slab exte extend ndin ing g on one one side ide
Nominal Moment Strength of Flanged Sections in Bending Case 1 ( ): Comp Compre ress ssiv ivee stre stress ss bloc block k with within in flan flange ge (wid (width th of comp compre ress ssio ion n zone zone = Anal Analyz yzed ed simi simila larr to a stan standa dard rd beam beam but but with with wide widerr comp compre ress ssio ion n zone zone.. •
)
•
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Case 2 ( ): Comp Compre ress ssiv ivee stre stress ss bloc block k exte extend ndss into into web web Sect Sectio ion n is divi divide ded d into into two two part partss (the (the core core blo block of width idth “b” “b” and and over overha hang ngiing port portio ions ns))
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Dete Determ rmin ined ed by doub doubly ly rein reinfo forc rced ed secti section on meth method od
“a” is unknown and can can be found here
when applicable include
c
ε 0.003 0.85 . a
N.A.
d
ε
⁄ 4 , 288 10.5 ⁄ 1 2 6 , . 0.80.585 .
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Flexural Concrete Beam Design Flexural Design of Beam Sections Flex Flexur ural al Desi Design gn of Beam Beam/S /Slab lab Secti Section onss Slab Slabss span spann ning ing beam beamss have have a long long dire direct ctio ion n and and a short hort dire direct ctio ion n If the the rati ratio o of the the lon long direc irecti tion on (les (lesss flex lexural ural stif stiffn fnes ess) s) and and the the shor shortt dire direct ctio ion n (more more flex flexur ural al stif tiffnes fness) s) is 2 or grea greate terr, it is comm common on prac practi tice ce to prov provid idee flex flexur ural al rein reinfforce orceme men nt to resi resisst the the enti entire re load load in the the short hort dire direct ctio ion n and and only only prov provid idee mini minimu mum m stee steell for for temp temper erat atur uree and and shri shrink nkag agee in the the long long dire direct ctio ion. n. The These slab labs are consider idereed One-W e-Way slabs becaus ause the majo ajority of the loads ads are transferred in a single direction. • •
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ACI ACI Mome Moment nt and and Shea Shearr Coef Coeffi fici cien ents ts (ACI (ACI 8.3. 8.3.3) 3) Give Given n at midmid-sp span an and and the the faces aces of cont contin inuo uous us beam beam suppo upport rtss Appl Applic icab able le if the the foll follow owin ing g are are sati satisf sfie ied: d: There are 2 or more spans Spans pans are are appr approx oxim imat atel ely y equa equall w/ lar larger ger note note grea greate terr than than shor shorte terr by 20% 20% Load Loadss are are unif unifor ormly mly dist distri ribu bute ted d Unfa Unfact ctor ored ed live live load loadss don’ don’tt exce exceed ed 3 time timess unfa unfact ctor ored ed dead dead load loadss Memb Member erss are are pris prisma matic tic Maxi Maximu mum m posi positi tive ve and and nega negati tive ve mome moment ntss and and shea shears rs are are comp comput uted ed from from • •
• • • • •
•
•
•
where
•
,
is the the clea clearr spaci pacing ng betw betwee een n colu column mn face facess and and
For For nega negati tive ve mome moment nt at inte interi rior or supp suppor orts ts,,
are coeff coefficie icients nts
can can be the the aver averag agee of adja adjace cent nt span spanss
Flexural Concrete Beam Design Flexural Design of Beam Sections ACII Fa AC Fact ctor ored ed De Desi sign gn Wor orkf kflo low w (p (pag agee 18 185 5 Tex extb tboo ook) k) Ma Make ke Co Comm mmen ents ts on Co Comp mpar arin ing g w/ St Stru ruct ctur ural al An Anal alys ysis is
