beam design functions xls

8/10/2019 Beam Design Functions Xls

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Elastic Analysis of Reinforced and Prestresse

Contents:

Name Purpose

Elastic

Quartic Find the real roots of quartic equations

Cubic Find the real roots of cubic equations

Quadratic Find the real roots of quadratic equations

PlotXY Plot cross section diagram

Parameters:

Conc A 6 column range with concrete cross section details

eo A 6 column range with reinforcement and prestress details

!omin "he applied bending moment

A#in "he applied a#ial load

Eccentric "he eccentricit$ of the applied load

%ut&'nde# An inde# number controlling the output data( see e#ample

*nits

esults are returned as single column arra$s( depending on the +alue

"o access the arra$s either,

Enter the function as an arra$ function -press ctrl.shift.ent

0'N1EX-E2A3"'C-Conc( eo( !omin( A#in( Eccentric( 4/(

"$pical input and output is shown in the following sheets

mpasha77)mp8gmail)com

Find strain( stress( force and moment in prestressed andreinforced concrete beams with linear elastic materialproperties) An$ section made up of rectangular ortrape9oidal la$ers

E2A3"'C-/ is a *ser 1efined Function -*1F/ that carries out elastic aassuming 9ero tensile strength for the concrete( and linear elastic pro

1etails of the anal$sis are pro+ided in the file, 1epthNA)pdf( which mhttp,::newtone#celbach)wordpress)com:

; for loads and eccentricit$ in N and metres( dimensionsconsistent units)

%r use the 'N1EX-/ function to return the required +alue)reinforcement enter,

Interactive Design Services
mailto:[email protected]:[email protected]


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Notes:4) "he beam section ma$ be made up of an$ arrangement o

) Datum for eccentricity of axial loads

7) Prestress forces

6) Plotting the cross section

'f the eccentricit$ is omitted or blan the a#ial load is assu"his allows results of frame anal$sis programs to be enterha+e been modelled on the concrete section centroid)

@here specified( the eccentricit$ is measured from the topeccentricit$ of 9ero will therefore be applied at the top faceunspecified eccentricit$( which will be applied at the concr

Prestress forces ma$ either be specified b$ entering a preentering the prestress force and eccentricit$ as an e#terna

@here the area of prestressing strand is included in the relosses deducted( since the strain in the strand is accounte

"he edraw 3ection button on the input sheet will draw treinforcement -in blac/ and prestressed reinforcement -in

@here +oids are specified( =4 and =< are the e#ternal coand => are the top and bottom width of the +oid)

"he +oid dimensions are required for plotting purposes onlthe width of concrete for each la$er( with +oid dimensions


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SectionsBer, 4);> 44.%ct.;

*sage

Quartic-A( =( C( 1( E( 1t( %ptional output inde#/

cubic-A( =( C/

Quadratic-A( =( C( %ptional output inde#/

output)

of %ut&'nde#)

r/ after selecting the number of rows of output required)

/

Elastic-conc( reo( momin( a#in( %ptional Deccentric(%ut&'nde#( *nits/

Creates diagram inside the range Plotange on thecurrent sheet( using the data in 2a$erange( eoange(1epth&NA( and "Face)

nal$sis of reinforced or prestressed concrete sections(erties for the reinforcement and concrete in compression)

$ be downloaded from,

in mm( stresses in !Pa -default/( an$ other number for an$

or instance to return the stress in the bottom la$er of


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rectangular or trape9oidal la$ers

from the top or compressi+e face)

ce( positi+e upwards)

ed to be applied at the centroid of the concrete section)d without ad?ustment( assuming that the frame elements

face of the concrete) An a#ial load with a specified( and will gi+e different results to the same a#ial load withte centroid)

tress force per strand for each la$er of strand( or b$l force)

inforcement list( the prestress force should not ha+e elasticd for in the anal$sis)

he concrete section to scale( including passi+ered/) "he concrete compression 9one is shaded blue)

crete dimensions -top and bottom of each la$er/( and =5

l$) "he same numerical results ma$ be obtained b$ enteringntered as 9ero or blan)


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Elastic Analysis of Reinforced and Prestressed Sections

Applied loads

!om A#ial Eccentricit$

N N m

)7;EG;5

Depth of Neutral Axis HNA!EI mm

Tension face HNA!EI HNA!EI

Section Details (enter layers from top face or compressive face for columns!

