# torsion design - the portland cement...

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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 x Concrete: normal weight (150 pcf), f’ c = 4,000 psi x Mild reinforcing steel: Grade 60 (f y = 60,000 psi) Loads x Dead load of joists = 77 psf

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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), f’c = 4,000 psi

Mild reinforcing steel: Grade 60 (fy = 60,000 psi)

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Torsion Design

Typical bay size = 24 × 32 ft (5 bays in N-S direction, 3 bays in E-W direction)

Typical story height = 12 ft

Factored 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:

⎟⎟

⎜⎜

⎛φ=

cp

2cp

cu pA

f4T '

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

⎟⎟

⎜⎜

⎛φ=

cp

2cp'

c,minu pA

fT

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 ( ) (20.5×24 + 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 in Figure 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:

=⎟⎠⎞

⎜⎝⎛ −×

==+

161222249.3

16wM

2

2nu

ul 119.8 ft-kips

=×==−

11168.119

11wM

2nu

ul

174.3 ft-kips

==2

wV nuu

l 43.2 kips

For solid sections:

⎟⎟⎠

⎞⎜⎜⎝

⎛+φ≤⎟

⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎞⎜⎜⎝

⎛ '

. cw

c2

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 at a 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

75000,120.431824

400,37 2

2

2=+×<=⎟

⎞⎜⎝

⎛×

××+⎟

⎠⎞

⎜⎝⎛

×, OK.

Transverse Reinforcement Required for Torsion

θφ=

cotfA2T

sA

yvo

ut

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Torsion Design

where = 0.85 oA 2ho .in2.2965.34885.0A =×=

°=θ 45

Therefore,

leg.in/.in019.0

45cot000,602.296275.0000,120.43

sA 2

t =°××××

×=

Transverse Reinforcement Required for Shear

( ) 018000,6075.0

983,40400,3718000,6075.0

18244000275.0400,37dfVV

sA

yv

cuv <××

−=

×××××−

φ−=

No transverse reinforcement for shear is required because cu VV φ< . However, since cu V5.0V φ> , 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

24000,475.0fbf75.0yv

w'c == in.2/in.

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

Required transverse reinforcement

=+s

A2s

A tvleg

.in/.in019.0legs202

×+ = 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 and torsion 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 .in43.145cot606075019.0cot

ff

ps

AA =°×⎟⎠⎞

⎜⎝⎛××=θ⎟

⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛=

ll

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Torsion Design

Minimum longitudinal reinforcement:

lll

y

yvh

t

y

cp'c

min, ff

ps

Af

Af5A ⎟

⎠⎞

⎜⎝⎛−=

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

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

606075019.0

000,60492000,45A =<=⎟

⎠⎞

⎜⎝⎛ ××−

×= ll

Use = 1.43 in.2 lA

Longitudinal Reinforcement Required for Flexure

The required is given in the table below, assuming rectangular section behavior and an average d = 18 in.

sA

Required Longitudinal Reinforcement for Flexure

Location uM

(ft-kips)

d4/MA us =

(in.2)

Support 174.3 2.42

Midspan 119.8 1.66

Total Required Longitudinal Reinforcement

The longitudinal reinforcement that is required for torsion will be combined with the longitudinal reinforcement that is required for flexure.

The longitudinal torsional reinforcement must be distributed around the perimeter of the section with a maximum spacing of 12 in. In order to have a uniform distribution of reinforcement around the perimeter, assign approximately one-quarter of (=lA 43.125.0 × = 0.36 in.2) to each face.

Use 1-No. 5 bar on each side (area = 0.31 in.2 ≅ 0.36 in.2, bar diameter = 0.625 in. > 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 support

Total top steel required = 2.42 + 0.41 = 2.83 in.2

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

Midspan

Total 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 tension reinforcement 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 2 of 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 the supports. 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 the factored 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 nMφ = 125 ft-kips. The distance x from the face of the support to where the factored bending moment = 125 ft-kips is obtained by summing moments about the section at this location:

uM

1253.174x2.43x29.3 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

dKcf

f403

⎟⎟⎟⎟⎟⎟

⎜⎜⎜⎜⎜⎜

⎟⎟

⎜⎜

⎛ +

αβγλ=l

where reinforcement location factor = 1.3 =α

coating factor = 1.0 =β

=γ reinforcement size factor = 1.0

lightweight aggregate concrete factor = 1.0 =λ

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Torsion Design

spacing or cover dimension = =c( )