Flexural Concrete Beam Design Flexural Design of Beam Sections Initial Consideratio Considerations ns Sugg Sugges ested ted mini minimum mum thick thickne ness ss of nonp nonpre rest stre ress ssed ed beams beams or oneone-wa way y slab slabss ACI ACI Table able 9.5( 9.5(a) a) Can Can be trum trumpe ped d by defl deflec ecti tion on anal analys ysis is Conc Concre rete te cove coverr and and bar bar spac spacin ing g (te text xtbo book ok pa page ge 19 199 9) Conc Concre rete te cove coverr (ACI (ACI 7.7) 7.7) Pres Prestr tres esse sed d and and prec precas astt are are dif differe ferent nt,, but but pres presen entt in the the chap chapte ter r Bar Bar spac spacin ing g based ased on: on: Maxim aximum um size size of coar coarse se aggr aggreg egat atee (ACI (ACI 3.3. 3.3.2) 2) which hich is smal smalle lest st of: 1/5 1/5 the the narr narrow owes estt dime dimens nsio ion n btw btw side sidess of forms orms 1/3 the depth of the slab ¾ the the mini minimum mum clear clear spac spacin ing g btw indi individ vidual ual rein reinfo forc rcin ing g bars bars/w /wire ires/ s/et etc. c... This This equa equate tess to a spac spacin ing g of 1.33 1.333 3 time timess aggr aggreg egat atee size. ize. Min. in. clea clearr spaci pacing ng btw btw para parall llel el bars bars is but not less than 1” (ACI 7.6.1) Multi ultipl plee laye layers rs of rein reinf. f. shal shalll be abo above each each othe otherr w/ spac spacin ing g (ACI (ACI 7.6. 7.6.2) 2) Maxi Maximu mum m spac spacin ing g of flex flexur ural al rein reinfo forc rcem emen entt in slab slabss is smal smalle lest st of: of: 3 time timess the the wall wall/s /sla lab b thic thickn knes esss ( ) 18” 18” (ACI (ACI 7.6. 7.6.5) 5) •
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For For tens tensio ion n face face:: ACI ACI 10.6 10.6.4 .4 •
•
1“ , 2.5 15 12 , 2“
= dist distan ance ce incl includ udes es stir stirru rup p widt width. h. Commo Commonl nly y
where:
for for beam beamss
= flex flexur ural al rein reinfo forc rcem emen entt stre stress ss Can Can be take taken n as 40,0 40,000 00
per ACI R10.6.4
. 10.5
Flexural Concrete Beam Design Flexural Design of Beam Sections Wor orkf kflo low: w: De Desi sign gn of Re Rein info forc rcem emen entt wh when en Se Sect ctio ion n Di Dime mens nsio ions ns ar aree Kn Know own n (p (pag agee 20 205 5 Tex extb tboo ook) k)
Flexural Concrete Beam Design Flexural Design of Beam Sections Wor orkf kflo low: w: Des esig ign n of Do Doub ubly ly Re Rein info forc rced ed Be Beam am Sec ecti tion onss (t (tex extb tboo ook k pg 22 220) 0)
Concrete Slab Design Design Design of Continuo Continuous us One-W One-Way Slabs/Syst Slabs/Systems ems (textboo (textbook k pg 229 also also little little ppiu book ch ch 7 or 8) General General Inform Informatio ation n on Contin Continuou uouss One-W One-Way ay Slabs/ Slabs/Sys System temss Assu Assume med d to act act as a seri series es of 1’ wide wide para parall llel el inde indepe pend nden entl tly y acti acting ng strip tripss of slab slab over over suppo upport rtin ing g beam beams. s. Desi Design gn Exam Exampl ples es:: CERM CERM 51-3 51-3,, MacG MacGre rego gorr (229 (229), ), & Conc Concre rete te PPI PPI (Ch (Ch • •
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ACI ACI Mome Moment nt and and Shea Shearr Coef Coeffi fici cien ents ts (ACI (ACI 8.3. 8.3.3) 3) Given iven at midmid-sp span an and and the the face facess of cont contin inuo uous us beam beam sup support portss Appl Applic icab able le if the the foll follow owin ing g are are sati satisf sfie ied: d: There are 2 or more spans Span Spanss are are appr appro oxima ximate tely ly equa equall w/ lar larger ger note note grea greate terr than than shor horter ter by 20% Load Loadss are are unif unifor orml mly y distr distrib ibute uted d Unfa Unfact ctor ored ed live live load loadss don’ don’tt exce exceed ed 3 time timess unfa unfact ctor ored ed dead dead load loadss Memb Member erss are are pris prismat matic ic Maximum positive and negative moments and shears are computed from • •
• •
• • •
•
•
•
where
fa
d
coeffic coefficien ien
is the the clea clearr spaci pacing ng betw betwee een n colu column mn
Concrete Slab Design Design of Continuous Two-Way Slabs/Systems (CERM 51-5 & MacGregor Ch 13 & Little PPI Ch 8)
2.2.
