timesaving-torsiondesign-ia

8/8/2019 Timesaving-TorsionDesign-IA

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TIME SAVING DESIGN AID Page 1 of 23

Torsion Design

The following example illustrates the design methods presented in the PCA book Simplified Design -

Reinforced Concrete Buildings of Moderate Size and Height third edition. Unless otherwise noted, all

referenced table, figure, and equation numbers are from that book.

Example Building

Below is a partial plan of a typical floor in a cast-in-place reinforced building. In this example, beam CD is

designed and detailed for the combined effects of flexure, shear, and torsion according to ACI 318-05.

Design Data

Materials

Concrete: normal weight (150 pcf), fc = 4,000 psi Mild reinforcing steel: Grade 60 (fy = 60,000 psi)Loads

Dead load of joists = 77 psf


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Torsion Design

Superimposed dead load = 30 psf Live load = 50 psfAdditional data

Typical bay size = 24 32 ft (5 bays in N-S direction, 3 bays in E-W direction) Typical story height = 12 ftFactored Torsional Moment uT

Since beam CD is part of an indeterminate framing system in which redistribution of internal forces can

occur following torsional cracking, the maximum factored torsional moment uT at the critical section

located at a distance d from the face of the support can be determined from the following:

=

cp

2cp

cu p

Af4T '

This type of torsion is referred to as compatibility torsion, the magnitude of which is greater than thefactored torsional moment min,uT below which torsional effects can be neglected, where

=

cp

2cp'

c,minu p

AfT

Since the beams and joists are cast monolithically, and for beam CD can include a portion of the

adjoining slab. The effective width of the overhanging flange must conform to 13.2.4:

cpA cpp

eb

eb = = 20.5 4.5 = 16.0 in. (governs)fhh

= = = 18.0 in.fh4 544 .

cpA = = 564.0 in.2( ) (20.524 + 16.0 4.5)

)

)

cpp = = 121 in.( )2 20.5+24+16.0

cp2cp pA / = 2,629 in.

3

The torsional properties of the beam ignoring the overhanging flange are the following:

cpA = = 492 in.2( 24520 .

cpp = = 89 in.( 245202 +.

cp2cp pA / = 2,720 in.3 > 2,629 in.

3

Therefore, ignore flange per 11.6.1.1.

720,2000,4475.0Tu = = 516,084 in.-lbs = 43.0 ft-kips

It is assumed that the torsional loading on beam CD is uniformly distributed along the span.


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Torsion Design

Shear Forces and Bending Moments in Beam CD

( ) ( ) 00012323077150144

24520wD ,//

.

++

= = 2.2 kips/ft

( ) 000123250wL ,//= = 0.8 kips/ft

LDu w61w21w .. += = 3.9 kips/ft

This framing system satisfies the conditions for analysis by the coefficients of 8.3.3, as illustrated inFigure 2-2. Thus, use Figures 2-3, 2-4, and 2-7 to determine the maximum positive moment, negative

moment, and shear force in an interior span:

=

==+16

12

22249.3

16wM

2

2nu

u l 119.8 ft-kips

===11

168.119

11

wM

2nu

ul

174.3 ft-kips

==2

wV nuu

l43.2 kips

Adequacy of Cross-sectional Dimensions

For solid sections:

+

+

'

.c

w

c

2

2oh

hu2

w

u f8db

VA71pT

dbV

Using an average d = 20.5 2.5 = 18.0 in., the factored shear force at the critical section located ata distance d from the face of the support is = 37.4 kips. Also, the nominal shear strength provided by

the concrete is

uV

dbf2V wcc'= .

Assuming a 1.5-in. clear cover to No. 4 closed stirrups:

( )[ ] ( )[ ] 2oh in5348505122450512520A ....... ==

( )[ ] ( )[ ]{ } ...... in755051224505125202ph =+=

Therefore,

( ) psi474000,48275.0psi2075.3487.1

75000,120.43

1824

400,372

2

2

=+


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Torsion Design

where = 0.85oA2

ho .in2.2965.34885.0A ==

= 45

Therefore,

leg

.in/.in019.0

45cot000,602.296275.0

000,120.43

s

A 2t =

=

Transverse Reinforcement Required for Shear

( )0

18000,6075.0

983,40400,37

18000,6075.0

18244000275.0400,37

df

VV

s

A

yv

cuv ,minimum area of transverse reinforcement shall be provided per ACI 11.5.6.1.

Total Required Transverse Reinforcement

For 4,000-psi concrete, minimum transverse reinforcement for shear and torsion

= 019.0000,60

24000,475.0

f

bf75.0

yv

w'c == in.

2/in.

= = 0.020 in.2/in. (governs)000,60/2450f/b50 yvw =

Required transverse reinforcement

=+s

A2

s

A tvleg

.in/.in019.0legs20

2

+ = 0.038 in.2/in. > 0.020 in.2/in. OK.

Maximum spacing of transverse reinforcement

= = 75 / 8 = 9.4 in. < 12.0 in.8/ph

= = 18 / 2 = 9.0 in. (governs)2/d

Assuming No. 4 closed stirrups (area per leg = 0.2 in.2), the required spacing s at the critical section =0.2/0.019 = 10.5 in. < 9.0 in.

