Longterm Deflection Comparison With Etabs

Structural Design Calculation

LONGTERM DEFLECTION (AS PER ACI318M-11)

Published by: E.G Navarro CE- Mindanao University of Science and Technology 20-May-14

1

Structural Design Calculation

LONG TERM DEFLECTION METHOD-1 (Manual) PARAMETERS Ms = Δi = fc' = b= h= d= d'= As= As' ξ= L=

2161.88 KN-m 17.66 mm 32.0 MPa 600.0 mm 1300.0 mm 1210.0 mm 310.0 mm 8000.0 mm² 6450.0 mm² 2 14000.00 mm

(sustained service maximum moment LC:DL+0.5LL) (immediate deflection LC: DL+LL) (concrete compressive strength) (breadth of cross section) (thickness of cross section) (effective depth based on tension steel) (effective depth based on compression steel) (area of steel of tension steel) (area of steel of compression steel) (time-dependent factor) (total clear span of the beam)

4700 x √fc' 0.62 x fc' bh3/12 Es/Ec

= 4700 x √32.00= = 0.62 x √32.00= = 600.0 x1,300.00^3 /12= = 26,587.2 /200,000.00=

26587.2 MPa 3.5 MPa 109850000000.0 mm3 7.52

= 1000/7.5 x8,000.00=

0.0166

CALCULATION Ec = fr = Ig = n=

(Neutral axis determination) B1 = 1000/ n As r = (n-1) x As' / n As

= (7.5 -1) x6,450.00/7.522 x 8,000.00=

0.69907

kd = ( √( (2 x d x B1 ( 1+(r x d')/d)) + (1+r2) ) - (1+r) ) / B1 kd =( √((2 x1,210.0x0.0166(1+(0.699x310.000)/1,210.00)+(1+0.6992) ) - (1+0.699) ) / 0.0166) kd=

324.6 mm

(Cracking Moment) Mcr = fr. Ig /yt 1 x 10^6 = 3.5 x109,850,000,000.00/650.00x 1 x 10^6 = (Cracking Moment of inertia) Icr = b.kd3/3 + n.As. (d-kd)2 + (n-1). As' . (kd-d')2

592.73 KN-m

Icr =((600.0)(324.573)/3) +(7.5)(8,000.0)(1,210.0-324.6^2 + (7.52-1)(6,450.00((324.57)-(310.00^2) 54027208977.9 mm3 Icr = Ie = (Mcr/Ms)^3 x Ig + ( 1 -(Mcr/Ms)^3 ) x Icr Ie = (592.73/2,161.88)^3 x 109,850,000,000.000 + ( 1 -(592.73/2,161.88^3)(54,027,208,977.863)) 55177683339.7 mm3 Ie = f = Ie / Ig = f=

55,177,683,339.73/109,850,000,000.00 0.50

2

Structural Design Calculation

(Reinforcement ratio for compression reinforcement) ρ'=

As' / b x d =

0.0089

(Multiplier for long-term deflection to account for creep and shrinkage) λ= λ= Δi=

ξ / ( 1 + 50 ρ ') = 1.384835 17.66 mm

Δ all = Δ all = Δ all =

L/240 = = 14,000.00 /240 58.33 mm

ΔL=

Δi x λ x Ig / Ie =

ΔL=

48.69 mm

(2 / (1+ 50 x 0.0089))

(17.66)(1.385)/(0.50)

<

58.33 mm

Calculated deflection is within permissible range -

SAFE!

METHOD-2 (ETABS)

3D MODEL

3

Structural Design Calculation

TO ACCOUNT FOR CRACKING OF SECTION INCLUDING CREEP AND SHRINKAGE GROSS INERTIA HAS TO BE REDUCE AS PER RECOMMENDATION BELOW.

4

Structural Design Calculation THEREFORE,

MODIFIER FOR BEAMS

MODIFIER FOR COLUMNS

5

Structural Design Calculation RESULTS:

SERVICE LONGTERM MOMENT (LC: DL +0.5LL)

ΔL=

48.77 mm

<

58.33 mm

Δ all =

6

SAFE!