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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 (fy = 60,000 psi) Loads x Dead load of joists = 77 psf

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Torsion Design x Superimposed dead load = 30 psf x Live load = 50 psf Additional data x Typical bay size = 24 × 32 ft (5 bays in N-S direction, 3 bays in E-W direction) x Typical story height = 12 ft Factored Torsional Moment Tu 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 Tu at the critical section located at a distance d from the face of the support can be determined from the following: 2 ⎛ Acp Tu = φ4 fc' ⎜ ⎜ pcp ⎝

⎞ ⎟ ⎟ ⎠

This type of torsion is referred to as compatibility torsion, the magnitude of which is greater than the factored torsional moment Tu, min below which torsional effects can be neglected, where 2 ⎛ Acp Tu,min = φ fc' ⎜ ⎜ pcp ⎝

⎞ ⎟ ⎟ ⎠

Since the beams and joists are cast monolithically, Acp and pcp for beam CD can include a portion of the adjoining slab. The effective width be of the overhanging flange must conform to 13.2.4: be = h − hf = 20.5 – 4.5 = 16.0 in. (governs)

= 4hf = 4 × 4 .5 = 18.0 in.

Acp = (20.5 ×24 ) + (16.0 × 4.5) = 564.0 in.2 pcp = 2(20.5 +24 +16.0 ) = 121 in. 3 2 Acp / p cp = 2,629 in.

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

Acp = (20.5 × 24 ) = 492 in.2 pcp = 2(20.5 + 24 ) = 89 in. 3 2 Acp / p cp = 2,720 in.3 > 2,629 in.

Therefore, ignore flange per 11.6.1.1. Tu = 0.75 × 4 4,000 × 2,720 = 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 ⎡⎛ 20 .5 × 24 ⎤ ⎞ w D = ⎢⎜ × 150 ⎟ + (77 + 30 ) × (32 / 2 )⎥ / 1,000 = 2.2 kips/ft ⎠ ⎣⎝ 144 ⎦

wL = 50 × (32 / 2) / 1,000 = 0.8 kips/ft wu = 1.2wD + 1.6w L = 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: 2

22 ⎞ ⎛ 3.9 × ⎜ 24 − ⎟ 2 l w 12 ⎠ ⎝ = 119.8 ft-kips Mu+ = u n = 16 16

Mu− =

Vu =

wu l n2 16 = 119.8 × = 174.3 ft-kips 11 11

wu ln = 43.2 kips 2

Adequacy of Cross-sectional Dimensions For solid sections: 2 ⎛ Tp ⎛ Vu ⎞ ⎜ ⎟ +⎜ u h ⎜b d⎟ ⎜ 1.7A2 ⎝ w ⎠ oh ⎝

2

⎞ ⎟ ≤ φ⎛⎜ Vc + 8 fc' ⎞⎟ ⎜b d ⎟ ⎟ ⎝ w ⎠ ⎠

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 Vu = 37.4 kips. Also, the nominal shear strength provided by the concrete is Vc = 2 fc' bw d . Assuming a 1.5-in. clear cover to No. 4 closed stirrups:

Aoh = [20.5 − (2 × 1.5) − 0.5] × [24 − (2 × 1.5) − 0.5] = 348.5 in.2 ph = 2 × { [20.5 − (2 × 1.5 ) − 0.5] + [24 − (2 × 1.5 ) − 0.5] } = 75 in.

Therefore, 2

⎛ 43 .0 × 12,000 × 75 ⎞ ⎛ 37,400 ⎞ ⎟ ⎜ ⎟ +⎜ 1.7 × 348 .5 2 ⎝ 24 × 18 ⎠ ⎝ ⎠

2

= 207 psi < 0.75 × (2 + 8 ) 4,000 = 474 psi , OK.