⎪⎪

⎪⎪

−+−

=++

.in7.422

128.15.05.1224

)governs(.in6.25.15.02128.1

= transverse reinforcement index trK

= 0 (conservative)

5.23.2128.1

06.2dKcb

tr <=+

=+

Therefore,

=⎟⎟⎠

⎞⎜⎜⎝

⎛ ×××= 128.1

3.20.10.10.13.1

000,4000,60

403

dl 45.4 in. = 3.8 ft > 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

nMφ

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

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

Project: Torsion Example

Frame: Exterior Engineer: DAF

TIME SAVING DESIGN AID

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Torsion Design

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

Project: Torsion Example

Frame: Exterior Engineer: DAF

CASE: SELF

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

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

Project: Torsion Example

Frame: Exterior Engineer: DAF

Mom

ent D

iagr

am -

k-ft

-250.0

250.0

She

ar D

iagr

am -

kip

50.0

-50.0

Tors

ion

Dia

gram

- 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

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

Project: Torsion Example

Frame: Exterior Engineer: DAF

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)/s Demand - At/s Demand - Av/s Demand - Al Provided - (Av+2At)/s Provided - Al Support Centerline Face of Support Critical 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

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

Project: Torsion Example

Frame: Exterior Engineer: DAF

Transverse Reinforcement

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Torsion Design

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

Project: Torsion Example

Frame: Exterior Engineer: DAF

Flexural Reinforcement

2-#9

(70.

8)1-

#9(3

4.5)

2-#9

(85.

7)1-

#9(4

2.9)

2-#8

(288

.0)c

1-#8

(36.

0)

2-#9

(85.

7)1-

#9(4

1.4)

2-#9

(85.

7)1-

#9(4

0.9)

2-#9

(85.

7)1-

#9(4

1.0)

2-#9

(85.

7)1-

#9(4

1.0)

2-#8

(288

.0)c

1-#8

(36.

0)

2-#9

(85.

7)1-

#9(4

0.9)

2-#9

(85.

7)1-

#9(4

1.4)

2-#9

(85.

7)1-

#9(4

2.9)

2-#9

(70.

8)1-

#9(3

4.5)

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-2C8D0 C:\Data\Time Saving Design Aid\Torsion example.slb Page 1

ooooooo oooooo ooooo oooooooo oooooooo ooooooo oo oo oo oo oo oo oo oo oo oo oo oooooooo oo ooooooo ooooo ooooooo oo oo ooooooo ooooo oo oo oo oo oo oo oooooooo oo oo oo oooooo oo oo OOOOO OOOOOO OOOOO OO OO OO OO OO OO OO OOO OOO OO OO OO OO OO OO O O OO OO OO OO OO OO OO O O OO OOOOO OOOOO OOOOOOO OO O OO OO OO OO OO OO OO OO OO OO OO OO OO OO OO OO OO OO OO OO OO OO OOOOO OOOOOO OO OO OO OO ============================================================================= pcaBeam v2.00 (TM) A Computer Program for Analysis, Design, and Investigation of Reinforced 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 or adequacy of the material supplied as input for processing by the pcaBeam computer program. Furthermore, PCA neither makes any warranty expressed nor implied with respect to the correctness of the output prepared by the pcaBeam program. Although PCA has endeavored to produce pcaBeam error free the program is not and cannot be certified infallible. The final and only responsibility for analysis, design and engineering documents is the licensees. Accordingly, PCA disclaims all responsibility in contract, negligence or other tort for any analysis, design or engineering documents prepared in connection with the use of the pcaBeam program. =============================================================================================[1] INPUT ECHO============================================================================================= General Information:==================== File name: C:\Data\Time Saving Design Aid\Torsion example.slb Project: Torsion Example Frame: Exterior Engineer: DAF Code: ACI 318-02 Reinforcement Database: ASTM A615 Mode: Design Number of supports = 6 Floor 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/ft3 f'c = 4 4 ksi Ec = 3834.3 3834.3 ksi fr = 0.47434 0.47434 ksi fy = 60 ksi, Bars are not epoxy-coated fyv = 60 ksi Es = 29000 ksi

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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-2C8D0 C:\Data\Time Saving Design Aid\Torsion example.slb Page 2

