Example of Flexure Design (Step 7)

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1 ENCE 4610 Founation Analysis an Design Sprea Footings: Strutural Design, Flexural Design

2 Example o Flexure Design (Step 7) Design or Flexure o o o o Given Use only the reinoring steel or lexure onsierations Determine the total steel area Chek reinorement evelopment length Determine the numer an size o reinoring ars neessary Founation esign etermine y two-way shear esign example, T 30" Fin Require steel area or lexure Numer an size o rears use One vs. Two Way Bening Footings in reality en in two perpeniular iretions Footings are esigne as i they en in only one iretion

Founation esign etermine y two-way shear esign example, T 30" Fin Require steel area or lexure Numer an size o rears use

3 Justiiation o One Way Sla Assumption, Steel Area (Step 7) Steel Area Usual proeure is to prepare a moment iagram an selet an appropriate amount o steel or eah portion o the memer For sprea ootings, we an simpliy this y ientiying a ritial setion or ening an use the moment etermine there to esign the steel or the entire ooting Loation o ritial setion or ening epens upon the type o olumn eing use Justiiation o One-Way Sla Assumption The ull-sale loa tests on whih this analysis metho is ase were interprete this way Founations shoul e esigne more onservatively than the superstruture Flexural stresses are low, so amount o steel require is nominal an oten governe y ρ min Aitional onstrution ost ue to this simpliie approah is minimal One ooting is analyse one way, we plae the same steel area in the perpeniular iretion

Justiiation o One-Way Sla Assumption The ull-sale loa tests on whih this analysis metho is ase were interprete this way Founations shoul e esigne more onservatively than the superstruture Flexural

4 Basi Consierations or Flexural Loas (Step 7) Fatore moment on the ritial surae M u etermines the neessary imensions o the memer an the neessary size an loation o the reinoring ars This an e a omplex proess; however, geotehnial onsierations ten to simpliy the esign proess, as it itates some o the options Amount o the steel require lexure epens upon the eetive epth Reinoring Steel Conrete's weakness in tension; thus, reinoring steel must e ae when tension is antiipate, whih is virtually guarantee with lexural loaing Reinoring steel in ounation almost inevitaly involves use o reinoring ars (rear); wele wire ari, neeles, et., are not generally use Sine lexural stresses are usually small, Grae 40 (Metri Grae 300, y 40 ksi or 300 MPa) steel is usually aequate, although unavailale or ars larger than #6, in whih ase Grae 60 (Metri Grae 40, y 60 ksi or 40 MPa) steel may have to e use Compression etive epth Tension

weakness in tension; thus, reinoring steel must e ae when tension is antiipate, whih is virtually guarantee with lexural loaing Reinoring steel in ounation almost inevitaly involves use o reinoring

5 Moment at Critial Bening Setion (Step 7) Fatore ening moment ssumes P u ats P l hrough entroi M u ooting + u M u atore moment at ritial setion or ening P u atore ompressive loa rom olumn M u atore moment loa rom olumn l antilever istane B ooting with B M B u l Base on soil earing pressure with assume eentriity o B/3

atore ompressive loa rom olumn M u atore moment loa rom olumn l antilever

6 Design Cantilever Distanes (Step 7) Notes Treat timer olumns in same way as onrete olumns I olumn has irular, otagonal or other similar shape, use a square with equivalent ross-setional area I olumn has a irular or regular polygon ross-setional area, ase the analysis on an equivalent square Loation o Critial Setion or Bening Conrete Columns l (B-)/ Masonry Columns l (B /)/ Steel Columns l (B ( + p ))/4 Variales B ooting with olumn with p ase plate with B 16 1 l 5.5 inhes

ross-setional area, ase the analysis on an equivalent square Loation o Critial Setion or Bening Conrete Columns l