Transverse Reinforcement Required for Torsion

Tu At = s φ 2Ao fyv cot θ

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Torsion Design where Ao = 0.85 Ao h = 0.85 × 348.5 = 296.2 in.2 θ = 45 °

Therefore,

At 43.0 × 12,000 in.2 / in. = = 0.019 s 0.75 × 2 × 296.2 × 60,000 × cot 45° leg Transverse Reinforcement Required for Shear

(

)

Av Vu − φVc 37,400 − 0.75 × 2 4000 × 24 × 18 37, 400 − 40,983 = = = 0.5φVc , 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 ' = 0.75 fc

bw 24 = 0.75 4,000 = 0.019 in.2/in. fyv 60,000

= 50bw / fyv = 50 × 24 / 60,000 = 0.020 in.2/in. (governs) Required transverse reinforcement

Av A in.2 / in. + 2 t = 0 + 2legs × 0.019 = 0.038 in.2/in. > 0.020 in.2/in. OK. leg s s Maximum spacing of transverse reinforcement = ph / 8 = 75 / 8 = 9.4 in. < 12.0 in. = d / 2 = 18 / 2 = 9.0 in. (governs) 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 bt + d = 24 + 18 = 42 in. = 3.5 ft past the location where it is no longer required. Longitudinal Reinforcement Required for Torsion ⎛ A ⎞ ⎛ fyv Al = ⎜ t ⎟ph ⎜ ⎝ s ⎠ ⎜⎝ fyl

⎞ ⎟ cot 2 θ = 0.019 × 75 × ⎛⎜ 60 ⎞⎟ × cot 2 45 ° = 1.43 in.2 ⎟ ⎝ 60 ⎠ ⎠

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Torsion Design Minimum longitudinal reinforcement: Al ,min =

5 fc' Acp fyl

⎛A −⎜ t ⎝ s

⎞ fyv ⎟ph ⎠ fyl

where At / s = 0.019 in.2/in. > 25bw / fyv = 25 × 24 / 60,000 = 0.010 in.2/in.

Al ,min =

5 4,000 × 492 ⎛ 60 ⎞ 2 2 − ⎜ 0.019 × 75 × ⎟ = 1.17 in. < Al = 1.43in. 60,000 60 ⎠ ⎝

Use A l = 1.43 in.2 Longitudinal Reinforcement Required for Flexure The required As is given in the table below, assuming rectangular section behavior and an average d = 18 in. Required Longitudinal Reinforcement for Flexure Mu

As = Mu / 4d

(ft-kips)

(in.2)

Support

174.3

2.42

Midspan

119.8

1.66

Location

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 A l (= 0 .25 × 1 .43 = 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. x Face of support Total top steel required = 2.42 + 0.41 = 2.83 in.2 For 4000-psi concrete, minimum As = 200bw d / fy = 1.44 in.2 Provide 3-No. 9 bars ( As = 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).

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Torsion Design x Midspan Total bottom steel required = 1.66 + 0.41 = 2.07 in.2 Provide 3-No. 8 bars ( As = 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). 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 ( As = 2.00 in.2) minus the area of steel that is required for torsion (0.41 in.2). Thus, with As = 2.00 – 0.41 = 1.59 in.2, φMn = 125 ft-kips. The distance x from the face of the support to where the factored bending moment Mu = 125 ft-kips is obtained by summing moments about the section at this location:

3.9 2 x − 43.2x + 174.3 = 125 2 Solution of this equation gives x = 1.2 ft. The 1-No. 9 bar must extend a distance d = 18 in. or 12 db = 12 × 1 .128 = 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 l d beyond

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

ld

⎛ ⎜ ⎜ 3 fy =⎜ ⎜ 40 fc' ⎜ ⎜ ⎝

⎞ ⎟ ⎟ αβγλ ⎟ db ⎛ c +K ⎞ ⎟ tr ⎜ ⎟⎟ ⎜ db ⎟ ⎟ ⎝ ⎠⎠

where α = reinforcement location factor = 1.3

β = coating factor = 1.0 γ = reinforcement size factor = 1.0 λ = lightweight aggregate concrete factor = 1.0

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Torsion Design ⎧1.128 ⎪ 2 + 0.5 + 1.5 = 2.6 in. (governs ) c = spacing or cover dimension = ⎪⎨ ⎪ 24 − 2(1.5 + 0.5 ) − 1.128 = 4.7in. ⎪ 2×2 ⎩

Ktr = transverse reinforcement index

= 0 (conservative)

c + Ktr 2.6 + 0 = = 2.3 < 2.5 db 1.128 Therefore,

⎛ 3 60,000 1.3 × 1.0 × 1.0 × 1.0 ⎞ ⎟ 1.128 = 45.4 in. = 3.8 ft > 2.7 ft ⎟ 2.3 ⎠

l d = ⎜⎜ ⎝ 40 4,000

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 3No. 8 bars will be terminated, the positive moment strength with an area of steel As equal to (2 × 0.79) –

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

the factored moment Mu = 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 l d = 2.4 ft (conservatively assuming Ktr = 0). 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