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 0.00 2 Int 24.000 0.00 1.000 1.000 24.00 0.00 3 Int 24.000 0.00 1.000 1.000 24.00 0.00 4 Int 24.000 0.00 1.000 1.000 24.00 0.00 5 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 15.57 2 0.00 0.00 0.00 24.00 20.50 13.71 3 0.00 0.00 0.00 24.00 20.50 13.71 4 0.00 0.00 0.00 24.00 20.50 13.71 5 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 12.000 100 2 22.00 22.00 12.000 22.00 22.00 12.000 100 3 22.00 22.00 12.000 22.00 22.00 12.000 100 4 22.00 22.00 12.000 22.00 22.00 12.000 100 5 22.00 22.00 12.000 22.00 22.00 12.000 100 6 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 Fixed 2 0 0 Fixed Fixed 3 0 0 Fixed Fixed 4 0 0 Fixed Fixed 5 0 0 Fixed Fixed 6 0 0 Fixed Fixed Load Data:========== Load Cases and Combinations: Case SELF Dead Live Wind EQ Type DEAD DEAD LIVE LATERAL LATERAL U1 1.400 1.400 0.000 0.000 0.000 U2 1.200 1.200 1.600 0.000 0.000 U3 1.200 1.200 1.600 0.800 0.000 U4 1.200 1.200 1.600 -0.800 0.000 U5 1.200 1.200 1.000 1.600 0.000 U6 1.200 1.200 1.000 -1.600 0.000 U7 0.900 0.900 0.000 1.600 0.000 U8 0.900 0.900 0.000 -1.600 0.000 U9 1.200 1.200 1.000 0.000 1.000 U10 1.200 1.200 1.000 0.000 -1.000 U11 0.900 0.900 0.000 0.000 1.000 U12 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 24 2 Dead 1712 0 1712 24 3 Dead 1712 0 1712 24 4 Dead 1712 0 1712 24 5 Dead 1712 0 1712 24 1 Live 800 0 800 24 2 Live 800 0 800 24 3 Live 800 0 800 24 4 Live 800 0 800 24 5 Live 800 0 800 24

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pcaBeam v2.00 © Portland Cement Association 05-03-2007, 09:33:38 AMLicensed to: PCA, License ID: 12345-1234567-4-2D2DE-2C8D0 C:\Data\Time Saving Design Aid\Torsion example.slb Page 3

Line Torque - Wa | Wb (k-ft/ft), La | Lb (ft): 1 Dead 35.83 0 35.83 24 2 Dead 35.83 0 35.83 24 3 Dead 35.83 0 35.83 24 4 Dead 35.83 0 35.83 24 5 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 0 2 EQ 0 0 3 EQ 0 0 4 EQ 0 0 5 EQ 0 0 6 EQ 0 0 1 Wind 0 0 2 Wind 0 0 3 Wind 0 0 4 Wind 0 0 5 Wind 0 0 Reinforcement Criteria:======================= _____Top bars___ ___Bottom bars__ ____Stirrups____ Min Max Min Max Min Max ------- ------- ------- ------- ------- ------- Slabs and Ribs: Bar Size #5 #8 #5 #8 Bar spacing 1.00 18.00 1.00 18.00 in Reinf ratio 0.14 5.00 0.14 5.00 % Cover 1.50 1.50 in Top bars have 12 in of concrete below them. Beams: Bar Size #9 #9 #8 #8 #4 #4 Bar spacing 1.00 18.00 1.00 18.00 6.00 18.00 in Reinf ratio 0.14 5.00 0.14 5.00 % Cover 2.00 2.00 in Side cover 1.50 1.50 in Layer dist. 1.00 1.00 in No. of legs 2 6 Top 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 *5 Middle 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 *5 Middle 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 *5 Middle 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 *5 Middle 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-#9 Middle 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