7 This image annot urrently e isplaye. Determine the Total Steel Area (Step 7) Setting M u φ M n (where M u atore moment at the setion eing analyse), A s an e solve to Nominal moment apaity o a lexural memer mae o reinore onrete with ' < 30 MPa (4 ksi) A s ' y.353 φ' M u M n a A s ρ y ρ 0.85 ' A s y a

moment at the setion eing analyse), A s an e solve to Nominal moment apaity

8 Equation or Steel Area (Step 7) A s ' Variales or equation: A s ross-setional area o reinoring steel (sq. in., m ) ' 8-ay ompressive strength o onrete (psi, MPa) y yiel strength o reinoring steel (psi, MPa) ρ steel ratio with o lexural memer (in, m) eetive epth (in., m) y φ 0.9 or lexure in reinore onrete.353 φ' M u atore moment at the setion eing analyse (in-ls, MJ) M u

, m ) ' 8-ay ompressive strength o onrete (psi, MPa) y yiel strength o reinoring steel (psi,

9 Steel Cross Setional Area, Spaing an Development Length (Step 7) Spaing o Rear Seletion o reinoring ar size an spaing must satisy the ollowing minimum an maximum spaing requirements Clear spae etween ars must e at least equal to, 5 mm (1"), or 4/3 times the nominal aggregate size Centre-to-entre spaing o the reinorement must not exee 3T or 500 mm (18"), whihever is less Development Length Development length I is the length rears must exten through the onrete in orer to evelop proper anhorage Assumptions or alulations o minimum evelopment length Clear spaing etween the ars is at least Conrete over is at least Minimum Steel Requirements (ACI an 7.1.) ρ A s /A g A s Cross-setional area o the steel A g B Gross Cross-setional area For Grae 40 (Metri Grae 300) Steel: ρ >0.00 For Grae 60 (Metri Grae 40) Steel: ρ > I ρ < ρ min, use ρ min. ρ is rarely larger than Carry the lexural steel to a point 70 mm (3") rom the ege o the ooting Maximum Steel Requirements (ACI 10.3) never govern the esign o sprea ootings, ut may e o onern in omine ootings an mats

Development length I is the length rears must exten through the onrete in orer to evelop proper anhorage Assumptions or alulations o minimum evelopment length Clear spaing etween the ars is at least

10 Fin Require Steel Area (Step 7) Determine atore ening moment at ritial setion Pu l M ul M u + B B 991, M u M 9,197,000 in - ls u A s A Determine steel area ase on atore ening moment at ritial setion s ' ,000 y A 4 s in.353 φ' M u.353 9,197,

5 M u + 0 16 M 9,197,000 in - ls u A s A Determine steel area ase on atore

11 Chek or Minimum Steel Area an Determine Numer an Size o Bars (Step 7) Chek ompute steel area against minimum steel requirements ρ A s /A g 7.5/(4 16) For Grae 60 (Metri Grae 40) Steel: ρ > Sine > , OK Determine Size an Numer o Rears Use #8 (1") ars: Area o eah ar 0.79 sq. in. Numer o ars 8.94/ so use 10 ars Spae etween ars 16/10 1.6" Minimum spaing 18" or 3T (3)(7) 81" so OK either way

0018 Sine 0.004 > 0.0018, OK Determine Size an Numer o Rears Use #8 (1") ars: Area o eah ar 0.79 sq. in.

12 Computation o Development Length (Step 7) The evelopment length is measure rom the ritial setion or ening to the en o the ars (usually 70 mm (3") rom the en o the ooting, even i loas on't require it) Supplie evelopment length ( I ) l 70 mm ( 3in ) supplie (I ) supplie supplie evelopment length l antilever istane This length must e greater than the require evelopment length. I not, est solution is to use smaller rears with shorter evelopment lengths

( I ) l 70 mm ( 3in ) supplie (I ) supplie supplie evelopment length l antilever istane This length must e

13 Development Length (Step 7) αβγλ ' I sn A K + K αβγλ ' I y yt tr tr tr y 40 3 ootings) sprea (or Units) (US 40 3 αβγλ ' I sn A K + K αβγλ ' I y yt tr tr tr y 10 9 ootings) sprea (or 0 10 Units) (SI 10 9

14 Development Length (Step 7) Variales or evelopment length variales α reinorement loation ator α 1.3 or horizontal reinorement with more than 300 mm (1") o resh onrete elow the ar α 1.0 or all other ases β oating ator β 1.5 or epoxy oate ars or wires with over less than 3 or lear spaing less than 6 β 1. or other epoxy oate ars or wires β 1.0 or unoate ars or wires Variales or evelopment length variales I minimum require evelopment length (in., mm) nominal rear iameter (in, mm) y yiel strength o reinoring steel (psi, MPa) yt yiel strength o transverse reinoring steel (psi, MPa) ' 8-ay ompressive strenght o onrete (psi, MPa)

5 or epoxy oate ars or wires with over less than 3 or lear spaing less than 6 β 1. or other epoxy oate ars or wires β 1.