General eral Informatio tion on Continu inuous Two-Way Slabs/Systems ems per ACI 318: Section 13 (CERM 51-5) Slab Slabss are are clas classi sifi fied ed as “two “two-w -way ay”” when when the the rati ratio o of long long-t -too-sh shor ortt side sidess is When no beams are used, the the slab can be cla classified ied as a “plate ate” or “flat slab”. Design moments are obtai tained the same w/ & w/out beams per ACI 13.5 Two main main meth method odss of desi design gn Dire Direct ct Desi Design gn Meth Method od (DDM (DDM)) CERM 51-6 MacG acGregor (653) & ACI (247) More popular lar method to use by hand Limit Limitat ation ionss are are pres presen entt Equi Equiva vale lent nt Fram Framee Meth Method od (EFM (EFM): ): See See MacG MacGre rego gorr (670 (670)) for for exam exampl ple. e. • •
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Gene Genera rall Step Stepss in Slab Slab Desi Design gn 1. Choose layout & type of slab to be used 2. Choo Choosse slab lab thic thickn knes esss: for for serv servic icee defle eflect ctio ion, n, fire fire,, colu column mn shea shearr, etc etc.. 3. Choose method of computing design moments (DDM or EDM): Just use DDM 4. Calc Calcul ulat atee the the dist distri rib butio ution n of mome moment ntss acro across ss slab lab widt width. h. Late Latera rall dist distri ribu buti tion on dep depend ends on slab slab geom geomet etry ry & beam beam stif stiffn fnes esss (if (if any) any) 5. If there are beams, assign a portion of the column strip moment to them 6. Design reinforcement for the moments in steps 4 & 5 (Steps 3 to 6 need to be done for each principal direction) 7. Check shear strength at a critical section around columns Beam-to Beam-to-Sl -Slab ab Stiff Stiffnes nesss Ratio Ratio ACI ACI deno denote tess the the effe effect ct of beam beam stif stiffn fnes esss on defl deflec ecti tion on and and dist distri ribu buti tion on of slab slab mome moment ntss with with the the func functi tion on for for flex flexur ural al stif stiffn fnes esss •
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when there is no beam
See See Macg Macgre rego gorr 649 649 for for exam exampl plee calc calcss
0.0.
when slab is same concre crete as beam eam
Concrete Slab Design Design of Continuous Two-Way Slabs/Systems (CERM 51-5 & MacGregor Ch 13 & Little PPI Ch 8) General eral Informatio tion on Continu inuous Two-Way Slabs/Systems ems per ACI 318: Section 13 Mini Minimu mum m thick thicknes nesss of Two-W wo-Way ay Slab Slabss Beams Beams only only betwe between en exte exteri rior or colu column mnss Use CERM Table on page 51-8
(CERM 51-5)
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Depen epends ds on the the aver averag agee valu valuee of
•
But mus must be over 5 inc inches thi thick.
∑ 10.63
in each each slab slab dire direct ctio ion n
(see (see Litt Little le PPI PPI book book 59 for for samp sample le calc calc.) .)
Relativ Relativee Torsion orsional al Stiff Stiffnes nesss ACI 13.6 13.6.4 .4 ACI Dist Distri ribu buti tion on of nega negati tive ve mome moment nt acro across ss slab slab widt width h at exte exteri rior or edge edgess depe depend ndss on the the tors torsio iona nall stif stiffn fnes esss of beam beam edge edgess also also.. •
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Beams Beams betw between een inte interio riorr colu column mnss
where:
See See desi design gn exam exampl plee MacG MacGre rego gorr (663 (663 to 667) 667)..