Concrete Boid

2a$er 1epth =4-top/ =-bottom/ Ec


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Elastic "utput

Elastic(conc reo momin axin "ptional #eccentric "ut$%ndex &nits'!

Ranges Concrete #NAME?

Reinforcement 'Elastic1 Input'.I21:N24

1 2

%tress" M&a %train" m(1 )orce"

1 Compression face #NAME? #NAME? Concrete

2 Compression steel #NAME? #NAME? &assi+e %teel

, Tension Steel #NAME? #NAME? &restress

4 -ension face #NAME? #NAME? Applied axial

/ocation of tension face #NAME? #NAME?

0

31

1112


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output column ine!" ut

, 4

*N Moment" *Nm

#NAME? Concrete #NAME?

#NAME? &assi+e %teel #NAME?

#NAME? &restress #NAME?

#NAME? Moment due to axial #NAME?

Applied moment #NAME?

&restress eccentricit5 #NAME?


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$ine!

0

6ept7 to NA etc %teel 85 la5er %tress

9 #NAME? Compression la5e #NAME?

Acomp #NAME? to #NAME?

NA #NAME? -ension la5er #NAME?

Ina #NAME? #NAME?

Eccentricit5 reaction force from comp. fa #NAME? -otal passi+e forc #NAME?

Eccentricit5 applie force from comp. fac #NAME? -otal prestress fo #NAME?

6ept7 centroi concrete section #NAME? #NAME?

6ept7 centroi reinforcement #NAME?

6ept7 centroi full composite section #NAME?

6ept7 centroi crac*e composite sectio #NAME?

I reinforcement #NAME?

#NAME?


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)orce

#NAME?

#NAME?

#NAME?

#NAME?

#NAME?

#NAME?

#NAME?

#NAME?

#NAME?


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Rayers

4, Es HNA!EI HNA!EI

, "ransformed la$er area in ten HNA!EI HNA!EI

7, Cumulati+e area in tension HNA!EI HNA!EI

6, Cumulati+e first !ofA about to HNA!EI HNA!EI

K Find la$er and ad?usted total transformed J, "ransformed la$er area in co HNA!EI HNA!EI K for NA down to current la$er , Cumulati+e transformed area HNA!EI HNA!EI

, Cumulati+e transformed first HNA!EI HNA!EI

4;, 2a$er 1epth HNA!EI HNA!EI

44, Cumulati+e Centroid depth HNA!EI HNA!EI

4, sum4 compression to NA HNA!EI HNA!EI

47, sum< compression to NA HNA!EI HNA!EI

46, ' about steel centroid HNA!EI HNA!EI

ayers

4 2a$er thicness HNA!EI HNA!EI

< "ransformed =4 HNA!EI HNA!EI

5 "ransformed =< HNA!EI HNA!EI

> "ransformed L HNA!EI HNA!EI

7 "ransformed la$er area HNA!EI HNA!EI

6 Cumulati+e area HNA!EI HNA!EI

J 2a$er centroid height from botto HNA!EI HNA!EI

Composite conc) 4st moment of HNA!EI HNA!EI

Meight of composite concrete ce HNA!EI HNA!EI

4; 1epth of bottom of la$er HNA!EI HNA!EI

44 2a$er second moment of area a HNA!EI HNA!EI4< 2a$er second moment of area a HNA!EI HNA!EI

45 Composite concrete second mo HNA!EI HNA!EI

4>.4, Composite transformed properties Area HNA!EI HNA!EI

47 First moment of area about top HNA!EI HNA!EI

46 1epth of centroid HNA!EI HNA!EI

4J First moment of area about botto HNA!EI HNA!EI

4 3econd moment of area about b HNA!EI HNA!EI

4 ' reinforcement in tension HNA!EI HNA!EI

)A

NA within section Full compression Full tension

4 Y Y Y< Qna Qna Qna

5 'na 'na 'na

> Qstna Qstna Qstna

7 Qconcna Qconcna .

6 'stna 'stna 'stna

J 'cconc 'cconc .