Page 8 of 23

TIME SAVING DESIGN AID

Page 9 of 23

Torsion Design

X

Z

Y

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

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Torsion Design

CASE: EQ

CASE: Wind

800

800

800

800

1712

1712

1712

1712

35.83

35.83

35.83

35.83

800

CASE: Live 1712 35.83

CASE: Dead

512.5

512.5

512.5

512.5

512.5

CASE: SELF

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

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Torsion Design

601.94

Torsion Diagram - k-ft

700.0

601.94

-601.94

-700.0 50.0 45.99

601.94

-601.94

-601.94 47.98

601.94

-601.94

-601.94 49.43

47.88

Shear Diagram - kip

48.09

601.94

LEGEND: Envelope

Moment Diagram - k-ft

-47.88

-49.43

-50.0 -250.0 -160.62

-204.87-196.15

107.14

-47.98

-193.56-194.23

99.63

-194.23-193.56

100.39

-196.15-204.87

99.63

250.0

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

-45.99

-48.09

Engineer: DAF

-160.62

107.14

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Torsion Design

Beam Shear and Torsion Capacity: Stirrup Intensity - in^2/in 0.05

0.039

1.5

0.039

1.5

0.039

1.5

0.039

1.5

0.039

0.039

0.039

1.5

1.5

0.039

1.5

1.5

0.039

1.5

0.039

1.5 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

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

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

TIME SAVING DESIGN AID

Page 13 of 23

Torsion Design

32-#[email protected]

32-#[email protected]

32-#[email protected]

32-#[email protected]

32-#[email protected]

Transverse Reinforcement

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

Frame: Exterior

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

Engineer: DAF 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)

2-#8(288.0)c 1-#8(36.0)

2-#8(288.0)c 1-#8(36.0)

2-#9(70.8) 1-#9(34.5)

1-#9(42.9) 2-#9(85.7)

2-#9(85.7) 1-#9(41.4)

1-#9(40.9) 2-#9(85.7)

2-#9(85.7) 1-#9(41.0)

1-#9(41.0) 2-#9(85.7)

2-#9(85.7) 1-#9(40.9)

1-#9(41.4) 2-#9(85.7)

2-#9(85.7) 1-#9(42.9)

1-#9(34.5) 2-#9(70.8)

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Torsion Design

Flexural Reinforcement

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Torsion Design pcaBeam v2.00 © Portland Cement Association Licensed to: PCA, License ID: 12345-1234567-4-2D2DE-2C8D0 C:\Data\Time Saving Design Aid\Torsion example.slb

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05-03-2007, 09:33:38 AM Page 1

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============================================================================= 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 -----------wc = 150 f'c = 4 Ec = 3834.3 fr = 0.47434 fy fyv Es

= = =

Columns -----------150 4 3834.3 0.47434

lb/ft3 ksi ksi ksi

60 ksi, Bars are not epoxy-coated 60 ksi 29000 ksi

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Torsion Design pcaBeam v2.00 © Portland Cement Association Licensed to: PCA, License ID: 12345-1234567-4-2D2DE-2C8D0 C:\Data\Time Saving Design Aid\Torsion example.slb

05-03-2007, 09:33:38 AM 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 b h Sp b h ---- -------- -------- --------------- -------1 0.00 0.00 0.00 24.00 20.50 2 0.00 0.00 0.00 24.00 20.50 3 0.00 0.00 0.00 24.00 20.50 4 0.00 0.00 0.00 24.00 20.50 5 0.00 0.00 0.00 24.00 20.50

__Span__ Hmin -------15.57 13.71 13.71 13.71 15.57

Support Data: ============= Columns: c1a, c2a, c1b, c2b (in); Ha, Hb (ft) Supp c1a c2a Ha c1b c2b Hb ---- -------- -------- --------------- -------- -------1 22.00 22.00 12.000 22.00 22.00 12.000 2 22.00 22.00 12.000 22.00 22.00 12.000 3 22.00 22.00 12.000 22.00 22.00 12.000 4 22.00 22.00 12.000 22.00 22.00 12.000 5 22.00 22.00 12.000 22.00 22.00 12.000 6 22.00 22.00 12.000 22.00 22.00 12.000