Provide No. 4 closed stirrups spaced at 9 in. on center at the critical section. In view of the shear andtorsion distribution along the span length, this same reinforcement and spacing can be provided from the

face of the support to a distance + d = 24 + 18 = 42 in. = 3.5 ft past the location where it is no longer

required.tb

Longitudinal Reinforcement Required for Torsion

222

y

yvh

t .in43.145cot60

6075019.0cot

f

fp

s

AA =

=

=

l

l


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Torsion Design

Minimum longitudinal reinforcement:

ll

l

y

yvh

t

y

cp'c

min, f

fp

s

A

f

Af5A

=

where = 0.019 in.2/in. > = 0.010 in.2/in.s/At 000,60/2425f/b25 yvw =

22min, .in43.1A.in17.160

6075019.0

000,60

492000,45A = 0.042 s = 0.38 in.).This bar distribution satisfies the maximum spacing requirement, since the spacing (20.5 3 1)/2 =8.25 in. < 12 in. Distribute the remaining steel required for torsion evenly between the top and bottom of

the section; thus, 0.5[1.43 (2 0.31)] = 0.41 in.2 will be added to the area of steel that is required for

flexure at both the top and bottom of the section.

Face of supportTotal top steel required = 2.42 + 0.41 = 2.83 in.2

For 4000-psi concrete, minimum = 1.44 in.2yws f/db200A =

Provide 3-No. 9 bars ( = 3.00 in.2) at top of section. This satisfies both minimum and maximum spacing

requirements for bars in a single layer (see Tables 3-2 and 3-3).sA


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Torsion Design

MidspanTotal bottom steel required = 1.66 + 0.41 = 2.07 in.2

Provide 3-No. 8 bars ( = 2.37 in.2) at bottom of section. This satisfies both minimum and maximum

spacing requirements for bars in a single layer (see Tables 3-2 and 3-3).sA

It can be shown that the section is tensioned-controlled.

Reinforcement Details

According to the provisions for structural integrity in 7.13, at least one-sixth of the tensionreinforcement required for negative moment at the support, but not less than 2 bars, and one-quarter of

the positive moment reinforcement at midspan, but not less than 2 bars, must be continuous and tied

with closed stirrups having not less than 135-deg hooks around the continuous top bars. Thus, at least 2of the 3-No. 9 top bars must be made continuous or spliced with a Class A splice or a mechanical or

welded splice satisfying 12.14.3 at midspan, and at least 2 of the 3-No. 8 bottom bars must be made

continuous or spliced with a Class A splice or a mechanical or welded splice satisfying 12.14.3 over thesupports. No. 4 closed stirrups spaced at 9 in. on center can also be used wherever torsion and shear

reinforcement is not required.

One of the 3-No. 9 bars at the top of the section can be theoretically cutoff at the location where thefactored bending moment is equal to the design moment strength of the section based on a total area of

steel equal to the area of 2-No. 9 bars ( = 2.00 in.2) minus the area of steel that is required for

torsion (0.41 in.2). Thus, with = 2.00 0.41 = 1.59 in.2,sA

sA nM = 125 ft-kips. The distance x from the

face of the support to where the factored bending moment = 125 ft-kips is obtained by summingmoments about the section at this location:uM

1253.174x2.43x2

9.3 2 =+

Solution of this equation gives x = 1.2 ft. The 1-No. 9 bar must extend a distance d = 18 in. or 12 =

= 13.5 in. beyond the distance x. Thus, from the face of the support, the total bar length must

be at least equal to 1.2 + (18/12) = 2.7 ft. Also, the bars must extend a full development length

bd

128.112

dl beyond

the face of the support. The development length for the No. 9 bar can be determined as follows:

b

b

tr'c

yd d

d

Kcf

f403

+=l

where reinforcement location factor = 1.3=

coating factor = 1.0=

= reinforcement size factor = 1.0

lightweight aggregate concrete factor = 1.0=


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Torsion Design

spacing or cover dimension ==c( )

=

+

=++

.in7.422

128.15.05.1224

)governs(.in6.25.15.02

128.1

= transverse reinforcement indextrK

= 0 (conservative)

5.23.2128.1

06.2

d

Kc

b

tr 2.7 ft

Thus, the total required length of the 1-No. 9 bar must extend at least 3.8 ft beyond the face of the

support.

The positive reinforcing bar cutoff location is determined in a similar manner. Assuming that 1 of the 3-

No. 8 bars will be terminated, the positive moment strength with an area of steel equal to (2 0.79)

0.41 = 1.17 in.2 is = 93 ft-kips. The distance from the centerline of the span to the location where

the factored moment = 93 ft-kips is 3.7 ft. Thus, the bar length on each side of the span centerline

must be at least equal to 3.7 + (18/12) = 5.2 ft, which is greater than the development length

sA

nM

uM

dl = 2.4 ft

(conservatively assuming = 0).trK

The following figure shows the reinforcement details for beam CD.

For comparison, output form pcaBeam program is also included on the following pages.


