Long Term Deflection Design

Project

MZ & PARTN ERS

Calculated by AA Checked and Approved by MN

Client

ARCHITECTURAL & ENGINEERING CONSULTANCY Tel: 43 63 813-Fax: 43 63 812-POBox: 5785Doha-Qatar

ST RU CTU RA L DEPA RTM ENT

Floor title

LONG TERM DEFLECTION CALCULATION ACI Width 318-08 Service moments MaMa+ 9.5.2.5 x 9.5.2.5 λ∆ Sustained live load

Bottom Reinforcement Top Reinforcement

8.5.1 8.5.2

40

cm t.m

Instantanuous deflections ΔDL 8.9 mm

0

-130 93

t.m

ΔLL

-130

2 5 years or more 0.97 20 % 80 % Midspan cm Ø32 @ 12.5 + Ø32 @ Ø32 @

25 +

Ø32 @

2.7 mm

93

0 -130

Time dependent factor for sustained load Percentage of sustained live load for p Percentage of intermittent load

cm2 cm 13 Asbot = 128.6 25 Astop = 64.3

2

cm2 Support cm cm Ø32 @ 13 + Ø32 @ 13 Asbot = 128.6 Ø32 @ 25 + Ø32 @ 25 Astop = 64.3

c

4

cm

h

80

cm2

Section depth

d f'c

76 32

Effective depth of section Concrete compressive strength

Ec

265.872

cm2 Mpa ton/cm2

Elastic modulus of concrete

4700√f'c

ton/cm2

Elastic modulus of steel Modular ratio

Es/Ec

kg/cm2

Modulus of rupture

0.62√f'c

Es n

2000 8

9.5.2.3 fr ρ ρ'

35.0725 0.04231 0.02115

Ig At midspan k j

1706667 0.54069 0.81977

Icr 9.5.2.3 Mcr

2104100 14.9643

9.5.2.3 Ie Ie,average

2102444 1738012

Additional deflection ΔDL,long term ΔLL,long term Sustained Total deflection

Concrete cover

4

cm At support 0.427 0.8577 4 1E+06 cm 14.964 t.m 4 1E+06 cm cm4

Moment of inertia about centroidal axis neglecting reinforcement Compression members eff. length factor Internal lever arm

√*(ρn)2+2.ρ.n+-ρ.n

Moment of inertia of cracked section Cracking moment

n.As.(1-k).j.d2

Effective moment of inertia

Icr+(Mcr/Ma)3.(Ig-Icr)

1-k/3 (fr.Ig)/yt

λ∆ .(Ig/Ie).ΔDL

8.49449

mm 0.5154 + ΔLL,Long term intermittent 2.12 mm 22.7

MOMENT (ton.m)

mm Deflection (mm)

-2.7

DL -8.9

LL Long term

-22.7

CRACK WIDTH CALCULATION fs dc cc β s Frosch w

1.16 4 2.4 1.124 6.25 0.03

ton/cm2 cm

mm

Tensile stress in reinforcement at service loads Concrete cover to center of outer bar Least distance from reinf. Surface to tenion face

M/(As.j.d) dc-db/2

Bar spacing closest to tension face

1+0.031.dc (cm) 380.(280/fs)-2.5.cc

Maximum width of crack

2(fs/Es).β.√(dc2+(s/2)2)