Red% ---100 100 100 100 100 100

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 Type DEAD DEAD LIVE U1 1.400 1.400 0.000 U2 1.200 1.200 1.600 U3 1.200 1.200 1.600 U4 1.200 1.200 1.600 U5 1.200 1.200 1.000 U6 1.200 1.200 1.000 U7 0.900 0.900 0.000 U8 0.900 0.900 0.000 U9 1.200 1.200 1.000 U10 1.200 1.200 1.000 U11 0.900 0.900 0.000 U12 0.900 0.900 0.000 Span Span ---Line 1 2 3 4 5 1 2 3 4 5

Wind LATERAL 0.000 0.000 0.800 -0.800 1.600 -1.600 1.600 -1.600 0.000 0.000 0.000 0.000

EQ LATERAL 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.000 -1.000 1.000 -1.000

Loads: Case Wa La Wb Lb -------- ------------ ------------ ------------ -----------Loads - Wa | Wb (lb/ft), La | Lb (ft): Dead 1712 0 1712 24 Dead 1712 0 1712 24 Dead 1712 0 1712 24 Dead 1712 0 1712 24 Dead 1712 0 1712 24 Live 800 0 800 24 Live 800 0 800 24 Live 800 0 800 24 Live 800 0 800 24 Live 800 0 800 24

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Torsion Design pcaBeam v2.00 © Portland Cement Association Licensed to: PCA, License ID: 12345-1234567-4-2D2DE-2C8D0 C:\Data\Time Saving Design Aid\Torsion example.slb Line 1 2 3 4 5

05-03-2007, 09:33:38 AM Page 3

Torque - Wa | Wb (k-ft/ft), La | Lb (ft): Dead 35.83 0 35.83 Dead 35.83 0 35.83 Dead 35.83 0 35.83 Dead 35.83 0 35.83 Dead 35.83 0 35.83

Support Loads:

24 24 24 24 24

--- 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 Bar spacing 1.00 18.00 1.00 18.00 Reinf ratio 0.14 5.00 0.14 5.00 Cover 2.00 2.00 Side cover 1.50 1.50 Layer dist. 1.00 1.00 No. of legs Top bars have 12 in of concrete below them.

% in in in

#4 6.00

2

#4 18.00 in

6

============================================================================================= [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 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

*5

2 Left Middle Right

2.00 2.00 2.00

153.72 0.00 151.32

0.917 12.000 23.083

1.435 0.000 1.435

7.775 7.775 7.775

9.308 0.000 9.308

1.985 0.000 1.953

3-#9 --3-#9

*5

3 Left Middle Right

2.00 2.00 2.00

151.90 0.00 151.90

0.917 12.000 23.083

1.435 0.000 1.435

7.775 7.775 7.775

9.308 0.000 9.308

1.961 0.000 1.961

3-#9 --3-#9

*5

4 Left Middle Right

2.00 2.00 2.00

151.32 0.00 153.72

0.917 12.000 23.083

1.435 0.000 1.435

7.775 7.775 7.775

9.308 0.000 9.308

1.953 0.000 1.985

3-#9 --3-#9

*5

5 Left 2.00 161.22 0.917 1.435 7.775 Middle 2.00 0.00 12.000 0.000 7.775 Right 2.00 120.11 23.083 1.435 7.775 NOTES: *5 - Number of bars governed by maximum allowable spacing.

9.308 0.000 9.308

2.087 0.000 1.537

3-#9 --3-#9

Top Bar Details: ================ Units: Length (ft) _____________Left______________ Span Bars Length Bars Length ---- ------- ------- ------- ------1 2-#9 5.90 1-#9 2.88

___Continuous__ Bars Length ------- ---------

_____________Right_____________ Bars Length Bars Length ------- ------- ------- ------2-#9 7.14 1-#9 3.58

*5

*5

*5

*5

TIME SAVING DESIGN AID

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05-03-2007, 09:33:38 AM Page 4

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

1.361

3-#8

*5

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 PhiMnPhiMn+ ---- --------- ----- ----- ------------ -----------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 0.917 0.918 3.449 4.612 7.144 8.675 10.624 11.887 12.000 12.362 13.626 15.325 16.856 19.347 20.592 23.082 23.083 24.000

3.00 3.00 3.00 2.00 2.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2.00 2.00 3.00 3.00 3.00

1.58 1.58 1.58 1.58 1.58 1.58 1.58 1.58 2.37 2.37 2.37 1.58 1.58 1.58 1.58 1.58 1.58 1.58 1.58