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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 *5 NOTES: *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 -227.25 123.85 0.917 3.00 1.58 -227.25 123.85 0.918 3.00 1.58 -227.25 123.85 2.877 2.00 1.58 -154.81 123.85 3.939 2.00 1.58 -154.81 123.85 5.898 0.00 1.58 0.00 123.85 8.675 0.00 1.58 0.00 123.85 10.125 0.00 1.58 0.00 123.85 11.487 0.00 2.37 0.00 182.68 11.766 0.00 2.37 0.00 182.68 12.000 0.00 2.23 0.00 172.71 13.127 0.00 1.58 0.00 123.85 15.325 0.00 1.58 0.00 123.85 16.856 0.00 1.58 0.00 123.85 19.517 2.00 1.58 -154.81 123.85 20.422 2.00 1.58 -154.81 123.85 23.082 3.00 1.58 -227.25 123.85 23.083 3.00 1.58 -227.25 123.85 24.000 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 -227.25 123.85 0.918 3.00 1.58 -227.25 123.85 3.449 2.00 1.58 -154.81 123.85 4.612 2.00 1.58 -154.81 123.85 7.144 0.00 1.58 0.00 123.85 8.675 0.00 1.58 0.00 123.85 10.624 0.00 1.58 0.00 123.85 11.887 0.00 2.37 0.00 182.68 12.000 0.00 2.37 0.00 182.68 12.362 0.00 2.37 0.00 182.68 13.626 0.00 1.58 0.00 123.85 15.325 0.00 1.58 0.00 123.85 16.856 0.00 1.58 0.00 123.85 19.347 2.00 1.58 -154.81 123.85 20.592 2.00 1.58 -154.81 123.85 23.082 3.00 1.58 -227.25 123.85 23.083 3.00 1.58 -227.25 123.85 24.000 3.00 1.58 -227.25 123.85

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Torsion Design

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3 0.000 3.00 1.58 -227.25 123.85 0.917 3.00 1.58 -227.25 123.85 0.918 3.00 1.58 -227.25 123.85 3.418 2.00 1.58 -154.81 123.85 4.643 2.00 1.58 -154.81 123.85 7.144 0.00 1.58 0.00 123.85 8.675 0.00 1.58 0.00 123.85 10.374 0.00 1.58 0.00 123.85 11.648 0.00 2.37 0.00 182.68 12.000 0.00 2.37 0.00 182.68 12.103 0.00 2.37 0.00 182.68 13.376 0.00 1.58 0.00 123.85 15.325 0.00 1.58 0.00 123.85 16.856 0.00 1.58 0.00 123.85 19.357 2.00 1.58 -154.81 123.85 20.582 2.00 1.58 -154.81 123.85 23.082 3.00 1.58 -227.25 123.85 23.083 3.00 1.58 -227.25 123.85 24.000 3.00 1.58 -227.25 123.85

4 0.000 3.00 1.58 -227.25 123.85 0.917 3.00 1.58 -227.25 123.85 0.918 3.00 1.58 -227.25 123.85 3.408 2.00 1.58 -154.81 123.85 4.653 2.00 1.58 -154.81 123.85 7.144 0.00 1.58 0.00 123.85 8.675 0.00 1.58 0.00 123.85 10.374 0.00 1.58 0.00 123.85 11.638 0.00 2.37 0.00 182.68 12.000 0.00 2.37 0.00 182.68 12.113 0.00 2.37 0.00 182.68 13.376 0.00 1.58 0.00 123.85 15.325 0.00 1.58 0.00 123.85 16.856 0.00 1.58 0.00 123.85 19.388 2.00 1.58 -154.81 123.85 20.551 2.00 1.58 -154.81 123.85 23.082 3.00 1.58 -227.25 123.85 23.083 3.00 1.58 -227.25 123.85 24.000 3.00 1.58 -227.25 123.85

5 0.000 3.00 1.58 -227.25 123.85 0.917 3.00 1.58 -227.25 123.85 0.918 3.00 1.58 -227.25 123.85 3.578 2.00 1.58 -154.81 123.85 4.483 2.00 1.58 -154.81 123.85 7.144 0.00 1.58 0.00 123.85 8.675 0.00 1.58 0.00 123.85 10.873 0.00 1.58 0.00 123.85 12.000 0.00 2.23 0.00 172.71 12.234 0.00 2.37 0.00 182.68 12.513 0.00 2.37 0.00 182.68 13.875 0.00 1.58 0.00 123.85 15.325 0.00 1.58 0.00 123.85 18.102 0.00 1.58 0.00 123.85 20.061 2.00 1.58 -154.81 123.85 21.123 2.00 1.58 -154.81 123.85 23.082 3.00 1.58 -227.25 123.85 23.083 3.00 1.58 -227.25 123.85 24.000 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 0.474 3 17.94 89.00 75.00 492.000 348.500 296.225 40.84 43.00 0.474 4 17.94 89.00 75.00 492.000 348.500 296.225 40.84 43.00 0.474 5 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 *4 5.151 7.891 19.76 43.00 0.193 5.15 U1/All 0.0000 0.0194 0.0387 *4 7.891 10.630 11.23 43.00 0.189 7.89 U1/All 0.0000 0.0194 0.0387 *4 10.630 13.370 5.84 43.00 0.188 13.37 U1/All 0.0000 0.0194 0.0387 *4 *5 13.370 16.109 14.37 43.00 0.190 16.11 U1/All 0.0000 0.0194 0.0387 *4 16.109 18.849 22.90 43.00 0.195 18.85 U1/All 0.0000 0.0194 0.0387 *4 18.849 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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Torsion Design