Use Use desi design gn exam exampl plee from from MacG MacGre rego gorr (663 (663 to 667) 667) and and CERM CERM 51-7 51-7 to get get desi design gn mome moment nts. s. Then Then desig esign n slab slab simil imilar ar to a oneone-w way slab slab.. Check Check spec special ialize ized d shear shear stre streng ngth th also. also. • •
Concrete Slab Design Design of Continuous Two-Way Slabs/Systems (CERM 51-5 & MacGregor Ch 13 & Little PPI Ch 8) General eral Informatio tion on Continu inuous Two-Way Slabs/Systems ems per ACI 318: Section 13 (CERM 51-5) Dire Direct ct Desi Design gn Metho Method d Flow Flow Exam Exampl plee to Desi Design gn Flex Flexur ural al Rein Reinfo forc rcem emen entt & Shea Shear r •
DDM Given: 1. Loadin Loading g (DL & LL & Slab Slab Weig Weight) ht) 2. Colu Column mn dist distan ance cess 3. Mate Materi rial al prop proper ertie tiess
Further Distribute into Column Strips & Middle Strips CERM Table 51.4 Caveat of 85% beams if they’re in column strip. SEE MacGregor (662) for the process! •
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Select Reinforcing Steel for Moment
Identify the Section in Question The section span direction determines spanning length (center to center of supports) transverse width (center to center of supports) face to face clear distance along span length •
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∑ •
Isolate Column Strips and Middle Strips (CERM 51-6)
Calculate Calculate the total Statical Statical Moment
•
where:
Divide into Positive and Negative Portions Depends on conditions & relative section location USE 65/35 spread or CERM Table 51-3 Whichever is applicable for span location •
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0. 111 . ⁄ . . . 0.0.2255 .. ∅ ∅ ∅ , ∅
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Estimate
First Iteration for Assume Tension Controlled •
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Find Adjusted Steel Area
=0.9
B Center to Center supports in transverse direction
Punching Shear See little PPI book (63)
•
Isolate w/ the Area of concrete required ( ) to balance the area of steel
∅ 2∅λ •
•
∅
Check Shear Strength of Slab =0.75 Controlled by Either Wide Beam Shear Occurs in longer span at distance from supports
•
4∅λ ∅ 22 ∅λ∅λ •
•
40 for interior column, 30 exterior, 20 for corner.
Transfer of Moment to Columns PPI little book (65)
Shear in Concrete Beams Shear in concrete beams General General Information Information Gene Genera rall prov provis isio ion n in ACI 318 318 Ch. Ch. 11 Seis Seismi micc provi rovissions ions in ACI 318 318 Ch. Ch. 21 ACI 9.3. 9.3.2.3 2.3 • • •
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∅ . ∅ ∅ 2λ 1.9λ 2500 25 00 3. 5 λ Shea Shearr Stre Streng ngth th of Slen Slende derr RC Beam Beamss
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For For memb member erss subj subjec ectt to shear hear and and flex flexur uree only only: Typicall ypically y λ from ACI 8.6.1 1.0 1.0 for for norm normal al wt conc conc., ., 0.85 0.85 for for sand sandlg lght htwt wt,, & 0.7 0.75 for for ligh lightw twt. t. If more more capa capacit city y is need needed ed,, alter alterna nate te meth method od for for calcu calculat latin ing g in ACI ACI 11.2. 1.2.2. 2.1 1 •
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ACI ACI 11.1. 1.1.3 3 – crit critic ical al sect sectio ion n may may be take taken n “d” from from face face of supp suppo ort if the the foll follow owin ing g are are sat satisfi isfied ed: Supp Suppor ortt rxn, rxn, in dire direct ctio ion n of appl applie ied d V, impa impart rtss comp compre ress ssio ion n into into memb member er end end regi region ons. s. Loads are applied at or near ear top top of mem member No concentrated load occurs btw face of support and location of critical section. • • •
2 1 λ 2/ 1 λ
•
For For memb member erss subj subjec ectt to Axia Axiall Comp Compre ress ssio ion n:
•
For For memb member erss subj subjec ectt to Axia Axiall Tensi ension on:
•
is posi positi tive ve in comp compre ress ssio ion n and and , , 500, & 2000 are in psi. For For Cir Circula cularr Cros Crosss Sect Sectio ions ns: diameter of circle & 0.8h or 0.8(diameter) if it can’t be calc calcul ulat ated ed quic quickl kly y in the the norm normal al fash fashio ion. n. •
ACI 11.2.1. 1.2.1.2 2