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Torsion Design


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Torsion Design

X

YZ

pcaBeam v2.00. Licensed to: PCA. License ID: 12345-1234567-4-2D2DE-2C8D0

File: C:\Data\Time Saving Design Aid\Torsion example.slb

Project: Torsion Example

Frame: Exterior Engineer: DAF


10/23


Torsion Design





CASE: SELF

CASE: Dead

CASE: Live

CASE: Wind

CASE: EQ

512.5 512.5 512.5 512.5 512.5

1712 1712 1712 1712 1712

800 800 800 800 800

35.83 35.83 35.83 35.83 35.83


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Torsion Design





Mo

mentDiagram-

k-ft-250.0

250.0

ShearDiagram-

kip

50.0

-50.0

TorsionDiagram-

k-ft

700.0

-700.0

LEGEND:Envelope

-160.62-204.87

107.14

-196.15 -193.56

99.63

-194.23 -194.23

100.39

-193.56 -196.15

99.63

-204.87-160.62

107.14

45.99

-49.43

48.09

-47.88

47.98

-47.98

47.88

-48.09

49.43

-45.99

601.94

-601.94

601.94

-601.94

601.94

-601.94

601.94

-601.94

601.94

-601.94


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Torsion Design





Beam Shear and Torsion Capacit y: Longitudinal Bar Area - in^2

Beam Shear and Torsion Capacity: Stirrup Intensity - in^2/in

0.05

7.0

LEGEND:Demand - (Av+2At)/sDemand - At/sDemand - Av/sDemand - AlProvided - (Av+2At)/sProvided - AlSupport CenterlineFace of SupportCritical Section

0.039

1.5

0.039

1.5

0.039

1.5

0.039

1.5

0.039

1.5

0.039

1.5

0.039

1.5

0.039

1.5

0.039

1.5

0.039

1.5


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Torsion Design





Transverse Reinforcement

32-#[email protected] 32-#[email protected] 32-#[email protected] 32-#[email protected] 32-#[email protected]


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Torsion Design





Flexural Reinforcement

2-#9(70.8

)

1-#9(34.5

)

2-#9(85.7

)

1-#9(42.9

)

2-#8(288.0

)c

1-#8(36.0

)

2-#9(85.7

)

1-#9(41.4

)

2-#9(85.7

)

1-#9(40.9

)

2-#9(85.7

)

1-#9(41.0

)

2-#9(85.7

)

1-#9(41.0

)

2-#8(288.0

)c

1-#8(36.0

)

2-#9(85.7

)

1-#9(40.9

)

2-#9(85.7

)

1-#9(41.4

)

2-#9(85.7

)

1-#9(42.9

)

2-#9(70.8

)

1-#9(34.5

)

2-#8(288.0

)c

1-#8(36.0

)

2-#8(288.0

)c

1-#8(36.0

)

2-#8(288.0

)c

1-#8(36.0

)


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Torsion Design

pcaBeam v2.00 Portland Cement Association 05-03-2007, 09:33:38 AMLicensed to: PCA, License ID: 12345-1234567-4-2D2DE-2C8D0C:\Data\Time Saving Design Aid\Torsion example.slb Page 1

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OOOOO OOOOOO OOOOO OO OOOO OO OO OO OO OOO OOOOO OO OO OO OO OO O O OOOO OO OO OO OO OO O O OOOOOOO OOOOO OOOOOOO OO O OOOO OO OO OO OO OO OOOO OO OO OO OO OO OOOO OO OO OO OO OO OOOOOOO OOOOOO OO OO OO OO

=============================================================================pcaBeam v2.00 (TM)

A Computer Program for Analysis, Design, and Investigation ofReinforced Concrete Beams and One-way Slab Systems

=============================================================================Copyright 1992-2006, Portland Cement Association

All rights reserved

Licensee stated above acknowledges that Portland Cement Association(PCA) is not and cannot be responsible for either the accuracy oradequacy of the material supplied as input for processing by thepcaBeam computer program. Furthermore, PCA neither makes any warrantyexpressed nor implied with respect to the correctness of the outputprepared by the pcaBeam program. Although PCA has endeavored toproduce pcaBeam error free the program is not and cannot be certifiedinfallible. The final and only responsibility for analysis, design andengineering documents is the licensees. Accordingly, PCA disclaims allresponsibility in contract, negligence or other tort for any analysis,design or engineering documents prepared in connection with the use ofthe pcaBeam program.

=============================================================================================[1] INPUT ECHO=============================================================================================General Information:====================

File name: C:\Data\Time Saving Design Aid\Torsion example.slbProject: Torsion ExampleFrame: ExteriorEngineer: DAFCode: ACI 318-02Reinforcement Database: ASTM A615Mode: DesignNumber of supports = 6Floor System: One-Way/Beam

Live load pattern ratio = 100%Deflections are based on cracked section properties.In negative moment regions, Ig and Mcr DO NOT include flange/slab contribution (if available)Long-term deflections are calculated for load duration of 60 months.0% of live load is sustained.Compression reinforcement calculations NOT selected.Moment redistribution NOT selected.

Effective flange width calculations selected.Rigid beam-column joint NOT selected.Torsion analysis and design selected.Stirrups in flanges (if available) NOT selected.Compatibility torsion selected.

Material Properties:====================

Slabs|Beams Columns------------ ------------

wc = 150 150 lb/ft3f'c = 4 4 ksiEc = 3834.3 3834.3 ksifr = 0.47434 0.47434 ksi

fy = 60 ksi, Bars are not epoxy-coatedfyv = 60 ksiEs = 29000 ksi


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Torsion Design


Reinforcement Database:===============

Units: Db (in), Ab (in^2), Wb (lb/ft)Size Db Ab Wb Size Db Ab Wb---- -------- -------- -------- ---- -------- -------- --------#3 0.38 0.11 0.38 #4 0.50 0.20 0.67#5 0.63 0.31 1.04 #6 0.75 0.44 1.50#7 0.88 0.60 2.04 #8 1.00 0.79 2.67#9 1.13 1.00 3.40 #10 1.27 1.27 4.30#11 1.41 1.56 5.31 #14 1.69 2.25 7.65#18 2.26 4.00 13.60