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5.151 7.891 21.45 43.00 0.194 5.15 U1/All 0.0000 0.0194 0.0387 *4 7.891 10.630 12.92 43.00 0.190 7.89 U1/All 0.0000 0.0194 0.0387 *4 10.630 13.370 4.39 43.00 0.188 10.63 U1/All 0.0000 0.0194 0.0387 *4 *5 13.370 16.109 12.68 43.00 0.190 16.11 U1/All 0.0000 0.0194 0.0387 *4 16.109 18.849 21.21 43.00 0.194 18.85 U1/All 0.0000 0.0194 0.0387 *4 18.849 21.589 29.74 43.00 0.200 21.59 U1/All 0.0000 0.0194 0.0387 *4

3 2.411 5.151 29.86 43.00 0.200 2.41 U1/All 0.0000 0.0194 0.0387 *4 5.151 7.891 21.33 43.00 0.194 5.15 U1/All 0.0000 0.0194 0.0387 *4 7.891 10.630 12.80 43.00 0.190 7.89 U1/All 0.0000 0.0194 0.0387 *4 10.630 13.370 4.27 43.00 0.188 10.63 U1/All 0.0000 0.0194 0.0387 *4 *5 13.370 16.109 12.80 43.00 0.190 16.11 U1/All 0.0000 0.0194 0.0387 *4 16.109 18.849 21.33 43.00 0.194 18.85 U1/All 0.0000 0.0194 0.0387 *4 18.849 21.589 29.86 43.00 0.200 21.59 U1/All 0.0000 0.0194 0.0387 *4

4 2.411 5.151 29.74 43.00 0.200 2.41 U1/All 0.0000 0.0194 0.0387 *4 5.151 7.891 21.21 43.00 0.194 5.15 U1/All 0.0000 0.0194 0.0387 *4 7.891 10.630 12.68 43.00 0.190 7.89 U1/All 0.0000 0.0194 0.0387 *4 10.630 13.370 4.39 43.00 0.188 13.37 U1/All 0.0000 0.0194 0.0387 *4 *5 13.370 16.109 12.92 43.00 0.190 16.11 U1/All 0.0000 0.0194 0.0387 *4 16.109 18.849 21.45 43.00 0.194 18.85 U1/All 0.0000 0.0194 0.0387 *4 18.849 21.589 29.98 43.00 0.200 21.59 U1/All 0.0000 0.0194 0.0387 *4

5 2.411 5.151 31.43 43.00 0.201 2.41 U1/All 0.0000 0.0194 0.0387 *4 5.151 7.891 22.90 43.00 0.195 5.15 U1/All 0.0000 0.0194 0.0387 *4 7.891 10.630 14.37 43.00 0.190 7.89 U1/All 0.0000 0.0194 0.0387 *4 10.630 13.370 5.84 43.00 0.188 10.63 U1/All 0.0000 0.0194 0.0387 *4 *5 13.370 16.109 11.23 43.00 0.189 16.11 U1/All 0.0000 0.0194 0.0387 *4 16.109 18.849 19.76 43.00 0.193 18.85 U1/All 0.0000 0.0194 0.0387 *4 18.849 21.589 28.29 43.00 0.199 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 *4 5.151 7.891 43.00 5.15 U1/All 1.452 *4 7.891 10.630 43.00 7.89 U1/All 1.452 *4 10.630 13.370 18.74 11.63 U1/All 1.843 *4 *5 13.370 16.109 43.00 13.37 U1/All 1.452 *4 16.109 18.849 43.00 16.11 U1/All 1.452 *4 18.849 21.589 43.00 18.85 U1/All 1.452 *4