Shear She ar Rein Reinfor forceme cement nt Limi Limits ts Spacin Spa cing: g: ACI 11.4 1.4.5 .5 Min. Mi n. Sh Shea earr Re Reinf infor orcem cemen ent: t: 11. 1.4. 4.6 6 Pref Pr efer erre red d Sp Spac acin ing? g??? (m (max ax,, min min,, ot othe herw rwis ise). e). • • •
Shear Reinforcement R einforcement Workflow Workflow
Shear in Concrete Beams Shear in concrete beams
•
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Spacing that prevents yield ACI 11.4.7 11.4.7 (vert. stirrups only). Fail Failur uree of Stir Stirru rup p Anch Anchor orag age: e: Stir Stirru rups ps must must deve develo lop p shea shearr stre streng ngth th ACI ACI 12.1 12.13. 3.3: 3: each each bend bend in U-sh U-shap aped ed stir stirru rups ps shal shalll encl enclos osee a long longit itud udin inal al bar bar ACI ACI 12.1 12.13 3.2. .2.1: #5 and and smal smalle lerr stir tirrups rups use use a stan standa dard rd hook hook aro around und long long.. rein reinf. f. w/ou w/outt spec specif ifie ied d embe embedm dmen entt leng length th (135 (135 & 90 degr degree ee pref prefer erre red) d) ACI 7.11: requires clos losed stir tirrups in beams w/ compr mpress ession reinforcement, stre stress ss reve revers rsals als,, or tors torsion ion ACI ACI 7.13 7.13.2 .2.3 .3:: requ requir ires es clos closed ed stir stirru rups ps arou around nd long long rein reinff in all all peri perime mete terr beam beams. s. Cap Cap tie tie good good if twotwo-pi piec ecee stir stirru rup p is need needed ed.. ACI 12.6: headed and mechanically anchored deformed bars. Reduce reinforcement reinforcement regions. regions. Serv Servic icea eabi bili lity ty fail failur uree due due to crac crack k widt width h at serv servic icee load load (pg (pg 275 275 text textbo book ok)) • •
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•
,, 8
ACI ACI 11.4. 1.4.7. 7.9: 9: limi limits ts max max shea shearr tran transm smit itte ted d by stir stirru rups ps to
⁄
Consider the Following: Place 1st stirrup at from face of support
•
•
• •
Stirrups must continue when
∅
Transition to smaller stirrups when is lower If a really small spacing governs, switch from a
using ACI 318 Section 11.2 (typically)
∅ ∅ with
1.al 9cλulat e2500 2500 3.3. 5λ 5 λ λλ λ 0.7505 ∅ ∅2 ∅ ? 24 ∅ 8 ? 4 ? 12 242 C
Shea Shearr Fail Failur uree Limi Limitt Stat States es:: Beam Beamss w/ Web Rein Reinfo forc rcem emen entt Fail Failur uree due due to stir stirru rup p yiel yieldi ding ng •
Compute design shear force at appropriate location (d or at support face)
OR
= 1.00 for normal weight concrete = 0.85 for sand-lightweight concrete = 0.75 for all lightweight concrete
?
Stirrups not required. (verify against seismic requirements)
Min. Stirrups Required.
Web Crushes. Redesign Beam
Per ACI 11.4.5.3
Shear in Concrete Beams, Brackets, & Corbels Shear Friction General General Information Information ACI ACI 11.6 1.6 prov provid ides es deta detail ilss for for Shea Shearr Fric Fricti tion on ACI ACI 11.6. 1.6.4 4 Shea Shearr Fric Fricti tion on desi design gn meth method od when when stir stirru rups ps are are perp perpen endi dicu cula larr to beam beam axis axis,, wher where: e: 1.4λ 1.4λ for for conc concre rete te plac placed ed mono monoli lithi thica cally lly 1.0λ 1.0λ for for conc concre rete te plac placed ed agai agains nstt hard harden ened ed conc concre rete te w/ surf surfac acee roug roughe hene ned d per per ACI ACI 11.6. 1.6.9 9 0.6λ 0.6λ for for conc concre rete te plac placed ed agai agains nstt hard harden ened ed conc concre rete te w/ou w/outt surf surfac acee roug roughe hene ned d 0.7λ 0.7λ for for conc concre rete te anch anchor ored ed to as-r as-rol olle led d stru struct ctur ural al stee steell by head headed ed stud studss (ACI (ACI 11.6. 1.6.10 10)) ACI 11.6. .6.5 Sets Sets max maximum imum valu valuee of normal-weightt concrete concrete placed monolithically or against concrete w/ surface roughened For normal-weigh •
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0. 2 4800.160008 2 0.800 • • • •
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all othe otherr case casess: For all
•
When When conc concre retes tes with with diff differ eren entt
where
is area area of conc concre rete te resi resist stin ing g shea shearr (
valu values es are are used used,, use use the the low lower valu valuee ACI 11.6. 1.6.5 5
)(d).
