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TIME SAVING DESIGN AID Page 1 of 23 Moment Redistribution A 3-span continuous beam has center-to-center span lengths of 30 ft-0 in. The beam is 20 in. by 28 in. and all columns are 20 in. by 20 in. In this example, the beam is designed for flexure using moment redistribution. 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 Superimposed dead load = 3.5 kips/ft x Live load = 2.75 kips/ft Determine factored loads U = 1.2D + 1.6L w D = 5 3 150 0 144 28 20 . . + × × = 4.1 kips/ft w L = 2.75 kips/ft w U = = = 9.3 kips/ft L D w 6 . 1 w 2 . 1 + ( ) ( 75 . 2 6 . 1 1 . 4 2 . 1 × + × ) Determine bending moments for pattern loading Maximum negative moments at faces of supports and positive midspan moments were determined by computer analysis for the following 4 load cases: x Case I: Live load applied to all 3 spans x Case II: Live load applied to end span and interior span only x Case III: Live load applied to end spans only x Case IV: Live load applied to interior span only

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Page 1: 9.3 kips/ft - Portland Cement Associationcement.org/buildings/Timesaving-MomentRedistribution-IA.pdf · TIME SAVING DESIGN AID Page 1 of 23 Moment Redistribution A 3-span continuous

TIME SAVING DESIGN AID

Page 1 of 23

Moment Redistribution

A 3-span continuous beam has center-to-center span lengths of 30 ft-0 in. The beam is 20 in. by 28 in. and all columns are 20 in. by 20 in. In this example, the beam is designed for flexure using moment redistribution.

Design Data

Materials

Concrete: normal weight (150 pcf), f’c = 4,000 psi

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

Loads

Superimposed dead load = 3.5 kips/ft

Live load = 2.75 kips/ft

Determine factored loads

U = 1.2D + 1.6L

wD = 531500144

2820 .. +×× = 4.1 kips/ft

wL = 2.75 kips/ft

wU = = = 9.3 kips/ft LD w6.1w2.1 + ( ) ( 75.26.11.42.1 ×+× )

Determine bending moments for pattern loading

Maximum negative moments at faces of supports and positive midspan moments were determined by computer analysis for the following 4 load cases:

Case I: Live load applied to all 3 spans

Case II: Live load applied to end span and interior span only

Case III: Live load applied to end spans only

Case IV: Live load applied to interior span only

Page 2: 9.3 kips/ft - Portland Cement Associationcement.org/buildings/Timesaving-MomentRedistribution-IA.pdf · TIME SAVING DESIGN AID Page 1 of 23 Moment Redistribution A 3-span continuous

TIME SAVING DESIGN AID

Page 2 of 23

Moment Redistribution

Factored Bending Moments Due to Pattern Loading

Location Load Case Mu (ft-kips) I 361.7 II 357.8 III 390.1

Exterior negative

IV 162.1 I 426.5 II 424.5 III 454.1

Positive

IV 201.8 I 662.8 II 674.8 III 574.3

End Span

Interior negative

IV 437.7 I 634.1 II 668.8 III 394.1

Negative

IV 543.8 I 330.2 II 361.2 III 113.9

Interior Span

Positive

IV 390.2

Determine maximum allowable percentage increase or decrease in negative moment

Use d = 25.44 in. (assuming 1.5 in. clear cover, No. 4 stirrups, and No. 9 flexural bars)

The required area of steel for the maximum bending moments due to pattern loading is summarized in the table below. Also given in the table is the corresponding net tensile strain in the extreme tension steel and the percent allowable adjustment in the negative moment tε t1000ε .

Moment Adjustments at Supports

Location Mu (ft-kips) As (in.2) tε (in./in.) t1000ε (%)*

End support 390.1 3.64 0.0172 17.2

Interior support 674.8 6.66 0.0080 8.0

*Permitted to increase or decrease negative moments by not more than t1000ε ≤ 20% per ACI 8.4.1. Redistribution of negative moments is permitted only when tε ≥ 0.0075 (ACI 8.4.3).

Page 3: 9.3 kips/ft - Portland Cement Associationcement.org/buildings/Timesaving-MomentRedistribution-IA.pdf · TIME SAVING DESIGN AID Page 1 of 23 Moment Redistribution A 3-span continuous

TIME SAVING DESIGN AID

Page 3 of 23

Moment Redistribution

( )

Adjustments of moments

In this example, it is decided to reduce the negative moment at the first interior support and accept the corresponding increase in the positive moment in the end span. It is also decided that the negative moments at the exterior supports will not be adjusted.

The following calculations illustrate the adjustment of the moments for Load Case II.

Negative moment at first interior support = −674.8 ft-kips with an allowable redistribution factor = 8.0% (see above table).