Span Data:==========

Slabs: L1, wL, wR (ft); t, bEff, Hmin (in)Span Loc L1 t wL wR bEff Hmin---- ---- -------- -------- -------- -------- -------- --------

1 Int 24.000 0.00 1.000 1.000 24.00 0.002 Int 24.000 0.00 1.000 1.000 24.00 0.003 Int 24.000 0.00 1.000 1.000 24.00 0.004 Int 24.000 0.00 1.000 1.000 24.00 0.005 Int 24.000 0.00 1.000 1.000 24.00 0.00

Ribs and Longitudinal Beams: b, h, Sp (in)__________Ribs____________ _______Beams_____ __Span__

Span b h Sp b h Hmin---- -------- -------- -------- -------- -------- --------

1 0.00 0.00 0.00 24.00 20.50 15.572 0.00 0.00 0.00 24.00 20.50 13.713 0.00 0.00 0.00 24.00 20.50 13.714 0.00 0.00 0.00 24.00 20.50 13.715 0.00 0.00 0.00 24.00 20.50 15.57

Support Data:=============

Columns: c1a, c2a, c1b, c2b (in); Ha, Hb (ft)Supp c1a c2a Ha c1b c2b Hb Red%---- -------- -------- -------- -------- -------- -------- ----

1 22.00 22.00 12.000 22.00 22.00 12.000 1002 22.00 22.00 12.000 22.00 22.00 12.000 1003 22.00 22.00 12.000 22.00 22.00 12.000 1004 22.00 22.00 12.000 22.00 22.00 12.000 1005 22.00 22.00 12.000 22.00 22.00 12.000 1006 22.00 22.00 12.000 22.00 22.00 12.000 100

Boundary Conditions: Kz (kip/in); Kry (kip-in/rad)Supp Spring Kz Spring Kry Far End A Far End B---- ------------ ------------ --------- ---------

1 0 0 Fixed Fixed2 0 0 Fixed Fixed3 0 0 Fixed Fixed4 0 0 Fixed Fixed5 0 0 Fixed Fixed6 0 0 Fixed Fixed

Load Data:==========

Load Cases and Combinations:Case SELF Dead Live Wind EQType DEAD DEAD LIVE LATERAL LATERALU1 1.400 1.400 0.000 0.000 0.000U2 1.200 1.200 1.600 0.000 0.000U3 1.200 1.200 1.600 0.800 0.000U4 1.200 1.200 1.600 -0.800 0.000U5 1.200 1.200 1.000 1.600 0.000U6 1.200 1.200 1.000 -1.600 0.000U7 0.900 0.900 0.000 1.600 0.000U8 0.900 0.900 0.000 -1.600 0.000

U9 1.200 1.200 1.000 0.000 1.000U10 1.200 1.200 1.000 0.000 -1.000U11 0.900 0.900 0.000 0.000 1.000U12 0.900 0.900 0.000 0.000 -1.000

Span Loads:Span Case Wa La Wb Lb---- -------- ------------ ------------ ------------ ------------Line Loads - Wa | Wb (lb/ft), La | Lb (ft):

1 Dead 1712 0 1712 242 Dead 1712 0 1712 243 Dead 1712 0 1712 244 Dead 1712 0 1712 245 Dead 1712 0 1712 241 Live 800 0 800 242 Live 800 0 800 243 Live 800 0 800 244 Live 800 0 800 245 Live 800 0 800 24


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Torsion Design


Line Torque - Wa | Wb (k-ft/ft), La | Lb (ft):1 Dead 35.83 0 35.83 242 Dead 35.83 0 35.83 243 Dead 35.83 0 35.83 244 Dead 35.83 0 35.83 245 Dead 35.83 0 35.83 24

Support Loads: --- NONE ---

Support Displacements: --- NONE ---

Lateral Load Effects - M (k-ft):Span Case Mleft Mright---- -------- ------------ ------------

1 EQ 0 02 EQ 0 03 EQ 0 04 EQ 0 05 EQ 0 06 EQ 0 01 Wind 0 02 Wind 0 0

3 Wind 0 04 Wind 0 05 Wind 0 0

Reinforcement Criteria:=======================

_____Top bars___ ___Bottom bars__ ____Stirrups____Min Max Min Max Min Max

------- ------- ------- ------- ------- -------Slabs and Ribs:Bar Size #5 #8 #5 #8Bar spacing 1.00 18.00 1.00 18.00 inReinf ratio 0.14 5.00 0.14 5.00 %Cover 1.50 1.50 inTop bars have 12 in of concrete below them.

Beams:Bar Size #9 #9 #8 #8 #4 #4Bar spacing 1.00 18.00 1.00 18.00 6.00 18.00 inReinf ratio 0.14 5.00 0.14 5.00 %Cover 2.00 2.00 inSide cover 1.50 1.50 inLayer dist. 1.00 1.00 in

No. of legs 2 6Top bars have 12 in of concrete below them.

