Design AssumptionDesign Assumption1. All the designs comply with
COP Structure Use of Concrete 2004 Cl 7.3.52. Elastic stress box is
adopted3. Section is assumed to be plane remaining plane4. Concrete
tensile stress for short term and long term are 1 N/mm2 and 0.55
N/mm2 respectively5. For uncrack section, the I includes the
stiffness of rebarNotes1.Dont move any cells2. Don't change the
name of cells3. Don't change the name of worksheet4. This entire
workbook only serves for one beam.
xpsHyder Consulting LimitedBy :Job No.Job :Date :SheetSubject
:Check x for short term permanent
loadMp=4017kN*mH=2300mmb=1000mmd=2240mmdc=30mmAst=12560mm^2Asc=2010mm^2Es=205000N/mm^2Ecs=26400N/mm^2ftd=0.55N/mm^2fct=(H-xps)/(d-xps)*ftd=0.5705543315fst=(M-(fct*b*(H-xps)*(H/3)))/((Ast*(d-xps/3))+(((xps-dc)/(d-xps))*(Ec/Es)*(xps/3-dc)*Asc))=128.9815245368fsc=((xps-dc)/(d-xps))*(Ec/Es)*fst=6.25fc1=xps/(d-xps)*(Ec/Es)*fst=6.56fc2=(fst*Ast+(1/2*fct*b*(H-xps))-(fsc*Asc))/(1/2*b*xps)=6.56fc1-fc2
=-0.00xps=634.50mmChecked byFileRef.K:\EB000376 City U 334 Phase 3
(Academic and Admin Bldg)\D-Calcs\4th
Submission(Superstructure)\Deflection
Check\[Deflection_rev_0_8HB10.xls]xtsChecked byFileRef.K:\EB000376
City U 334 Phase 3 (Academic and Admin Bldg)\D-Calcs\4th
Submission(Superstructure)\Deflection
Check\[Deflection_rev_0_8HB10.xls]xts
xtsHyder Consulting LimitedBy :Job No.Job :Date :SheetSubject
:Check x for short term temporary
loadMt=6735kN*mH=2300mmb=1000mmd=2240mmdc=30mmAst=12560mm^2Asc=2010mm^2Es=205000N/mm^2Ecs=26400N/mm^2ftd=0.55N/mm^2fct=(H-xts)/(d-xts)*ftd=0.5702086836fst=(M-(fct*b*(H-xts)*(H/3)))/((Ast*(d-xts/3))+(((xts-dc)/(d-xts))*(Ec/Es)*(xts/3-dc)*Asc))=234.0964568866fsc=((xts-dc)/(d-xts))*(Ec/Es)*fst=10.65fc1=xts/(d-xts)*(Ec/Es)*fst=11.21fc2=(fst*Ast+(1/2*fct*b*(H-xts))-(fsc*Asc))/(1/2*b*xts)=11.21fc1-fc2
=-0.00xts=607.04mmChecked byFileRef.K:\EB000376 City U 334 Phase 3
(Academic and Admin Bldg)\D-Calcs\4th
Submission(Superstructure)\Deflection
Check\[Deflection_rev_0_8HB10.xls]xtsChecked byFileRef.K:\EB000376
City U 334 Phase 3 (Academic and Admin Bldg)\D-Calcs\4th
Submission(Superstructure)\Deflection
Check\[Deflection_rev_0_8HB10.xls]xts
xplHyder Consulting LimitedBy :Job No.Job :Date :SheetSubject
:Check x for Long term permanent
loadMp=4017kN*mH=2300mmb=1000mmd=2240mmdc=30mmAst=12560mm^2Asc=2010mm^2Es=205000N/mm^2Ecl=15161N/mm^2ftd=1N/mm^2fct=(H-xpl)/(d-xpl)*ftd=1.043054378fst=(Mp-(fct*b*(H-xpl)*(H/3)))/((Ast*(d-xpl/3))+(((xpl-dc)/(d-xpl))*(Ecl/Es)*(xpls/3-dc)*Asc))=115.9808764555fsc=((xpl-dc)/(d-xpl))*(Ecl/Es)*fst=5.02fc1=xpl/(d-xpl)*(Ec/Es)*fst=5.21fc2=(fst*Ast+(1/2*fct*b*(H-xpl))-(fsc*Asc))/(1/2*b*xpl)=5.21fc1-fc2
=-0.00xpl=846.41mmChecked byFileRef.K:\EB000376 City U 334 Phase 3
(Academic and Admin Bldg)\D-Calcs\4th
Submission(Superstructure)\Deflection
Check\[Deflection_rev_0_8HB10.xls]xtsChecked byFileRef.K:\EB000376
City U 334 Phase 3 (Academic and Admin Bldg)\D-Calcs\4th
Submission(Superstructure)\Deflection
Check\[Deflection_rev_0_8HB10.xls]xts
creep coeff & shrinkage strainHyder Consulting LimitedBy
:Job No.Job :Date :SheetSubject :KLc=2.3Fig 3.1Km=1.0Fig
3.2Kc=0.8Fig 3.3Kec=0.7Fig 3.4Kj=0.6Fig
3.5Ks=1/(1+r*ae)=0.96modular ratio (r)=Es/Ecs=7.77steel ratio