1epth centroid conc compression 1ref .

Acomp Acomp Acomp

4; 1ref 1ref 1ref


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44 1efComp 1efComp 1efComp

4< a

45 b

4> c

47 d

46 e

4J sum4

4 sum


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Public Function FindNA-reo( la$ers( rla$ers( lla$er( a#in( momin( out


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Lb 0 -=( ( 5/ 0 Lb : < 1t < . =b 1t

XCoeff->( >/ 0 -=b : < 1t < . Lb : 6 1t 5/ XCoeff-7( 5/ 0 At

XCoeff-7( >/ 0 .At 1ct

Qa 0 XCoeff->( 4/

Qb 0 XCoeff->( "o 6

Qc 0 XCoeff-?( 5/ G Qc

Ne#t ?

Qd 0 ;

For ? 0 > "o 6

Qd 0 XCoeff-?( >/ G Qd

Ne#t ?

'f Qa 0 ; And Qb 0 ; "hen

X; 0 .Qd : Qc

Else

X; 0 quartic-;( Qa( Qb( Qc( Qd( 1t/

End 'f

'f X; O 1t And X; 0 db "hen

2a$er; 0 i E#it For

End 'f

Ne#t i

e1im XCoeff-4 "o 6( 4 "o 7/

End 'f

'f a#in 0 ; "hen Ro"o FindX

KA#ial load O ;


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E&4 0 momin : a#in

E&< 0 E&4 . la$ers-lla$er( /

KFind first section under NA

K 'f a#in ; "hen Firsti 0 ; Else Firsti 0 4

K For i 0 Firsti "o lla$er G 4

K Coefficients for #

K einforcementK e1im XCoeff-4 "o 6( 4 "o 7/

K 's4 0 ;

K 's; 0 ;

K A#s4 0 ;

K A#s; 0 ;

K For ? 0 4 "o numreo

K 'f i 0 lla$er "hen

K 'f reo-?( 4/ O0 la$ers-i( 4/ "hen Ar 0 la$ers-?( 4/ Else Ar 0 la$ers-?(


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Lb 0 ;

End 'f

Qa 0 .Lb : 4/ G Qd

K Ne#t ?

K Qe 0 ;

K For ? 0 4 "o 6

K Qe 0 XCoeff-?( 7/ G Qe

K Ne#t ?

'f Qa 0 ; And Qb 0 ; And Qc 0 ; "hen

'f Qd O ; "hen X 0 .Qe : Qd Else X 0 4;;;;;;;;;;H

Else

X 0 quartic-Qa( Qb( Qc( Qd( Qe( 1t/

End 'f

K 'f -X O 1t And X db/ %r i O lla$er %r -i 0 ; And -X ; %r X O 1base// "hen

out G Qb X 5 G Qc X < G Qd X G Qe/ : Qe

FindX,

'f 3mallA# 0 ; "hen

X 0 X;

i 0 2a$er;

K Ro"o endfunc

Else'f Abs-3mallA#/ Abs-a#in/ "hen

X 0 X; G -X . X;/ 3mallA# : a#in

End 'f

K Find top face strain

K Factor on moment if E&4 O 4 or a#in 0 ;( otherwise a#ial load

K Find steel transformed area and 4st and


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Ne#t ?