Reduction to moment = −674.8 × 0.08 = −54.0 ft-kips

Adjusted negative moment = −674.8 − (−54.0) = −620.8 ft-kips

Increase in positive moment in end span:

For Load Case II, negative moment at exterior support = −357.8 ft-kips

Midspan ordinate on line from exterior support to interior support = 2

83578620 .. −+− = −489.3 ft-kips

Moment due to uniform load = = = 933.0 ft-kips 8/w 2nu l 8/33.283.9 2×

Adjusted positive moment at midspan = 933.0 + (−489.3) = 443.7 ft-kips

Similar calculations can be performed for the other load cases.

Determine flexural reinforcement based on adjusted moments

The table below gives a summary of the required reinforcement at the negative and positive locations in both an exterior and interior span, based on the redistributed bending moments. Note that if an additional adjustment of the bending moments is warranted, further cycles of redistribution may be made.

Summary of Flexural Reinforcement

Required Provided Location Mu

(ft-kips) Load Case As (in.2) ρ Bars ρ

Exterior negative -390.1 III 3.64 0.0071 4-No. 9 0.0079

Positive 473.7 III 4.49 0.0088 5-No. 9 0.0098 End span

Interior negative -620.8 II 6.06 0.0119 6-No. 9 0.0118

Interior span Positive 390.2 IV 3.64 0.0072 4-No. 9 0.0079

ρmin = 200/fy = 0.0033

For comparison, output from pcaBeam program is presented on the following pages.

Page 4: 9.3 kips/ft - Portland Cement Associationcement.org/buildings/Timesaving-MomentRedistribution-IA.pdf · TIME SAVING DESIGN AID Page 1 of 23 Moment Redistribution A 3-span continuous

TIME SAVING DESIGN AID

Page 4 of 23

Moment Redistribution

X

YZ

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

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

Project: Time Saving Design Aid

Frame: Moment Redistribution Engineer: DAA

Page 5: 9.3 kips/ft - Portland Cement Associationcement.org/buildings/Timesaving-MomentRedistribution-IA.pdf · TIME SAVING DESIGN AID Page 1 of 23 Moment Redistribution A 3-span continuous

TIME SAVING DESIGN AID

Page 5 of 23

Moment Redistribution

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

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

Project: Time Saving Design Aid

Frame: Moment Redistribution Engineer: DAA

CASE: SELF

CASE: Dead

CASE: Live

CASE: Wind

CASE: EQ

583.333 583.333 583.333

3500 3500 3500

2750 2750 2750

Page 6: 9.3 kips/ft - Portland Cement Associationcement.org/buildings/Timesaving-MomentRedistribution-IA.pdf · TIME SAVING DESIGN AID Page 1 of 23 Moment Redistribution A 3-span continuous

TIME SAVING DESIGN AID

Page 6 of 23

Moment Redistribution

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

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

Project: Time Saving Design Aid

Frame: Moment Redistribution Engineer: DAA

Mom

ent D

iagr

am -

k-ft

-800.0

800.0

She

ar D

iagr

am -

kip

160.0

-160.0

LEGEND:Envelope

-495.63

-799.18

454.06

-755.39 -755.39

389.71

-799.18

-495.63

454.06

132.91

-150.87

144.09

-144.09

150.87

-132.91

(Non-Redistributed)

Page 7: 9.3 kips/ft - Portland Cement Associationcement.org/buildings/Timesaving-MomentRedistribution-IA.pdf · TIME SAVING DESIGN AID Page 1 of 23 Moment Redistribution A 3-span continuous

TIME SAVING DESIGN AID

Page 7 of 23

Moment Redistribution

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

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

Project: Time Saving Design Aid

Frame: Moment Redistribution Engineer: DAA

Mom

ent D

iagr

am -

k-ft

-800.0

800.0

She

ar D

iagr

am -

kip

160.0

-160.0

LEGEND: Envelope (Redist.)

-495.63

-719.74

487.21

-672.40 -672.40

461.84

-719.74

-495.63

487.21

135.21

-148.22

143.58

-143.58

148.22

-135.21

Mom

ent D

iagr

am -

k-ft

-800.0

800.0

She

ar D

iagr

am -

kip

160.0

-160.0

-495.63

-719.74

487.21

-672.40 -672.40

461.84

-719.74

-495.63

487.21

135.21

-148.22

143.58

-143.58

148.22

-135.21

Page 8: 9.3 kips/ft - Portland Cement Associationcement.org/buildings/Timesaving-MomentRedistribution-IA.pdf · TIME SAVING DESIGN AID Page 1 of 23 Moment Redistribution A 3-span continuous

TIME SAVING DESIGN AID

Page 8 of 23

Moment Redistribution

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

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

Project: Time Saving Design Aid

Frame: Moment Redistribution Engineer: DAA

Flexural Reinforcement

2-#9

(80.

1)2-

#9(6

0.2)

3-#9

(114

.1)

3-#9

(87.

6)

3-#9

(110

.7)

3-#9

(81.

4)

3-#9

(110

.7)

3-#9

(81.

4)

3-#9

(114

.1)

3-#9

(87.

6)

2-#9

(80.