Shear in Brackets, & Corbels Capacity Check of Brackets and Corbels (small book general Structures) Show all all Steel An Asc etc…
Torsion
0.85 Øλ Ø
45
General Information Ø=0.75 per AC A CI 318 Section 9.3.2.3 pure tors torsio ion, n, crac cracks ks w/ angl anglee off off hor hor. ACI ACI 11.5. 1.5.3. 3.6 6 allo allows ws ACI ACI 318: 318: Sect Sectio ion n 11.5 1.5 Gove Govern rnss Torsi orsion on In pure After torsi rsional cracking: Closed stirrup rups resist vert component. Long reinf inf to res resist ist horiz. Components of torsional torsional stresses stresses Gross area enclosed by shear flow where = area inside centerline of outermost outermost torsional torsional reinforc reinforcement ement/stirr /stirrups ups . It incl includ udes es open open spac spaces es and and are are insi inside de flan flange gess w/ stir stirru rups ps.. •
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Thre Thresh shol old d Torsi orsion on:: Torsi orsion on may may be negl neglec ecte ted d if
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Shea Shearr Stre Stress ss in the the wall walls: s:
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Crac Cracki king ng is assu assume med d to occu occurr when when prin princi cipl plee tens tensile ile stre stress ss
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Cracking Cracking Torsion/T orsion/Torque orque =
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2
4λ τ
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acco accoun unts ts for for two two stir stirru rup p legs legs,, whil whilee •
∑ 2 4 4 Ø Ø .Ø
only only acco accoun unts ts for for one, one, resu result ltin ing g in: in:
The The spac spacin ing g of the the rein reinfo forc rcem emen entt is limi limite ted d by the the mini minimu mum m requ requir ired ed by shea shearr or tors torsio ion. n.
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ACI ACI 11.4. 1.4.5 5 Shea Shearr spac spacin ing g max max
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ACI ACI 11.5. 1.5.6 6 Torsi orsion on spac spacin ing g max max
for
for
but less than 12”. 12”max spacing default
When When thre thresh shol old d tors torsio ion n is exce exceed eded ed:: clos closed ed stir stirru rups ps and and long long.. rein reinf. f. Must Must be prov provid ided ed.. •
ACI ACI 11.5. 1.5.3. 3.6 6 Requ Requir ired ed are are of 1 leg leg of clos closed ed stir stirru rup: p:
0.042 ⁄
ACI ACI 11.5.3 .5.3.7 .7 & R11.5 1.5.3. .3.10 •
When When thre thresh shol old d is exce exceed eded ed,, rein reinfo forc rcem emen entt must must resi resist st full full tors torsio ion, n, conc concre rete te is negl neglec ecte ted. d. ACI ACI 11.5. 1.5.2. 2.4: 4: crit critic ical al sect sectio ion n is loca locate ted d “d” “d” from from the the end end of the the sect sectio ion n at a supp suppor ortt . Exce Except pt when when a conc concen entr trat ated ed tors torsio ion n is appl applie ied d with within in “d”, “d”, then then the the crit critic ical al sect sectio ion n is at the the join jointt face face.. Stir Stirru rup p Area Area:: Stee Steell area area to acco accoun untt for for Shea Shear r and Torsion ACI 11.5. 11.5.3.8 3.8 •
•
4λ
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= Area Area encl enclos osed ed by peri perime mete terr of the the sect sectio ion. n. = peri perime mete terr of the the sect sectio ion n Unif Unifor orm m Shea Shearr Flow Flow:: Appl Applie ied d Torsi orsion on is resi resist sted ed by mome moment nt of shea shearr flow flow in wall wallss abou aboutt sect sectio ion n cent centro roid id::
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ACI 11.5.1 1.5.1
ACI 11.5. 11.5.5.3 5.3 •
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Requi equire red d are area of Long. ong. Reinf einf..
Where:
ACI ACI 11.5. 1.5.6. 6.2 2 Mini Minimu mum m diam diamet eter er long long rein reinff bar bar •
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To prev preven entt conc concre rete te crus crushi hing ng comb combin ined ed torsi torsion on and and shea shearr forc forces es limit limited ed by ACI ACI 11.5. 1.5.3. 3.1. 1. Dime Dimens nsio ions ns of sect sectio ion n must must be: be: •
. ∅ 8
For hollow hollow section sections: s:
ACI 11.5.3 1.5.3
Torsion Flowchart Different for HOLLOW SECTIONS!
Factored torsional moment exceeds threshold of Section 11.5.1. Provide transverse and longitudinal reinforcement to resist
Assume
45 &
&
w/ #4 stirrups and 1.5” cc.