=============================================================================================[2] DESIGN RESULTS=============================================================================================Top Reinforcement:==================

Units: Width (ft), Mmax (k-ft), Xmax (ft), As (in^2), Sp (in)Span Zone Width Mmax Xmax AsMin AsMax SpReq AsReq Bars---- ------ -------- ------------ -------- -------- -------- -------- -------- -------

1 Left 2.00 120.12 0.917 1.435 7.775 9.308 1.537 3-#9 *5Middle 2.00 0.00 12.000 0.000 7.775 0.000 0.000 ---Right 2.00 161.22 23.083 1.435 7.775 9.308 2.087 3-#9

2 Left 2.00 153.72 0.917 1.435 7.775 9.308 1.985 3-#9 *5Middle 2.00 0.00 12.000 0.000 7.775 0.000 0.000 ---Right 2.00 151.32 23.083 1.435 7.775 9.308 1.953 3-#9 *5

3 Left 2.00 151.90 0.917 1.435 7.775 9.308 1.961 3-#9 *5Middle 2.00 0.00 12.000 0.000 7.775 0.000 0.000 ---

Right 2.00 151.90 23.083 1.435 7.775 9.308 1.961 3-#9 *5

4 Left 2.00 151.32 0.917 1.435 7.775 9.308 1.953 3-#9 *5Middle 2.00 0.00 12.000 0.000 7.775 0.000 0.000 ---Right 2.00 153.72 23.083 1.435 7.775 9.308 1.985 3-#9 *5

5 Left 2.00 161.22 0.917 1.435 7.775 9.308 2.087 3-#9Middle 2.00 0.00 12.000 0.000 7.775 0.000 0.000 ---Right 2.00 120.11 23.083 1.435 7.775 9.308 1.537 3-#9 *5

NOTES:*5 - Number of bars governed by maximum allowable spacing.

Top Bar Details:================

Units: Length (ft)_____________Left______________ ___Continuous__ _____________Right_____________

Span Bars Length Bars Length Bars Length Bars Length Bars Length---- ------- ------- ------- ------- ------- ------- ------- ------- ------- -------

1 2-#9 5.90 1-#9 2.88 --- 2-#9 7.14 1-#9 3.58


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Torsion Design


2 2-#9 7.14 1-#9 3.45 --- 2-#9 7.14 1-#9 3.41

3 2-#9 7.14 1-#9 3.42 --- 2-#9 7.14 1-#9 3.42

4 2-#9 7.14 1-#9 3.41 --- 2-#9 7.14 1-#9 3.45

5 2-#9 7.14 1-#9 3.58 --- 2-#9 5.90 1-#9 2.88

Bottom Reinforcement:=====================

Units: Width (ft), Mmax (k-ft), Xmax (ft), As (in^2), Sp (in)Span Width Mmax Xmax AsMin AsMax SpReq AsReq Bars---- -------- ------------ -------- -------- -------- -------- -------- -------

1 2.00 107.14 11.626 1.440 7.803 9.354 1.361 3-#8 *5

2 2.00 99.63 12.125 1.440 7.803 9.354 1.263 3-#8 *5

3 2.00 100.39 11.875 1.440 7.803 9.354 1.272 3-#8 *5

4 2.00 99.63 11.875 1.440 7.803 9.354 1.263 3-#8 *5

5 2.00 107.14 12.374 1.440 7.803 9.354 1.361 3-#8 *5NOTES:*5 - Number of bars governed by maximum allowable spacing.

Bottom Bar Details:===================

Units: Start (ft), Length (ft)_______Long Bars_______ ______Short Bars_______

Span Bars Start Length Bars Start Length---- ------- ------- ------- ------- ------- -------

1 2-#8 0.00 24.00 1-#8 10.13 3.00

2 2-#8 0.00 24.00 1-#8 10.62 3.00

3 2-#8 0.00 24.00 1-#8 10.37 3.00

4 2-#8 0.00 24.00 1-#8 10.37 3.00

5 2-#8 0.00 24.00 1-#8 10.87 3.00

Flexural Capacity:==================

Units: x (ft), As (in^2), PhiMn (k-ft)

Span x AsTop AsBot PhiMn- PhiMn+---- --------- ----- ----- ------------ ------------

1 0.000 3.00 1.58 -227.25 123.850.917 3.00 1.58 -227.25 123.850.918 3.00 1.58 -227.25 123.852.877 2.00 1.58 -154.81 123.853.939 2.00 1.58 -154.81 123.855.898 0.00 1.58 0.00 123.858.675 0.00 1.58 0.00 123.8510.125 0.00 1.58 0.00 123.8511.487 0.00 2.37 0.00 182.6811.766 0.00 2.37 0.00 182.6812.000 0.00 2.23 0.00 172.7113.127 0.00 1.58 0.00 123.8515.325 0.00 1.58 0.00 123.8516.856 0.00 1.58 0.00 123.8519.517 2.00 1.58 -154.81 123.8520.422 2.00 1.58 -154.81 123.8523.082 3.00 1.58 -227.25 123.8523.083 3.00 1.58 -227.25 123.8524.000 3.00 1.58 -227.25 123.85

2 0.000 3.00 1.58 -227.25 123.85

0.917 3.00 1.58 -227.25 123.850.918 3.00 1.58 -227.25 123.853.449 2.00 1.58 -154.81 123.854.612 2.00 1.58 -154.81 123.857.144 0.00 1.58 0.00 123.858.675 0.00 1.58 0.00 123.8510.624 0.00 1.58 0.00 123.8511.887 0.00 2.37 0.00 182.6812.000 0.00 2.37 0.00 182.6812.362 0.00 2.37 0.00 182.6813.626 0.00 1.58 0.00 123.8515.325 0.00 1.58 0.00 123.8516.856 0.00 1.58 0.00 123.8519.347 2.00 1.58 -154.81 123.8520.592 2.00 1.58 -154.81 123.8523.082 3.00 1.58 -227.25 123.8523.083 3.00 1.58 -227.25 123.8524.000 3.00 1.58 -227.25 123.85


