mathcad - rc pier design

RC Pier Design.mcd Program

Reference:H:\References\Concrete\MathCad\Utilities.mcd(R)

A. INTRODUCTION

A.1 FOR UNDERGROUND PIPES, AT LOCATIONS WHERE THE PIPE EXITS FROM OR ENTERS TO THE GROUND, CONCRETEANCHOR BLOCKS SHALL BE PROVIDED IN ORDER O RESIT THER HORIZONTAL FORCE CAUSED BY THE PIPE.

A.2 THE HORIZONTAL FORE CAUSED BY THE PIPE IS RESISTED BY THE FOLLOWING:- FRICTION FORCE BETWEEN THE CONCRETE BLOCK AND THE GROUND.- PASSIVE EARTH PRESSURE AGAINST THE CONCRETE BLOCK.

A.3 ANCHOR BLOCKS USUALLY HAVE A RECTANGULAR PLAN BUT FOR LARGE FORCES H-SHAPE PLANS MAY BE USED IN ORDERTO INCREASE THE PASSIVE EARTH PRESSURE.

A.4 NO TENSION IS ALLOWED WHEN COMPUTING THE BEARING PRESSURE UNDER THE BLOCK.

A.5 THE FACTOR OF SAFETY AGAINST SLIDING SHALL NOT BE LESS THAN 1.20

A.6 THE FACTOR OF SAFETY AGAINST OVERTURNING SHALL NOT BE LESS THAN 1.50

C. INPUT PARAMETERS

MATERIAL PROPERTIES

CONCRETE COMPRESSIVE STRENGTH fc 4ksi:=kcf

kips

ft3:=

UNIT WEIGHT OF CONCRETE c 0.15kcf:=TENSILE STRENGTH OF REINFORCING BARS fy 60ksi:=MODULUS OF ELASTICITY Es 29000ksi:=CONCRETE COVER Cc 1.5in:=

PIER DIMENSIONS

PIER WIDTH bx 36in:=PIER LENGTH by 36in:=PIER HEIGHT hpier 4ft:=MATH/FOOTING THICKNESS T 8ft:=

CONCRETE STRENGTH REDUCTION FACTORS [ACI 318-05, Sec. 9.3]

BENDING/TENSION t 0.9:=COMPRESSION c 0.65:=SHEAR s 0.75:=BEARING b 0.65:=MODIFICATION FACTOR 1.0:= NORMAL WEIGHT CONCRETE (ACI 318-05, Sec. 11.7.4.3)

B. DESIGN LOADS

MAX TENSION Tu 100 kip:=MAX COMPRESSION Pu 1000kip:=SHEAR ALONG X Vux 30kip:=SHEAR ALONG Y Vuy 30kip:=

RC Pier Design.mcd LNT - Page 1 of 7


TOTAL SHEARS VuTotal Vux2 Vuy

2+:= VuTotal 42.43kip=

MOMENT, Mux Mux 10kip ft:=MOMENT, Muy Muy 20kip ft:=

C. RECTANGULAR PIER ANALYSIS AND DESIGN

FACTORED LOADS ACTING AT BOTTOM OF PIER

MAX COMPRESSION Pub Pu LF c bx by hpier+:= Pub 4481.85kN=CONSERVATIVELY USE A LOAD FACTOR LF 1.4 FOR PIERSELFWEIGHT IN STRENGTH DESIGN

MOMENT ABOUT X Mux Mux Vuy hpier+:= Mux 176.26kN m=

MOMENT ABOUT Y Muy Muy Vux hpier+:= Muy 189.81kN m=

MAX SHEAR LIMIT BY CROSS SECTION PROVIDED

ASSUME TO USE A FACTOR 0.9 TO CALCULATE THE EFFECTIVE SECTION DEPTH. IT CAN BERE-EVALUATED AFTER REBAR DESIGN IF NECESSARY

dx 0.9bx:= dx 0.823m=

Vys.max s 0.67 fc MPa dx by:= Vys.max 446.431kip=

Vys.max >=? Vuy "YES!.. SATISFACTORY"=

dy 0.9by:= dy 0.823m=

Vxs.max s 0.67 fc MPa dy bx:= Vxs.max 446.431kip=

Vxs.max >=? Vux "YES!.. SATISFACTORY"=

CHECK MINIMUM/MAXIMUM REINFORCEMENT REQUIREMENTS

MINIMUM REINFORCEMENT RATIO min 0.005:= [ACI 318-05, Sec. 10.8.4,10.9.1 & 15.8.2.1]

MINIMUM REINFORCEMENT As.min min bx by:=

As.min 6.48in2=

MINIMUM REINFORCEMENT RATIO max 0.04:= [ACI 318-05, 10.9.1]ALTHOUGH 0.08 IS ALLOWED BY THE CODE, PRACTICALLY0.04 MAY BE USED.