2 2.411 5.151 43.00 2.41 U1/All 1.452 *4 5.151 7.891 43.00 5.15 U1/All 1.452 *4 7.891 10.630 43.00 7.89 U1/All 1.452 *4 10.630 13.370 18.74 11.63 U1/All 1.843 *4 *5 13.370 16.109 43.00 13.37 U1/All 1.452 *4 16.109 18.849 43.00 16.11 U1/All 1.452 *4 18.849 21.589 43.00 18.85 U1/All 1.452 *4

3 2.411 5.151 43.00 2.41 U1/All 1.452 *4 5.151 7.891 43.00 5.15 U1/All 1.452 *4 7.891 10.630 43.00 7.89 U1/All 1.452 *4 10.630 13.370 18.74 11.63 U1/All 1.843 *4 *5 13.370 16.109 43.00 13.37 U1/All 1.452 *4 16.109 18.849 43.00 16.11 U1/All 1.452 *4 18.849 21.589 43.00 18.85 U1/All 1.452 *4

4 2.411 5.151 43.00 2.41 U1/All 1.452 *4 5.151 7.891 43.00 5.15 U1/All 1.452 *4 7.891 10.630 43.00 7.89 U1/All 1.452 *4 10.630 13.370 18.74 11.63 U1/All 1.843 *4 *5 13.370 16.109 43.00 13.37 U1/All 1.452 *4 16.109 18.849 43.00 16.11 U1/All 1.452 *4 18.849 21.589 43.00 18.85 U1/All 1.452 *4

5 2.411 5.151 43.00 2.41 U1/All 1.452 *4 5.151 7.891 43.00 5.15 U1/All 1.452 *4 7.891 10.630 43.00 7.89 U1/All 1.452 *4 10.630 13.370 18.74 11.63 U1/All 1.843 *4 *5 13.370 16.109 43.00 13.37 U1/All 1.452 *4 16.109 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 @ 8.4 3 #4 32 @ 8.4 4 #4 32 @ 8.4 5 #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 0.474 2 17.94 89.00 75.00 492.000 348.500 296.225 40.84 43.00 0.474 3 17.94 89.00 75.00 492.000 348.500 296.225 40.84 43.00 0.474 4 17.94 89.00 75.00 492.000 348.500 296.225 40.84 43.00 0.474 5 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 *4 1.167 11.875 0.400 8.39 0.0477 2.41 28.29 43.00 U1/All 0.20 0.0387 *4 *5 11.875 12.125 0.400 8.39 0.0477 12.12 1.96 6.25 U1/All 0.03 0.0000 *2 12.125 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 *4 1.167 11.875 0.400 8.39 0.0477 2.41 29.98 43.00 U1/All 0.20 0.0387 *4 *5 11.875 12.125 0.400 8.39 0.0477 11.88 0.51 6.25 U1/All 0.03 0.0000 *2 12.125 22.833 0.400 8.39 0.0477 21.59 29.74 43.00 U1/All 0.20 0.0387 *4 *5 22.833 24.000 ----- ----- ------ 24.00 47.24 43.00 U2/All 0.22 0.0466 *4

3 0.000 1.167 ----- ----- ------ 0.00 47.39 43.00 U2/All 0.22 0.0468 *4 1.167 11.875 0.400 8.39 0.0477 2.41 29.86 43.00 U1/All 0.20 0.0387 *4 *5 11.875 12.125 0.400 8.39 0.0477 11.88 0.39 6.25 U1/All 0.03 0.0000 *2 12.125 22.833 0.400 8.39 0.0477 21.59 29.86 43.00 U1/All 0.20 0.0387 *4 *5 22.833 24.000 ----- ----- ------ 24.00 47.39 43.00 U2/All 0.22 0.0468 *4

4 0.000 1.167 ----- ----- ------ 0.00 47.24 43.00 U2/All 0.22 0.0466 *4 1.167 11.875 0.400 8.39 0.0477 2.41 29.74 43.00 U1/All 0.20 0.0387 *4 *5 11.875 12.125 0.400 8.39 0.0477 12.12 0.51 6.25 U1/All 0.03 0.0000 *2 12.125 22.833 0.400 8.39 0.0477 21.59 29.98 43.00 U1/All 0.20 0.0387 *4 *5 22.833 24.000 ----- ----- ------ 24.00 47.55 43.00 U2/All 0.22 0.0470 *4