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3 0.000 3.00 1.58 -227.25 123.850.917 3.00 1.58 -227.25 123.850.918 3.00 1.58 -227.25 123.853.418 2.00 1.58 -154.81 123.854.643 2.00 1.58 -154.81 123.857.144 0.00 1.58 0.00 123.858.675 0.00 1.58 0.00 123.8510.374 0.00 1.58 0.00 123.8511.648 0.00 2.37 0.00 182.6812.000 0.00 2.37 0.00 182.6812.103 0.00 2.37 0.00 182.6813.376 0.00 1.58 0.00 123.8515.325 0.00 1.58 0.00 123.8516.856 0.00 1.58 0.00 123.8519.357 2.00 1.58 -154.81 123.8520.582 2.00 1.58 -154.81 123.8523.082 3.00 1.58 -227.25 123.8523.083 3.00 1.58 -227.25 123.8524.000 3.00 1.58 -227.25 123.85

4 0.000 3.00 1.58 -227.25 123.850.917 3.00 1.58 -227.25 123.85

0.918 3.00 1.58 -227.25 123.853.408 2.00 1.58 -154.81 123.854.653 2.00 1.58 -154.81 123.857.144 0.00 1.58 0.00 123.858.675 0.00 1.58 0.00 123.8510.374 0.00 1.58 0.00 123.8511.638 0.00 2.37 0.00 182.6812.000 0.00 2.37 0.00 182.6812.113 0.00 2.37 0.00 182.6813.376 0.00 1.58 0.00 123.8515.325 0.00 1.58 0.00 123.8516.856 0.00 1.58 0.00 123.8519.388 2.00 1.58 -154.81 123.8520.551 2.00 1.58 -154.81 123.8523.082 3.00 1.58 -227.25 123.8523.083 3.00 1.58 -227.25 123.8524.000 3.00 1.58 -227.25 123.85

5 0.000 3.00 1.58 -227.25 123.850.917 3.00 1.58 -227.25 123.850.918 3.00 1.58 -227.25 123.853.578 2.00 1.58 -154.81 123.854.483 2.00 1.58 -154.81 123.85

7.144 0.00 1.58 0.00 123.858.675 0.00 1.58 0.00 123.8510.873 0.00 1.58 0.00 123.8512.000 0.00 2.23 0.00 172.7112.234 0.00 2.37 0.00 182.6812.513 0.00 2.37 0.00 182.6813.875 0.00 1.58 0.00 123.8515.325 0.00 1.58 0.00 123.8518.102 0.00 1.58 0.00 123.8520.061 2.00 1.58 -154.81 123.8521.123 2.00 1.58 -154.81 123.8523.082 3.00 1.58 -227.25 123.8523.083 3.00 1.58 -227.25 123.8524.000 3.00 1.58 -227.25 123.85

Longitudinal Beam Shear And Torsion Reinforcement Required:===========================================================

Section properties:Units: d, pcp, pch (in), Acp, Ach, Ao (in^2)

PhiVc (kip), PhiTcr (k-ft), PhiSvt (ksi)Span d pcp ph Acp Aoh Ao PhiVc PhiTcr PhiSvt---- -------- -------- -------- ---------- ---------- ---------- -------- -------- --------

1 17.94 89.00 75.00 492.000 348.500 296.225 40.84 43.00 0.474

2 17.94 89.00 75.00 492.000 348.500 296.225 40.84 43.00 0.4743 17.94 89.00 75.00 492.000 348.500 296.225 40.84 43.00 0.4744 17.94 89.00 75.00 492.000 348.500 296.225 40.84 43.00 0.4745 17.94 89.00 75.00 492.000 348.500 296.225 40.84 43.00 0.474

Required transverse reinforcement:Units: Start, End, Xu (ft), Vu (kip), Tu (k-ft), vf (ksi)

Av/s, Av/s, A(v+2t)/s (in^2/in)Span Start End Vu Tu vf Xu Case/Patt Av/s At/s A(v+2t)/s---- -------- -------- -------- -------- -------- -------- --------- -------- -------- ---------

1 2.411 5.151 28.29 43.00 0.199 2.41 U1/All 0.0000 0.0194 0.0387 *45.151 7.891 19.76 43.00 0.193 5.15 U1/All 0.0000 0.0194 0.0387 *47.891 10.630 11.23 43.00 0.189 7.89 U1/All 0.0000 0.0194 0.0387 *410.630 13.370 5.84 43.00 0.188 13.37 U1/All 0.0000 0.0194 0.0387 *4 *513.370 16.109 14.37 43.00 0.190 16.11 U1/All 0.0000 0.0194 0.0387 *416.109 18.849 22.90 43.00 0.195 18.85 U1/All 0.0000 0.0194 0.0387 *418.849 21.589 31.43 43.00 0.201 21.59 U1/All 0.0000 0.0194 0.0387 *4

2 2.411 5.151 29.98 43.00 0.200 2.41 U1/All 0.0000 0.0194 0.0387 *4


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5.151 7.891 21.45 43.00 0.194 5.15 U1/All 0.0000 0.0194 0.0387 *47.891 10.630 12.92 43.00 0.190 7.89 U1/All 0.0000 0.0194 0.0387 *410.630 13.370 4.39 43.00 0.188 10.63 U1/All 0.0000 0.0194 0.0387 *4 *513.370 16.109 12.68 43.00 0.190 16.11 U1/All 0.0000 0.0194 0.0387 *416.109 18.849 21.21 43.00 0.194 18.85 U1/All 0.0000 0.0194 0.0387 *418.849 21.589 29.74 43.00 0.200 21.59 U1/All 0.0000 0.0194 0.0387 *4




NOTES:*4 - Design torsional moment reduced to PhiTcr due to compatibility torsion.*5 - Minimum transverse (stirrup) reinforcement required.