(ae)=As/Ac=Ast/(b*H)=0.005cs=3.0KLs=275.0x10^-6Fig 3.6Kes=0.5Fig
3.7creep coefficient (fc)=KLc*Km*Kc*Kec*Kj*Ks=0.74free shrinkage
strain (ecs)=cs*KLs*10^-6*Kc*Kes*Kj=1.98E-04Checked
byFileRef.K:\EB000376 City U 334 Phase 3 (Academic and Admin
Bldg)\D-Calcs\4th Submission(Superstructure)\Deflection
Check\[Deflection_rev_0_8HB10.xls]xtsChecked byFileRef.K:\EB000376
City U 334 Phase 3 (Academic and Admin Bldg)\D-Calcs\4th
Submission(Superstructure)\Deflection
Check\[Deflection_rev_0_8HB10.xls]xts
DEFLECTIONHyder Consulting LimitedBy :KWJob No.EB000376Job
:CityU 334 Phrase 3 (AAB)Date :May-10SheetSubject :8HB10Beam
Deflection CheckingCONCRETE GRADEElastic Modulus Ec
(N/mm^2)Complying with COP Structure Use of Concrete 2004 Cl
7.3.5C2018700PARAMETERSC2520500C3022200Total Moment
(Mt)=6735kN*mBasic CheckingC3523700Permanent Moment
(Mp)=4017kN*mConcrete Compressive
stressC4025100def=11mmfcts11.21C4526400H=2300mmL/250=48mmfcps6.56C5027700b=1000mmfcpl5.21C5528900d=2240mmDeflectionSectionC6030000dc=30mmShort
term total9.869(cracked)C6531100Ast=12560mm^2Short term
perm5.530(cracked)C7032200Asc=2010mm^2Long term
perm5.729(cracked)C7533200Effective span
(l)=12000mmShrinkage0.699C8034200Second moment of area
(I)=1031360546666.67mm^4I is considered rebar =
H^3*b/12+Ast*(H/2-d)^2+Asc*(H/2-dc)^2C8535100C9036000Concrete
Grade=C45C9536900Short-term modulus of concrete
(Ecs)=26400N/mm^2Cl. 7.1.5C10037800KLc=2.3Fig 3.1Km=1.0Fig
3.2Kc=0.8Fig 3.3Kec=0.7Fig 3.4Kj=0.6Fig 3.5Creep coefficient
(fc)=0.74Cl. 3.1.7Long-term modulus of concrete
(Ecl)=15160.54N/mm^2Modulus of elasticity of reinforcement
(Es)=205000N/mm^2cs=3.0KLs=275.0x10^-6Fig 3.6Kes=0.5Fig 3.7Free
shrinkage strain (ecs)=1.98E-04ro=0.56Table 7.7K=0.098Table
7.6Total short term fcts=11.21N/mm^2Permanent short term
fcps=6.56N/mm^2Permanent long term fcpl=5.21N/mm^2Total short term
cracked xts=607.04mmPermanent short term cracked
xps=634.50mmPermanent long term cracked xpl=846.41mmCURVATURE1)
Instantaneous Curvature under Total Loada) Cracked Section
(Partially)1/rb=fcts/(xts*Ecs)=11.2068950362/(607.038609514431x26400)=6.99E-07mm^-1b)
Uncracked
Section1/rb=Mt/(Ecs*I)=6735x1000^2/(26400x1031360546666.67)=2.47E-07mm^-11/rb
(cracked)=6.99E-07mm^-1>=1/rb
(uncracked)=2.47E-07mm^-11/rb=6.99E-07mm^-1(cracked)(1)2)
Instantaneous Curvature under Permanent Loada) Cracked Section
(Partially)1/rb=fcps/(xps*Ecs)=6.5644436389/(634.498990187979x26400)=3.92E-07mm^-1b)
Uncracked
Section1/rb=Mp/(Ecs*I)=4017x1000^2/(26400x1031360546666.67)=1.48E-07mm^-11/rb
(cracked)=3.92E-07mm^-1>=1/rb
(uncracked)=1.48E-07mm^-11/rb=3.92E-07mm^-1(cracked)(2)3) Long-term
Curvature Under Permanent Loada) Cracked Section
(Partially)1/rb=fcpl/(xpl*Ecl)=5.2094972962/(846.41349926246x15160.5389753453)=4.06E-07mm^-1b)
Uncracked
Section1/rb=Mp/(Ecl*I)=4017x1000^2/(15160.5389753453x1031360546666.67)=2.57E-07mm^-11/rb
(cracked)=4.06E-07mm^-1>=1/rb
(uncracked)=2.57E-07mm^-11/rb=4.06E-07mm^-1(cracked)(3)4) Shrinkage
Curvature1/rcs=ro*ecs/d=0.56x1.98E-04/2240=4.95E-08mm^-1(4)Total
Long-term Curvature1/rtotal=(3) + (1) - (2) +
(4)=4.06E-07+6.99E-07-3.92E-07+4.95E-08=7.63E-07mm^-1DEFLECTIONa=K*L^2(1/rtotal)=0.098x12000^2x7.63E-07=11mm