-227.25 -227.25 -227.25 -154.81 -154.81 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -154.81 -154.81 -227.25 -227.25 -227.25

123.85 123.85 123.85 123.85 123.85 123.85 123.85 123.85 182.68 182.68 182.68 123.85 123.85 123.85 123.85 123.85 123.85 123.85 123.85

TIME SAVING DESIGN AID

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0.000 0.917 0.918 3.418 4.643 7.144 8.675 10.374 11.648 12.000 12.103 13.376 15.325 16.856 19.357 20.582 23.082 23.083 24.000

3.00 3.00 3.00 2.00 2.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2.00 2.00 3.00 3.00 3.00

1.58 1.58 1.58 1.58 1.58 1.58 1.58 1.58 2.37 2.37 2.37 1.58 1.58 1.58 1.58 1.58 1.58 1.58 1.58

-227.25 -227.25 -227.25 -154.81 -154.81 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -154.81 -154.81 -227.25 -227.25 -227.25

123.85 123.85 123.85 123.85 123.85 123.85 123.85 123.85 182.68 182.68 182.68 123.85 123.85 123.85 123.85 123.85 123.85 123.85 123.85

4

0.000 0.917 0.918 3.408 4.653 7.144 8.675 10.374 11.638 12.000 12.113 13.376 15.325 16.856 19.388 20.551 23.082 23.083 24.000

3.00 3.00 3.00 2.00 2.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2.00 2.00 3.00 3.00 3.00

1.58 1.58 1.58 1.58 1.58 1.58 1.58 1.58 2.37 2.37 2.37 1.58 1.58 1.58 1.58 1.58 1.58 1.58 1.58

-227.25 -227.25 -227.25 -154.81 -154.81 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -154.81 -154.81 -227.25 -227.25 -227.25

123.85 123.85 123.85 123.85 123.85 123.85 123.85 123.85 182.68 182.68 182.68 123.85 123.85 123.85 123.85 123.85 123.85 123.85 123.85

5

0.000 0.917 0.918 3.578 4.483 7.144 8.675 10.873 12.000 12.234 12.513 13.875 15.325 18.102 20.061 21.123 23.082 23.083 24.000

3.00 3.00 3.00 2.00 2.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2.00 2.00 3.00 3.00 3.00

1.58 1.58 1.58 1.58 1.58 1.58 1.58 1.58 2.23 2.37 2.37 1.58 1.58 1.58 1.58 1.58 1.58 1.58 1.58

-227.25 -227.25 -227.25 -154.81 -154.81 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -154.81 -154.81 -227.25 -227.25 -227.25

123.85 123.85 123.85 123.85 123.85 123.85 123.85 123.85 172.71 182.68 182.68 123.85 123.85 123.85 123.85 123.85 123.85 123.85 123.85

05-03-2007, 09:33:38 AM Page 5

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

TIME SAVING DESIGN AID

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05-03-2007, 09:33:38 AM Page 6

5.151 7.891 10.630 13.370 16.109 18.849

7.891 10.630 13.370 16.109 18.849 21.589

21.45 12.92 4.39 12.68 21.21 29.74

43.00 43.00 43.00 43.00 43.00 43.00

0.194 0.190 0.188 0.190 0.194 0.200

5.15 7.89 10.63 16.11 18.85 21.59

U1/All U1/All U1/All U1/All U1/All U1/All

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0194 0.0194 0.0194 0.0194 0.0194 0.0194

0.0387 0.0387 0.0387 0.0387 0.0387 0.0387

*4 *4 *4 *5 *4 *4 *4

3

2.411 5.151 7.891 10.630 13.370 16.109 18.849

5.151 7.891 10.630 13.370 16.109 18.849 21.589

29.86 21.33 12.80 4.27 12.80 21.33 29.86

43.00 43.00 43.00 43.00 43.00 43.00 43.00

0.200 0.194 0.190 0.188 0.190 0.194 0.200

2.41 5.15 7.89 10.63 16.11 18.85 21.59

U1/All U1/All U1/All U1/All U1/All U1/All U1/All

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0194 0.0194 0.0194 0.0194 0.0194 0.0194 0.0194