out


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out


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CF%ut-/ 0 1cg

CF%ut-/ 0 1cr

CF%ut-44/ 0 Comp1rct

CF%ut-4/

1epth 0 la$ers-lla$er( 4/

For i 0 4 "o lla$er

KFor ? 0 4 "o 45

"emp2a$ers-i( 4/ 0 1epth . la$ers-lla$er . i G 4( 4/"emp2a$ers-i( / 0 la$ers-lla$er . i G 4( 5/

"emp2a$ers-i( 7/ 0 la$ers-lla$er . i G 4( 7/


"emp2a$ers-i( J/ 0 la$ers-lla$er . i G 4( J/

"emp2a$ers-i( / 0 la$ers-lla$er . i G 4( /

"emp2a$ers-i( / 0 1epth . la$ers-lla$er . i G 4( /

"emp2a$ers-i( 4;/ 0 la$ers-lla$er . i G 4( 4;/


"emp2a$ers-i( 4


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Public 3ub Elastic5-/

K Ret mom( a#( e&4( concrete and reo arra$s and number la$ers

K Concrete and steel propertiesK Ad?ust concrete wid$hs for concrete modular ratio

K 3plit concrete la$ers at reinforcement la$ers

K Form la$ers arra$( columns 4 to 6,

K 4, 2e+el of bottom of la$er

K , =ottom width

K 7, Concrete E

K 6, ate of change of width( L

K Form rla$ers arra$( columns ( 4;( 4 to 5( > to J( ,K 4, "ransformed area in tension

K


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End 3ub

Pri+ate 3ub Cum2a$ers


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Public Function FindNA2a$er-reo( la$ers( rla$ers( lla$er( E&


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HNA!EI HNA!EI HNA!EI






HNA!EI HNA!EI HNA!EIHNA!EI HNA!EI HNA!EI









HNA!EI HNA!EI HNA!EI HNA!EI










HNA!EI HNA!EI HNA!EI HNA!EIHNA!EI HNA!EI HNA!EI HNA!EI








HBA2*ESHBA2*ES

HBA2*ES

HBA2*ES

HBA2*ES

HBA2*ES

HBA2*ES

HBA2*ES

HBA2*ES

HBA2*ES


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HBA2*ES

HBA2*ES

HBA2*ES

HBA2*ES

HBA2*ES

HBA2*ES

HBA2*ES

HBA2*ES

enumber

4 4 4, 1epth of bottom of l

< < > >, "otal area to la$er

7 7 7, Centroid depth to l

6 6 6, Cumulati+e ' about

J J J, Cumulati+e ' about

, 1epth of top of la$e

, Cumulati+e First m4; 4; 4;, Cumulati+e transf

44 44 44, "otal transformed

4< 4< 4 4> 4>, eaction centroid

47 47 47, "otal transformed

46 46 46, "ransformed centr

4J 4J 4J, "otal "ransformed

4

4


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constant

constant


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a$er

from top of la$er

$er

base to la$er

centroid to la$er

r

onemt of area about baseormed reinforcement Q about base

Q about base

er( 'rt

eccentricit$ . applied load eccentricit$( from base of la$er

rea

oid height abo+e base of la$er

' about transformed centroid


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E#amples . cop$ data to 'nput sheet

*ircular section + ,-- dia.

Concrete Boid

1epth =4 =< =5 => Ec

4; ;); 475)6 5555;

47 475)6 J)< 74)6

7; 74)6 767)J

7; 767)J 74)6

7; 74)6 6;;);

7; 6;;); 74)6

7; 74)6 767)J

7; 767)J 74)6

7; 74)6 >>J)>J)< 57)


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einforcement and prestress

1epth 1ia No Es 3ide Co+er

7;);;


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A/out 0eam Design 1unctions

Disclaimer

This program is distri/uted in the hope that it 2ill /e useful

/ut 2ithout any 2arranty3 2ithout even the implied 2arranty of

merchanta/ility or fitness for a particular purpose.

Cop$right


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s to B=A pro?ect not allowed

beam design functions xls

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