15 Development Length (Step 7) Variales or evelopment length variales A tr total ross-setional area o all transverse reinorement that is within the spaing s an whih rosses the potential plae o splitting through the reinorement eing evelopment (in, mm ) may onservatively e taken to e zero s maximum entre-to-entre spaing o transverse reinorement within l (in, mm) The term ( + K tr )/ <.5 Prout α β< 1.7 Development length I > 300 mm (1") Variales or evelopment length variales γ reinorement ator γ 0.8 or #6 (metri #19) an smaller ars γ 1.0 or #7 (metri #) an larger ars λ lightweight onrete ator 1.0 or normal onrete (lightweight onrete is not use in ounations) spaing or over imension (in, mm) the smaller o the istane rom the entre o the ar to the nearest onrete surae or onehal the entre-to-entre spaing o the ars

7 Development length I > 300 mm (1") Variales or evelopment length variales γ reinorement ator γ 0.8 or #6 (metri #19) an smaller ars γ 1.0 or #7 (metri #) an larger ars λ lightweight onrete ator 1.

16 Development Length (Step 7) Chek evelopment length I I ' + K tr I 8 For 1" ars, I 8" Sine (I ) applie 49.5, evelopment length is OK y αβγλ Chek evelopment length (I ) supplie l " Chek require inequalities The term ( + K tr )/ <.5: ( )/1 3.5 >.5 Prout αβ < 1.7: (1)(1) 1 < 1.7 (using 3" over an unoate ars) Development length I > 300 mm (1"): 49.5 > 1, so evelopment length meets this riterion

5, evelopment length is OK y αβγλ Chek evelopment length (I ) supplie l 3 5.5 3 49.

17 Example o Flexure Design Final Design

18 Design o Retangular Footings Chek or one an two way shear using the ritial shear suraes shown at right top Design the long steel using the ollowing values or l: Conrete Columns l (L - )/ Masonry Columns l (L /)/ Steel Columns l (L ( + p ))/4 Also use the ollowing equation or M u : Pu l M ul M u + L L

values or l: Conrete Columns l (L - )/ Masonry Columns l (L /)/ Steel

19 Design o Retangular Footings Design the short steel using the same equations or square ounations, an the ollowing equation or steel area: o A s ρ L Sine the lexural stresses ten to e onentrate in the enter o the ounation, plae more o the short steel in the inner zone. The portion o the total short steel area to e plae in the inner zone is given as /(L/B+1) Distriute the rest o the steel evenly etween the two outer zones.

the ounation, plae more o the short steel in the inner zone.

20 Design o Continuous Footings With ontinuous ootings, we only have one-way shear Solving or, B B P V u u ( ) Units) (SI (US Units) P B B P P B B P u u u u φ φ

or, B B P V u u ( ) Units) (SI 3 500 1500

21 Design o Continuous Footings Design or Flexure o o o Longituinal steel an e onigure y a rosssetional area o.0018a g < As <.000A g with at least two () #4 ars (#13 metri ars) Lateral steel is unneessary or narrow ontinuous ootings ut an e important or wier ounations Lateral steel esign or ontinuous ootings is asially the same as or inite ootings exept that the ore/moment per unit length is sustitute or the ore/moment Pu M u M l u + B B ' A s y l M.353 φ' u

22 Strutural Design o Footings (pp )

23 Strutural Design o Footings (p. 146)

24 Questions?

Fig. 1.1 Rectangular foundation plan.

Fig. 1.1 Rectangular foundation plan. Footings Example 1 Design of a square spread footing of a seven-story uilding Design and detail a typial square spread footing of a six ay y five ay seven-story uilding, founded on stiff soil, supporting