ENCE 4610 Founation Analysis an Design Sprea Footings: Strutural Design, Flexural Design
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
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
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
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
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
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 ' 1.176 y.353 φ' M u M n a A s ρ y ρ 0.85 ' A s y a
Equation or Steel Area (Step 7) A s ' 1.176 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
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 10.5.4 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 > 0.0018 I ρ < ρ min, use ρ min. ρ is rarely larger than 0.004 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
Fin Require Steel Area (Step 7) Determine atore ening moment at ritial setion Pu l M ul M u + B B 991,000 5.5 M u + 0 16 M 9,197,000 in - ls u A s A Determine steel area ase on atore ening moment at ritial setion s ' 1.176 4000 16 1.176 60,000 y A 4 s 4 7.5 in.353 φ' M u.353 9,197,000 0.9 4000 16
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) 0.004 For Grae 60 (Metri Grae 40) Steel: ρ > 0.0018 Sine 0.004 > 0.0018, OK Determine Size an Numer o Rears Use #8 (1") ars: Area o eah ar 0.79 sq. in. Numer o ars 8.94/0.79 9.17 so use 10 ars Spae etween ars 16/10 1.6" Minimum spaing 18" or 3T (3)(7) 81" so OK either way
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
Development Length (Step 7) αβγλ ' I sn A K + K αβγλ ' I y yt tr tr tr y 40 3 ootings) sprea (or 0 1500 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
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)
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
Development Length (Step 7) Chek evelopment length I I 3 40 3 40 ' + K tr 60000 1 1 1 1 4000.5 I 8 For 1" ars, I 8" Sine (I ) applie 49.5, evelopment length is OK y αβγλ Chek evelopment length (I ) supplie l 3 5.5 3 49.5" Chek require inequalities The term ( + K tr )/ <.5: (3.5 + 0)/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
Example o Flexure Design Final Design
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
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.
Design o Continuous Footings With ontinuous ootings, we only have one-way shear Solving or, B B P V u u ( ) Units) (SI 3 500 1500 (US Units) 48 + + P B B P P B B P u u u u φ φ
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 1.176 y l M.353 φ' u
Strutural Design o Footings (pp. 144 145)
Strutural Design o Footings (p. 146)
Questions?