Structural Design Calculation

Published by:

E.G Navarro

CE- Mindanao University of Science and Technology

20-May-14

LONGTERM DEFLECTION(AS PER ACI318M-11)

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Structural Design Calculation

METHOD-1 (Manual)

Ms = 2161.88 KN-m (sustained service maximum moment LC:DL+0.5LL)

i = 17.66 mm (immediate deflection LC: DL+LL)

fc' = 32.0 MPa (concrete compressive strength)

b = 600.0 mm (breadth of cross section)

h= 1300.0 mm (thickness of cross section)

d= 1210.0 mm (effective depth based on tension steel)

d'= 310.0 mm (effective depth based on compression steel)

As= 8000.0 mm (area of steel of tension steel)

As' 6450.0 mm (area of steel of compression steel)

= 2 (time-dependent factor)

L = 14000.00 mm (total clear span of the beam)

Ec = 4700 x fc' = 4700 x 32.00=

fr = 0.62 x fc' = 0.62 x 32.00=

Ig = bh3/12 = 600.0 x1,300.00^3 /12=

n= Es/Ec = 26,587.2 /200,000.00= 7.52

(Neutral axis determination)

B1 = 1000/ n As = 1000/7.5 x8,000.00= 0.0166

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

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)

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))

Ie =

f = Ie / Ig = 55,177,683,339.73/109,850,000,000.00

f = 0.50

LONG TERM DEFLECTION

CALCULATION

PARAMETERS

26587.2 MPa

3.5 MPa

109850000000.0 mm3

592.73 KN-m

54027208977.9 mm3

55177683339.7 mm3

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Structural Design Calculation

(Reinforcement ratio for compression reinforcement)

' = As' / b x d = 0.0089

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

= / ( 1 + 50 ') =

=

i = 17.66 mm

all = L/240 =

all = = 14,000.00 /240

all = 58.33 mm

L = i x x Ig / Ie = (17.66)(1.385)/(0.50)

L = 48.69 mm < 58.33 mm

Calculated deflection is within permissible range - SAFE!

METHOD-2 (ETABS)

3D MODEL

(2 / (1+ 50 x 0.0089))

1.384835

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Structural Design Calculation

TO ACCOUNT FOR CRACKING OF SECTION INCLUDING CREEP AND SHRINKAGE

GROSS INERTIA HAS TO BE REDUCE AS PER RECOMMENDATION BELOW.

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Structural Design Calculation

THEREFORE,

MODIFIER FOR BEAMS

MODIFIER FOR COLUMNS

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Structural Design Calculation

L = 48.77 mm < all = 58.33 mm SAFE!

RESULTS:

SERVICE LONGTERM MOMENT (LC: DL +0.5LL)

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