5 0.000 1.167 ----- ----- ------ 0.00 49.38 43.00 U2/All 0.22 0.0493 *4 1.167 11.875 0.400 8.39 0.0477 2.41 31.43 43.00 U1/All 0.20 0.0387 *4 *5 11.875 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 *5 22.833 24.000 ----- ----- ------ 24.00 45.40 43.00 U2/All 0.22 0.0444 *4 NOTES: *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 *4 1.167 11.875 6.320 11.63 18.74 U1/All 1.843 *4 *5 11.875 12.125 ----- 11.88 6.25 U1/All 0.000 *2 12.125 22.833 6.320 12.37 18.74 U1/All 1.843 *4 *5 22.833 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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Torsion Design

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1.167 11.875 6.320 11.63 18.74 U1/All 1.843 *4 *5 11.875 12.125 ----- 11.88 6.25 U1/All 0.000 *2 12.125 22.833 6.320 12.37 18.74 U1/All 1.843 *4 *5 22.833 24.000 ----- 22.83 43.00 U2/All 1.452 *4

3 0.000 1.167 ----- 0.00 43.00 U2/All 1.452 *4 1.167 11.875 6.320 11.63 18.74 U1/All 1.843 *4 *5 11.875 12.125 ----- 11.88 6.25 U1/All 0.000 *2 12.125 22.833 6.320 12.37 18.74 U1/All 1.843 *4 *5 22.833 24.000 ----- 22.83 43.00 U2/All 1.452 *4

4 0.000 1.167 ----- 0.00 43.00 U2/All 1.452 *4 1.167 11.875 6.320 11.63 18.74 U1/All 1.843 *4 *5 11.875 12.125 ----- 11.88 6.25 U1/All 0.000 *2 12.125 22.833 6.320 12.37 18.74 U1/All 1.843 *4 *5 22.833 24.000 ----- 22.83 43.00 U2/All 1.452 *4

5 0.000 1.167 ----- 0.00 43.00 U2/All 1.452 *4 1.167 11.875 6.320 11.63 18.74 U1/All 1.843 *4 *5 11.875 12.125 ----- 11.88 6.25 U1/All 0.000 *2 12.125 22.833 6.320 12.37 18.74 U1/All 1.843 *4 *5 22.833 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 5751 2 14389 11863 Left 17230 4797 66.45 -108.21 7675 -147.13 5942 Middle 17230 3996 66.45 52.98 17230 72.03 14386 Right 17230 4797 66.45 -106.15 7846 -144.33 6010 3 14401 11683 Left 17230 4797 66.45 -106.71 7798 -145.09 5991 Middle 17230 3996 66.45 53.43 17230 72.65 14122 Right 17230 4797 66.45 -106.71 7798 -145.09 5991 4 14389 11863 Left 17230 4797 66.45 -106.15 7846 -144.33 6010 Middle 17230 3996 66.45 52.98 17230 72.03 14386 Right 17230 4797 66.45 -108.21 7675 -147.13 5942 5 15725 10689 Left 17230 4797 66.45 -115.00 7195 -156.35 5751 Middle 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 0.114 2 0.057 0.033 0.090 3 0.058 0.035 0.092 4 0.057 0.033 0.090 5 0.064 0.050 0.114 Maximum Long-term Deflections ----------------------------- Time dependant factor for sustained loads = 2.000 Units: D (in) Span Dsust Lambda Dcs Dcs+lu Dcs+l Dtotal ---- -------- ------ -------- -------- -------- -------- 1 0.064 2.000 0.128 0.178 0.178 0.242 2 0.057 2.000 0.114 0.147 0.147 0.204 3 0.058 2.000 0.115 0.150 0.150 0.208 4 0.057 2.000 0.114 0.147 0.147 0.204 5 0.064 2.000 0.128 0.178 0.178 0.242 Material Takeoff:================= Reinforcement in the Direction of Analysis

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TIME SAVING DESIGN AID

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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-2C8D0 C:\Data\Time Saving Design Aid\Torsion example.slb Page 9

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