1.7 ∅ 8 ∅ ∅ .∅
?
NO
Compression struts control: REDESIGN SECTION
128 min"" @ ACI 11.5.6.1 ?
Design Variables ariables
∅ 0.75
outsid outsidee perime perimeter ter of cross cross sectio section n area area of the the cros crosss sect sectio ion n = perimeter along centerline of outermost closed closed transv transvers ersee torsio torsional nal reinfo reinforce rcemen mentt bar. bar.
Or a known stirrup size
5 Where
at spacing “s”
Check min Long Reinf. For Torsion
Compute ratio of stirrup area required for Torsion
=
Min. Governs: Use larger value of
Min
. 11.5.5.2 0.22
Select Stirrups:
Use value of
Considering #3
NO
.
# 0.40
& #4 bars
from support
45
Add stirrup areas and verify min. rqd:
Design Long. Reinf. For Torsion
Compute ratio of stirrup area required for Shear
See Previous Slides Last step for
NO
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ACI 11.5.6.2 Longitudinal bars have to be spaced less than 12 inches around perimeter. ENTIRE PERIMETER. Even mid height. Must be within stirrups •
Column Design General Interaction Diagrams indicate failure envelopes that columns should stay within. (CERM Appendix 52.N) General breakdown of strain corresponding to points on interaction diagram PPI little book (39 to 41) & MacGregor (510 & 516) •
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ACI 10.9.1 Longitudinal reinforcement ratio
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Typically is between 1 to 3 percent for tied columns and 2.5 to 5 for spirals. ACI 7.6.6 & 12.14.2.2 Bundled bards to resist high axial loads ACI 10.9.2 Min. bars in a rectangle column is 4. Spiral columns need 6. •
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0.01 0.08 0.06 for special moment frames 1. 5 1. 5 1 ⁄ , 0.60.03
Pertinent ACI Codes (See CERM 52-2 & section 6 small PPI book)
must be:
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ACI 7.7.1 Min. clear distance btw longitudinal bars
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ACI 10.10.6.5 MINIMUM END MOMENT =
(
Typ. governs at splice locations
Ties layouts: CERM 52-2 MacGregor (537) Categorized into SHORT SHORT (no sway) and long (sway-affected) columns •
34 12 40
22
ACI 10.10.1 permissible to neglect slenderness affect for columns braced against sidesway if “Slednerness “Slednerness ratio •
• • •
or
in unbraced structures
K can be conservatively taken as 1.0. = unsupported height of column from top of floor to bottom of beam/slab r = radius of gyration. can be taken as per ACI 10.10.1.2 is the larger moment. Values u ratio of moments at the two ends.
0.3
is
alally 0.0.5 0.5
Short Column Design General Reinforcement Splices MacGregor (531 to 535) DERP Design for Small Eccentricity when flexural effects can be neglected (CERM 52-3) •
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Concentrically Loaded Tied Column Axial Strength given by: ACI 10.3.6.1 & 10.3.6.2 For tied columns •
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∅,, 0.8∅ 0.85
Design using Interaction Diagrams (CERM A-135 & MacGregor (1106) Example PPI small book (43) & MacGregor (539 is better) •
Slender Column Design General ACI 318 requires a second-order analysis to account for P-delta affect with 1 of 3 approaches: 1. Nonline Nonlinear ar seco secondnd-ord order er analy analysis sis (too (too compl complex ex for for routi routine ne calcs calcs)) 2. Elastic Elastic second second-or -order der analysi analysiss (too (too complex complex for routin routinee calcs calcs)) 3. MOME MOMEN NT MAG MAGNIF NIFICA ICATION TION •
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Moment Magnification: doesn’t need to be over 1.4 *(first order moment)
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Moment Magnification for BRACED/NON-SWAY frames (CERM 53-5 53-5 & PPI book (44) & MacGregor (581))
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Moment Magnification for UNBRACED/SWAY frames (see comprehensive design example MacGregor (610) Also see CERM 53-6 example & little PPI book (47) •
Column Design Beam Beam Colu Column mn Join Joints ts (pg (pg 953 953 Textb extboo ook) k)
Development, Hooks, & Bar Cut-off Bar Development ent and Lon Longitu itudinal Continuous Bars in Tension (Ch 9 ppi book & Ch 8 Text extbook ACI 318 permits 3 ways for bars to develop in tension 1. Straig Straight ht embe embedmen dmentt of the bar beyond beyond the point point of of maxim maximum um stress stress TWO WAYS TO T O CALCUL CA LCULA ATE ACI 318 Table Table 12.2.2 Gives development length for different clear cover and spacing scenarios. •
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Ψ 1.1.30 12 1. 0 1. 2 Ψ 1.5 / 3 .. ... 6 ΨΨ Ψ0.8 #6 1. 0 #6 λ 1.0.075 1212 maxmax 100
In the equations:
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EXPLAIN & Ktf Ktf TE TERM RMS S Values given in the Table Table 12.2.2 can vary drastically from the results of Eqn ACI 318: 12-1. If you can’t get enough straight tension use Eqn. 12-1 to get a smaller •
•
need not be > 1.7
Bundled Bars
1. 2.