0.0387 0.0387 0.0387 0.0387 0.0387 0.0387 0.0387

*4 *4 *4 *4 *5 *4 *4 *4

4

2.411 5.151 7.891 10.630 13.370 16.109 18.849

5.151 7.891 10.630 13.370 16.109 18.849 21.589

29.74 21.21 12.68 4.39 12.92 21.45 29.98

43.00 43.00 43.00 43.00 43.00 43.00 43.00

0.200 0.194 0.190 0.188 0.190 0.194 0.200

2.41 5.15 7.89 13.37 16.11 18.85 21.59

U1/All U1/All U1/All U1/All U1/All U1/All U1/All

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0194 0.0194 0.0194 0.0194 0.0194 0.0194 0.0194

0.0387 0.0387 0.0387 0.0387 0.0387 0.0387 0.0387

*4 *4 *4 *4 *5 *4 *4 *4

5

2.411 5.151 7.891 10.630 13.370 16.109 18.849

5.151 7.891 10.630 13.370 16.109 18.849 21.589

31.43 22.90 14.37 5.84 11.23 19.76 28.29

43.00 43.00 43.00 43.00 43.00 43.00 43.00

0.201 0.195 0.190 0.188 0.189 0.193 0.199

2.41 5.15 7.89 10.63 16.11 18.85 21.59

U1/All U1/All U1/All U1/All U1/All U1/All U1/All

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0194 0.0194 0.0194 0.0194 0.0194 0.0194 0.0194

0.0387 0.0387 0.0387 0.0387 0.0387 0.0387 0.0387

*4 *4 *4 *4 *5 *4 *4 *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 7.891 10.630 13.370 16.109 18.849

5.151 7.891 10.630 13.370 16.109 18.849 21.589

43.00 43.00 43.00 18.74 43.00 43.00 43.00

2.41 5.15 7.89 11.63 13.37 16.11 18.85

U1/All U1/All U1/All U1/All U1/All U1/All U1/All

1.452 1.452 1.452 1.843 1.452 1.452 1.452

*4 *4 *4 *4 *5 *4 *4 *4

3

2.411 5.151 7.891 10.630 13.370 16.109 18.849

5.151 7.891 10.630 13.370 16.109 18.849 21.589

43.00 43.00 43.00 18.74 43.00 43.00 43.00

2.41 5.15 7.89 11.63 13.37 16.11 18.85

U1/All U1/All U1/All U1/All U1/All U1/All U1/All

1.452 1.452 1.452 1.843 1.452 1.452 1.452

*4 *4 *4 *4 *5 *4 *4 *4

4

2.411 5.151 7.891 10.630 13.370 16.109 18.849

5.151 7.891 10.630 13.370 16.109 18.849 21.589

43.00 43.00 43.00 18.74 43.00 43.00 43.00

2.41 5.15 7.89 11.63 13.37 16.11 18.85

U1/All U1/All U1/All U1/All U1/All U1/All U1/All

1.452 1.452 1.452 1.843 1.452 1.452 1.452

*4 *4 *4 *4 *5 *4 *4 *4

5

2.411 5.151 7.891 10.630 13.370 16.109 18.849

5.151 7.891 10.630 13.370 16.109 18.849 21.589

43.00 43.00 43.00 18.74 43.00 43.00 43.00

2.41 5.15 7.89 11.63 13.37 16.11 18.85

U1/All U1/All U1/All U1/All U1/All U1/All U1/All

1.452 1.452 1.452 1.843 1.452 1.452 1.452

*4 *4 *4 *4 *5 *4 *4 *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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#4 #4 #4 #4

32 32 32 32

@ @ @ @

05-03-2007, 09:33:38 AM Page 7

8.4 8.4 8.4 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 1.167 11.875 0.400 8.39 0.0477 2.41 28.29 43.00 U1/All 0.20 0.0387 11.875 12.125 0.400 8.39 0.0477 12.12 1.96 6.25 U1/All 0.03 0.0000 12.125 22.833 0.400 8.39 0.0477 21.59 31.43 43.00 U1/All 0.20 0.0387 22.833 24.000 -------------24.00 49.38 43.00 U2/All 0.22 0.0493