MAXIMUM REINFORCEMENT As.max max bx by:=

As.max 51.84 in2=



VERTICAL BAR SIZE bar 7:=

BAR DIAMETER dbbar 0.866 in=

BAR AREA Abbar 0.589 in2=

TIE BAR SIZE tie 4:=

TIE DIAMETER dbtie 0.472 in=

TIE BAR AREA Abtie 0.175 in2=

MINIMUM TIE SIZE dtie.min38

in bar 10if

48

in bar 10>if

:= dtie.min 0.375 in=

dbtie >=? dtie.min "YES!.. SATISFACTORY"=

BAR ARRANGEMENT (PER FACE)

NUMBER OF BARS IN A1 n1 7:= A1 n1 Abbar:= A1 4.123in2=

NUMBER OF BARS IN A2 n2 5:= A2 n2 Abbar:= A2 2.945in2=

NUMBER OF BARS n 2 n1 n2+( ):= n 24=AREA OF STEEL PROVIDED As n Abbar:= As 14.136in

2=

As >=? As.min "YES!.. SATISFACTORY"=

As


PIER BEARING CAPACITY (AT BASE OF PIER) PER ACI 318-05 Sec 10.17.1

Pbrg b 0.85 fc bx by:= Pbrg 2864.16kip= [ACI 318-05 Eqn 10-2]

Pub


HORIZONTAL TIES [ACI 318-05 Sec 7.10.5 &11.5.5]

PROVIDE THE TIE BAR DIAMETER

TIE SIZE tie 4=

TIE DIAMETER dbtie 0.472 in=

TIE BAR AREA Abtie 0.175 in2=

Se 0:=

[ACI 318-05 Sec 7.10.5]

Smax

min 16dbbar 48dbtie, bx, by, ( )min 8dbbar 24dbtie,

min bx by, ( )2

, 12in,

:=

[ACI 318-05 Sec 21.12.5.2]

SmaxSe 14in=

PROVIDE THE TIE VERTICAL SPACING

Spacingtie 12in:=

Spacingtie =? VuTotal "YES!.. SATISFACTORY"=

kcs if12Vnc

>=? VuTotal "YES!.. SATISFACTORY" 1, 0,

:= kcs 0=

SHRINKAGE REINFORCEMENT DESIGN

SHEAR AREA OF SINGLE TIE Abtie 0.175 in2=



NUMBER OF LEGS NoLeg 3:=

Av NoLeg Abtie:= Av 0.525in2=

SHEAR REINFORCEMENT AREA

Av.min max 0.062 fc MPamax bx by, ( ) Spacingtie

fy 0.345MPamax bx by, ( ) Spacingtie

fy,

:= [ACI 318-05 Sec 11.5.6.3]

Av.min 0.36in2=

Av >=? Av.min "YES!.. SATISFACTORY"=

dp min bx by, ( ) Cc dbtie 12 dbbar:= dp 33.594in=SHEAR BY TIES PROVIDED

Vsprovkcs s Av fy dp

Spacingtie:= Vsprov 0kip= [ACI 318-05 Sec 11.5.7.2]

Vsprov =? VuTotal "YES!.. SATISFACTORY"=

E. DEVELOPMENT LENGTH OF REBARS (ACI 318-05 SECTION 12.2)

CENTER TO CENTER BAR SPACING Sp

bx 2Cc2 n2+( ) 1by 2Ccn1( ) 1

:= Sp

5.5

5.5

in=

REINFORCEMENT LOCATION FACTOR t 1:= (FOR VERTICAL DOWELS)

REINFORCEMENT LOCATION FACTOR e 1:= (FOR UNCOATED REBARS)

CONCRETE TYPE FACTOR d 1:= (FOR NORMAL WEIGHT OF CONCRETE)

cb min Cc dbtie( )+ dbbar2+ min Sp( )2, := cb 2.406in=TRANSVERSE REINFORCMENT INDEX Ktr 0in:= AS A DESIGN SIMPLIPICATION, IT IS CONSERVATIVE TO

ASSUME Ktr=0, EVEN IF TRANSVERSE REINFORCEMENT ISPRESENT (PER ACI 318-05 SECTION 12.2.3)

DEVELOPMENT LENGTH OF STRAIGHT BAR

Ld340

e t 0.80 12d fy

fc MPa mincb Ktr+dbbar

2.5,

dbbar bar 6if

340

e t 1.0 12d fy

fc MPa mincb Ktr+dbbar

2.5,

dbbar bar 7if

:= [ACI 318-05 Sec 12.2.3, Eqn12-1]



Ld 24.562in=

DEVELOPMENT LENGTH OF BAR WITH STANDARD HOOK

Ldh max 0.24 ed fyfc MPa

dbbar 150mm, 8 dbbar,

:= Ldh 16.375in=[ACI 318-05 Sec 12.5.2]

CHECK THE DEVELOPMENT LENGTH OF THE STRAIGHT BAR INTO THE PIER

REDUCTION FACTOR PER ACI 318-05 SECTION 12.2.5 & 12.5.3.D

IR maxMuyMny

MuxMnx

, TubTn

, := IR 0.509=

IR

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