Required longitudinal reinforcement:Units: Start, End, Xu (ft), Tu (k-ft), Al (in^2)Span Start End Tu Xu Case/Patt Al---- -------- -------- -------- -------- --------- --------

1 2.411 5.151 43.00 2.41 U1/All 1.452 *45.151 7.891 43.00 5.15 U1/All 1.452 *47.891 10.630 43.00 7.89 U1/All 1.452 *410.630 13.370 18.74 11.63 U1/All 1.843 *4 *513.370 16.109 43.00 13.37 U1/All 1.452 *416.109 18.849 43.00 16.11 U1/All 1.452 *418.849 21.589 43.00 18.85 U1/All 1.452 *4



4 2.411 5.151 43.00 2.41 U1/All 1.452 *45.151 7.891 43.00 5.15 U1/All 1.452 *47.891 10.630 43.00 7.89 U1/All 1.452 *410.630 13.370 18.74 11.63 U1/All 1.843 *4 *513.370 16.109 43.00 13.37 U1/All 1.452 *416.109 18.849 43.00 16.11 U1/All 1.452 *4

18.849 21.589 43.00 18.85 U1/All 1.452 *4


NOTES:*4 - Design torsional moment reduced to PhiTcr due to compatibility torsion.*5 - Minimum longitudinal reinforcement required.

Longitudinal Beam Shear Reinforcement Details:==============================================

Units: spacing & distance (in).Span Size Stirrups (2 legs each unless otherwise noted)---- ---- ---------------------------------------------

1 #4 32 @ 8.4


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2 #4 32 @ 8.43 #4 32 @ 8.44 #4 32 @ 8.45 #4 32 @ 8.4

Longitudinal Torsional Reinforcement Details:==============================================

Units: Start (ft), Length (ft)_______Long Bars_______ ______Short Bars_______

Span Bars Start Length Bars Start Length---- ------- ------- ------- ------- ------- -------

1 --- 8-#8 0.00 13.00--- 8-#8 11.00 13.00

2 --- 8-#8 0.00 13.00--- 8-#8 11.00 13.00

3 --- 8-#8 0.00 13.00--- 8-#8 11.00 13.00

4 --- 8-#8 0.00 13.00--- 8-#8 11.00 13.00

5 --- 8-#8 0.00 13.00--- 8-#8 11.00 13.00

Beam Shear And Torsion Capacity:================================

Section properties:Units: d, pcp, pch (in), Acp, Ach, Ao (in^2)

PhiVc (kip), PhiTcr (k-ft), PhiSvt (ksi)Span d pcp ph Acp Aoh Ao PhiVc PhiTcr PhiSvt---- -------- -------- -------- ---------- ---------- ---------- -------- -------- --------

1 17.94 89.00 75.00 492.000 348.500 296.225 40.84 43.00 0.4742 17.94 89.00 75.00 492.000 348.500 296.225 40.84 43.00 0.4743 17.94 89.00 75.00 492.000 348.500 296.225 40.84 43.00 0.4744 17.94 89.00 75.00 492.000 348.500 296.225 40.84 43.00 0.4745 17.94 89.00 75.00 492.000 348.500 296.225 40.84 43.00 0.474

Beam shear and torsion transverse reinforcement capacity in terms of provided and required area:Units: Start, End, Xu (ft), Sp (in), A(v+2t)/s (in^2/in)

Vu (kip), Tu (k-ft), vf (ksi)___________________Provided__________________ _______________________Required________________________

Span Start End A(v+2t) Sp A(v+2t)/s Xu Vu Tu Case/Patt vf A(v+2t)/s---- -------- -------- -------- -------- --------- -------- -------- -------- --------- -------- ---------

1 0.000 1.167 ----- ----- ------ 0.00 45.40 43.00 U2/All 0.22 0.0444 *41.167 11.875 0.400 8.39 0.0477 2.41 28.29 43.00 U1/All 0.20 0.0387 *4 *511.875 12.125 0.400 8.39 0.0477 12.12 1.96 6.25 U1/All 0.03 0.0000 *212.125 22.833 0.400 8.39 0.0477 21.59 31.43 43.00 U1/All 0.20 0.0387 *4 *5

22.833 24.000 ----- ----- ------ 24.00 49.38 43.00 U2/All 0.22 0.0493 *4

2 0.000 1.167 ----- ----- ------ 0.00 47.55 43.00 U2/All 0.22 0.0470 *41.167 11.875 0.400 8.39 0.0477 2.41 29.98 43.00 U1/All 0.20 0.0387 *4 *511.875 12.125 0.400 8.39 0.0477 11.88 0.51 6.25 U1/All 0.03 0.0000 *212.125 22.833 0.400 8.39 0.0477 21.59 29.74 43.00 U1/All 0.20 0.0387 *4 *522.833 24.000 ----- ----- ------ 24.00 47.24 43.00 U2/All 0.22 0.0466 *4