3.
Development, Hooks, & Bar Cut-off Bar Bar Deve Develo lopm pmen entt and and Long Longit itud udin inal al Cont Contin inuo uous us Bars Bars in Tensi ension on (Ch (Ch 9 ppi ppi book book & pg 381T 381Tex extb tboo ook k ACI 318 permits 3 ways for bars to develop in tension 2. Hook Hooked ed Anch Anchor orag agee ACI ACI 318: 318: 12.5 12.5 Must meet minimum ACI 318: R12.5 dimensions to qualify a 90 or 180 degree hook. •
1. 2.
•
3.
Serviceability, Cracking, Structural Integrity, & Deflections Gener eneral al Infor nforma mati tion on (cha (chapt pter er 9 Textb extbo ook & Ch 4 Ppi Ppi book book& & some some Ch1& Ch1& ACI 318 318 Ch7. Ch7.12 12&o &on) n).. G •
Bar Development ent and Lon Longitu itudinal Continuous Bars (Ch 9 ppi book & Ch 8 Textbook ACI 7.13.2.2: perimeter beams shall have continuous reinforcement at columns At leas east 1/6th tens tensio ion n steel teel for for neg negativ ativee mome moment nt.. Not Not less less than than 2 bars bars At leas east 1/4 of ten tension ion stee teel for positiv tive mome momen nt at mid-span. an. At lea least 2 bars Fir Fir disc discon onti tinu nuou ouss supp suppor orts ts:: Use Use hook hookss to deve develo lop p at face face.. •
• • •
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Failu Failure re due due d •
Walls, Foundations, & Footings Walls alls and and Reta Retain inin ing g Walls alls (CER (CERM M 54, 54, ACI ACI 14.3 14.3 Minimum Minimum Reinforcemen Reinforcementt Reta Retain inin ing g Wall all desi design gn exam exampl plee on CERM CERM 54-5 54-5.. • •
Walls alls and and Reta Retain inin ing g Walls alls (CER (CERM M 54, 54, Reta Retain inin ing g Wall all desi design gn exam exampl plee on CERM CERM 54-5 54-5.. •
Walls, Foundations, & Footings Rein Reinfo forc rced ed Conc Concre rete te Foot Footin ings gs (CER (CERM M 55, 55, MacG MacGre rego gorr (812 (812)) Genera Generall Footin Footing g Inform Informatio ation n Desig esigne ned d in 2 steps teps 1) sele select ctin ing g the the foot footin ing g area area based on service soil pressure Bear Bearin ing g stre stress ss and and Kern Kern eccen eccentr tric icity ity thre thresh shol old d (Mac (MacGr Greg egor or 819) 819) 2) sele select ctin ing g ftg ftg thic thickn knes esss & rein reinfo forc rcem emen entt for for shea shearr & bend bendin ing g stre stress sses es •
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Sele Selecti cting ng the the Foot Footing ing Area Area USE USE SER SERVICE VICE LOAD LOADS S Rectangular Rectangular Footings Footings •
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Bewa eware: The There may be biaxial ial moments on columns. This adds an add additi itional load on
the the soil soil.. If this this happ happen ens, s, add add ano another ther •
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Wall all Foot Footin ings gs – MacG MacGre rego gorr (827 (827))
term erm with B & L switched.
Combi Combine ned d Foot Footin ings gs (mul (multi tipl plee colu column mnss on a rect rectan angu gula larr foot footin ing) g) MacG MacGre rego gorr (845 (845)) Do CE CERM RM Ex Exam ampl plee Pr Prob oble lem m 55 55-7 -7.. •