*4 *4 *5 *2 *4 *5 *4

2

0.000 1.167 11.875 12.125 22.833

1.167 11.875 12.125 22.833 24.000

----0.400 0.400 0.400 -----

----8.39 8.39 8.39 -----

-----0.0477 0.0477 0.0477 ------

0.00 2.41 11.88 21.59 24.00

47.55 29.98 0.51 29.74 47.24

43.00 43.00 6.25 43.00 43.00

U2/All U1/All U1/All U1/All U2/All

0.22 0.20 0.03 0.20 0.22

0.0470 0.0387 0.0000 0.0387 0.0466

*4 *4 *5 *2 *4 *5 *4

3

0.000 1.167 11.875 12.125 22.833

1.167 11.875 12.125 22.833 24.000

----0.400 0.400 0.400 -----

----8.39 8.39 8.39 -----

-----0.0477 0.0477 0.0477 ------

0.00 2.41 11.88 21.59 24.00

47.39 29.86 0.39 29.86 47.39

43.00 43.00 6.25 43.00 43.00

U2/All U1/All U1/All U1/All U2/All

0.22 0.20 0.03 0.20 0.22

0.0468 0.0387 0.0000 0.0387 0.0468

*4 *4 *5 *2 *4 *5 *4

4

0.000 1.167 11.875 12.125 22.833

1.167 11.875 12.125 22.833 24.000

----0.400 0.400 0.400 -----

----8.39 8.39 8.39 -----

-----0.0477 0.0477 0.0477 ------

0.00 2.41 12.12 21.59 24.00

47.24 29.74 0.51 29.98 47.55

43.00 43.00 6.25 43.00 43.00

U2/All U1/All U1/All U1/All U2/All

0.22 0.20 0.03 0.20 0.22

0.0466 0.0387 0.0000 0.0387 0.0470

*4 *4 *5 *2 *4 *5 *4

5

0.000 1.167 11.875 12.125 22.833

1.167 11.875 12.125 22.833 24.000

----0.400 0.400 0.400 -----

----8.39 8.39 8.39 -----

-----0.0477 0.0477 0.0477 ------

0.00 2.41 11.88 21.59 24.00

49.38 31.43 1.96 28.29 45.40

43.00 43.00 6.25 43.00 43.00

U2/All U1/All U1/All U1/All U2/All

0.22 0.20 0.03 0.20 0.22

0.0493 0.0387 0.0000 0.0387 0.0444

*4 *4 *5 *2 *4 *5 *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

TIME SAVING DESIGN AID

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1.167 11.875 12.125 22.833

11.875 12.125 22.833 24.000

6.320 ----6.320 -----

11.63 11.88 12.37 22.83

18.74 6.25 18.74 43.00

U1/All U1/All U1/All U2/All

1.843 0.000 1.843 1.452

*4 *5 *2 *4 *5 *4

3

0.000 1.167 11.875 12.125 22.833

1.167 11.875 12.125 22.833 24.000

----6.320 ----6.320 -----

0.00 11.63 11.88 12.37 22.83

43.00 18.74 6.25 18.74 43.00

U2/All U1/All U1/All U1/All U2/All

1.452 1.843 0.000 1.843 1.452

*4 *4 *5 *2 *4 *5 *4

4

0.000 1.167 11.875 12.125 22.833

1.167 11.875 12.125 22.833 24.000

----6.320 ----6.320 -----

0.00 11.63 11.88 12.37 22.83

43.00 18.74 6.25 18.74 43.00

U2/All U1/All U1/All U1/All U2/All

1.452 1.843 0.000 1.843 1.452

*4 *4 *5 *2 *4 *5 *4

5

0.000 1.167 11.875 12.125 22.833

1.167 11.875 12.125 22.833 24.000

----6.320 ----6.320 -----

0.00 11.63 11.88 12.37 22.83

43.00 18.74 6.25 18.74 43.00

U2/All U1/All U1/All U1/All U2/All

1.452 1.843 0.000 1.843 1.452

*4 *4 *5 *2 *4 *5 *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 ------------------------------------------

TIME SAVING DESIGN AID

Page 23 of 23

Torsion Design pcaBeam v2.00 © Portland Cement Association Licensed to: PCA, License ID: 12345-1234567-4-2D2DE-2C8D0 C:\Data\Time Saving Design Aid\Torsion example.slb Top Bars: Bottom Bars: Torsion Bars: Stirrups: Total Steel: Concrete:

582.6 680.9 2776.7 2057.4 6097.6 410.0

lb lb lb lb lb ft^3



4.85 5.67 23.14 17.15 50.81 3.42

lb/ft lb/ft lb/ft lb/ft lb/ft ft^3/ft



2.427 2.837 11.569 8.573 25.407 1.708

05-03-2007, 09:33:38 AM Page 9 lb/ft^2 lb/ft^2 lb/ft^2 lb/ft^2 lb/ft^2 ft^3/ft^2