5 0.000 1.167 ----- ----- ------ 0.00 49.38 43.00 U2/All 0.22 0.0493 *41.167 11.875 0.400 8.39 0.0477 2.41 31.43 43.00 U1/All 0.20 0.0387 *4 *511.875 12.125 0.400 8.39 0.0477 11.88 1.96 6.25 U1/All 0.03 0.0000 *2

12.125 22.833 0.400 8.39 0.0477 21.59 28.29 43.00 U1/All 0.20 0.0387 *4 *522.833 24.000 ----- ----- ------ 24.00 45.40 43.00 U2/All 0.22 0.0444 *4NOTES:*2 - Torsion ignored (Tu < PhiTcr/4).*4 - Design torsional moment reduced to PhiTcr due to compatibility torsion.*5 - Minimum transverse (stirrup) reinforcement required.

Beam torsion longitudinal reinforcement capacity in terms of provided and required area:Units: Start, End, Xu (ft), Al (in^2), Tu (kip)

_________Provided_________ _____________Required_______________Span Start End Al Xu Tu Case/Patt Al---- -------- -------- -------- -------- -------- --------- --------

1 0.000 1.167 ----- 0.00 43.00 U2/All 1.452 *41.167 11.875 6.320 11.63 18.74 U1/All 1.843 *4 *511.875 12.125 ----- 11.88 6.25 U1/All 0.000 *212.125 22.833 6.320 12.37 18.74 U1/All 1.843 *4 *522.833 24.000 ----- 22.83 43.00 U2/All 1.452 *4

2 0.000 1.167 ----- 0.00 43.00 U2/All 1.452 *4


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1.167 11.875 6.320 11.63 18.74 U1/All 1.843 *4 *511.875 12.125 ----- 11.88 6.25 U1/All 0.000 *212.125 22.833 6.320 12.37 18.74 U1/All 1.843 *4 *522.833 24.000 ----- 22.83 43.00 U2/All 1.452 *4




NOTES:*2 - Torsion ignored (Tu < PhiTcr/4).*4 - Design torsional moment reduced to PhiTcr due to compatibility torsion.*5 - Minimum longitudinal reinforcement required.

Slab Shear Capacity:====================

Units: b, d (in), Xu (ft), PhiVc, Vu(kip)Span b d Vratio PhiVc Vu Xu---- -------- -------- -------- ------------ ------------ ------------

1 --- Not checked ---2 --- Not checked ---3 --- Not checked ---4 --- Not checked ---5 --- Not checked ---

Deflections:============

Section properties------------------Units: Ig, Icr, Ie (in^4), Mcr, Mmax (k-ft) ________________Load Level_______________

________Ie,avg_________ _________Dead_______ ______Dead+Live_____Span Dead Dead+Live Zone Ig Icr Mcr Mmax Ie Mmax Ie

---- ----------- ----------- ------ ----------- ----------- -------- -------- ----------- -------- -----------1 15725 10689 Middle 17230 3996 66.45 58.89 17230 80.07 11560

Right 17230 4797 66.45 -115.00 7195 -156.35 57512 14389 11863 Left 17230 4797 66.45 -108.21 7675 -147.13 5942

Middle 17230 3996 66.45 52.98 17230 72.03 14386Right 17230 4797 66.45 -106.15 7846 -144.33 6010

3 14401 11683 Left 17230 4797 66.45 -106.71 7798 -145.09 5991Middle 17230 3996 66.45 53.43 17230 72.65 14122Right 17230 4797 66.45 -106.71 7798 -145.09 5991

4 14389 11863 Left 17230 4797 66.45 -106.15 7846 -144.33 6010Middle 17230 3996 66.45 52.98 17230 72.03 14386Right 17230 4797 66.45 -108.21 7675 -147.13 5942

5 15725 10689 Left 17230 4797 66.45 -115.00 7195 -156.35 5751Middle 17230 3996 66.45 58.89 17230 80.07 11560

Maximum Instantaneous Deflections---------------------------------Units: D (in)Span Ddead Dlive Dtotal---- -------- -------- --------

1 0.064 0.050 0.1142 0.057 0.033 0.0903 0.058 0.035 0.092

4 0.057 0.033 0.0905 0.064 0.050 0.114

Maximum Long-term Deflections-----------------------------Time dependant factor for sustained loads = 2.000Units: D (in)Span Dsust Lambda Dcs Dcs+lu Dcs+l Dtotal---- -------- ------ -------- -------- -------- --------

1 0.064 2.000 0.128 0.178 0.178 0.2422 0.057 2.000 0.114 0.147 0.147 0.2043 0.058 2.000 0.115 0.150 0.150 0.2084 0.057 2.000 0.114 0.147 0.147 0.2045 0.064 2.000 0.128 0.178 0.178 0.242

Material Takeoff:=================

Reinforcement in the Direction of Analysis------------------------------------------


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Torsion Design


Top Bars: 582.6 lb 4.85 lb/ft 2.427 lb/ft^2Bottom Bars: 680.9 lb 5.67 lb/ft 2.837 lb/ft^2Torsion Bars: 2776.7 lb 23.14 lb/ft 11.569 lb/ft^2Stirrups: 2057.4 lb 17.15 lb/ft 8.573 lb/ft^2Total Steel: 6097.6 lb 50.81 lb/ft 25.407 lb/ft^2Concrete: 410.0 ft^3 3.42 ft^3/ft 1.708 ft^3/ft^2

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