Dr. Hazim Dwairi 10/16/2008

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1 10/16/2008 Department o Civil Engineering Flexural Design o R.C. Beams Tpes (Modes) o Failure Tension Failure (Dutile Failure): Reinorement ields eore onrete ruses. Su a eam is alled under- reinored eam. ACI ode ( ): reinorement in te extreme laer o tensile steel as ε su wen onrete ruses, tis provides ample warning o ailure wit exessive deletion and raking. 1

2 10/16/2008 ε u = ε u = N.A. d A s ε su > ε Traditional Deinition ε su ACI 2002 Deinition Compression Failure (Brittle Failure): onrete ruses eore steel ields, su a eam is alled over-reinored reinored eam. Su eam provides little warning o impending ailure. ε u = N.A. d A s ε su < ε Balaned Failure (Brittle Failure): Reinorement ields wen onrete ruses. A s s = alaned area o steel ρ = Balaned steel ratio = A s /d 2

3 10/16/2008 N.A. A s d ε u = ε su = ε = d = (0.003) = 0.59d a = β = 0.59β d T s = C ρ = 0.5β1 A ' s 1 1 a 0.85 ' 0.85 (0.59 β1 d ) = = 0.5β1 ' T s d I =28MPa and =414MPa, ten ρ = = 2.87% C Loation o Flexural Reinorement Consider a simpl P supported eam Moment Diagram M u Compression Deleted Sape φm n Tension Reinorement Loation 3

4 10/16/2008 Consider a Cantilever eam M u Moment Diagram Tension Deleted Sape Compression φm n Reinorement Loation Design Aids Eonomial Retangular Setion / 2 Plae reinorement in a single laer, i possile. Make sure ars it, use Tale 2 in te andout Estimate eetive dept d auratel. Provides minimum onrete over to Bond reinorement to onrete Corrosion protetion Fire protetion 4

10/16/2008 Conrete Minimum Cover Minimum Conrete Cover

7) Exposure to Cover (mm) weater ground 75 Exposed 50

stirrups and φ25 ars Not exposed: d = 40-10 -25/2 65

-25/2 90 mm Not exposed eams wit two laers o steel

5 10/16/2008 Conrete Minimum Cover Minimum Conrete Cover (ACI 7.7) Exposure to Cover (mm) weater ground 75 Exposed 50 Not exposed 40 Not exposed (slas) 20 Assume φ10 stirrups and φ25 ars Not exposed: d = /2 65 mm Exposed: d = /2 75 mm Ground: d = /2 90 mm Not exposed eams wit two laers o steel assume d 90 mm One-wa slas wit spans up to 3.5 m assume d 25 mm One-wa slas wit spans more tan 3.5 m assume d 30 mm 5

10/16/2008 Deletion Control (ACI 9.5): Use tale 9.

is eing alulated, it sould e limited to te values in ACI Tale 9.

6 10/16/2008 Deletion Control (ACI 9.5): Use tale 9.5(a) in te ACI ode to ek minimum tikness required. For simpl supported eams: min = L/16 min = 1000mm/16 = 62.6 mm/m o span Rule o Tump: use 70 mm tikness or ea meter o span In ase deletion is eing alulated, it sould e limited to te values in ACI Tale 9.5(): Make sure: φm n M u ; provided strengt required strengt A s A s,min ε su 0.005, so tat φ = 0.9 or lexure For eonom, selet eam size so tat: A s = 0.01 d ; i.e. ρ = 1% 6

10/16/2008 Minimum Beam Widt ( min ) A = over to stirrups B = stirrups

larger o (25mm or d ) Example: not exposed (2φ25 & 3φ20) min =

2(40+10+20-25/2) + 2(25) + 3(20) + 4(25) = 325 mm Minimum Area o Steel

7 10/16/2008 Minimum Beam Widt ( min ) A = over to stirrups B = stirrups diameter (d s ) C = 2d s or φ32 or less D = lear distane etween ar larger o (25mm or d ) Example: not exposed (2φ25 & 3φ20) min = 2(A+B+C-d /2) + nd + (n-1)d Were n is numer o ars min = 2( /2) + 2(25) + 3(20) + 4(25) = 325 mm Minimum Area o Steel (A s,min ) Wat appens i te strengt o a eam is less tan its raking moment (M r )? Answer: a sudden ailure ould our wit little or no warning Moment Reall tat at te verge o raking: M u M M r N.A. /2 M r φm n urvature M = r r 2 '

8 10/16/2008 Te tension ore sed raking o te onrete needs to e arried te steel. N.A. A s,min a 0.85 ' T s C M n M r = M A, min = n 2 ' a = As,min ( d ) 2 a ut, is too small so ignore 2 and usuall d = 0.91 s ' d Teoretial ACI speiies: A s,min ' 1 wd 4 = larger o 1.4 wd Design o Reinorement wen and are known Example 1 Compute and selet reinorement required at mid span. Use =28MPa and = 414 MPa. For aritetural reasons = 400mm and = 600 mm. 400mm LL L.L. =30kN/m D.L. = 12 kn/m 600 mm 7000 mm 8

9 10/16/2008 Design o nonretangular eams Example 2 Compute and selet reinorement or te eam sown i: M u = 400 m.kn, = 28 MPa and = 414 MPa 3@100mm 50 mm 600 mm Design o Beams wen and are unknown Example 3 9

10 10/16/2008 Load Cases (Patterns) Load Cases (Patterns) Consider a two span eam wit servie dead d load w D and servie live load w L 1.6w L 1.2w D 1.2w D 1.6w L Max. ve M Max. +ve M Load Case I Load Case II 10

11 10/16/ w L 1.2w D Max. -ve M Notes: Max. +ve M Load Case III Dead load ats on all spans all te time Live load sould e arranged to produe maximum positive and negative moments Max. positive moment: load span under onsideration and alternate spans Max. negative moment: live load on te support adjaent spans ten alternate Max. +ve M Max. +ve M Moment Envelope -ve Moment steel +ve Moment steel 11

Purpose of reinforcement P/2 P/2 P/2 P/2

Purpose of reinforcement P/2 P/2 P/2 P/2 Department o Civil Engineering Purpose o reinorement Consider a simpl supported beam: P/2 P/2 3 1 2 P/2 P/2 3 2 1 1 Purpose o Reinorement Steel reinorement is primaril use beause o the nature o onrete