1)2-

#9(6

0.2)

3-#9

(360

.0)c

2-#9

(229

.7)

3-#9

(360

.0)c

2-#9

(212

.7)

3-#9

(360

.0)c

2-#9

(229

.7)

Page 9: 9.3 kips/ft - Portland Cement Associationcement.org/buildings/Timesaving-MomentRedistribution-IA.pdf · TIME SAVING DESIGN AID Page 1 of 23 Moment Redistribution A 3-span continuous

TIME SAVING DESIGN AID

Page 9 of 23

Moment Redistribution

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

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

Project: Time Saving Design Aid

Frame: Moment Redistribution Engineer: DAA

Mom

ent C

apac

ity -

k-ft

-800.0

800.0

Mom

ent C

apac

ity -

k-ft

-800.0

800.0

LEGEND:Envelope CurveCapacity CurveSupport CentereFace of Supporto

Page 10: 9.3 kips/ft - Portland Cement Associationcement.org/buildings/Timesaving-MomentRedistribution-IA.pdf · TIME SAVING DESIGN AID Page 1 of 23 Moment Redistribution A 3-span continuous

TIME SAVING DESIGN AID

Page 10 of 23

Moment Redistribution

pcaBeam v2.00 © Portland Cement Association 05-04-2007, 09:55:25 AMLicensed to: PCA, License ID: 12345-1234567-4-2D2DE-2C8D0 C:\Data\Time Saving Design Aid\Moment redistribution 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\Moment redistribution example.slb Project: Time Saving Design Aid Frame: Moment Redistribution Engineer: DAA Code: ACI 318-05 Reinforcement Database: ASTM A615 Mode: Design Number of supports = 4 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 selected. Effective flange width calculations NOT selected. Rigid beam-column joint NOT selected. Torsion analysis and design NOT selected. Material Properties:==================== Slabs|Beams Columns ------------ ------------ wc = 150 150 lb/ft3 f'c = 4 4 ksi Ec = 3834.3 3834.3 ksi fr = 0.474342 0.47434 ksi fy = 60 ksi, Bars are not epoxy-coated fyt = 60 ksi Es = 29000 ksi Reinforcement Database:===============

Page 11: 9.3 kips/ft - Portland Cement Associationcement.org/buildings/Timesaving-MomentRedistribution-IA.pdf · TIME SAVING DESIGN AID Page 1 of 23 Moment Redistribution A 3-span continuous

TIME SAVING DESIGN AID

Page 11 of 23

Moment Redistribution

pcaBeam v2.00 © Portland Cement Association 05-04-2007, 09:55:25 AMLicensed to: PCA, License ID: 12345-1234567-4-2D2DE-2C8D0 C:\Data\Time Saving Design Aid\Moment redistribution example.slb Page 2

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, Hmin (in) Span Loc L1 t wL wR Hmin ---- ---- -------- -------- -------- -------- -------- 1 Int 30.000 0.00 0.833 0.833 0.00 2 Int 30.000 0.00 0.833 0.833 0.00 3 Int 30.000 0.00 0.833 0.833 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 20.00 28.00 19.46 2 0.00 0.00 0.00 20.00 28.00 17.14 3 0.00 0.00 0.00 20.00 28.00 19.46 Support Data:============= Columns: c1a, c2a, c1b, c2b (in); Ha, Hb (ft) Supp c1a c2a Ha c1b c2b Hb Red% ---- -------- -------- -------- -------- -------- -------- ---- 1 20.00 20.00 12.000 20.00 20.00 12.000 100 2 20.00 20.00 12.000 20.00 20.00 12.000 100 3 20.00 20.00 12.000 20.00 20.00 12.000 100 4 20.00 20.00 12.000 20.00 20.00 12.000 100 Moment Redistribution Limits Supp Left[%] Right[%] ---- -------- -------- 1 0 0 2 20 20 3 20 20 4 0 0 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 Load Data:========== Load Cases and Combinations: Case SELF Dead Live Wind EQ Type DEAD DEAD LIVE LATERAL LATERAL U1 1.200 1.200 1.600 0.000 0.000 Span Loads: Span Case Wa La Wb Lb ---- -------- ------------ ------------ ------------ ------------ Line Loads - Wa | Wb (lb/ft), La | Lb (ft): 1 Dead 3500 0 3500 30 2 Dead 3500 0 3500 30 3 Dead 3500 0 3500 30 1 Live 2750 0 2750 30 2 Live 2750 0 2750 30 3 Live 2750 0 2750 30 Support Loads - Fz (kip), My (k-ft): Supp Case Fz My ---- -------- ------------ ------------ 1 SELF 0 0 2 SELF 0 0 3 SELF 0 0 4 SELF 0 0 1 Live 0 0 2 Live 0 0 3 Live 0 0 4 Live 0 0 Support Displacements - D (in), R (rad): Supp Case D R ---- -------- ------------ ------------ 1 SELF 0 0

Page 12: 9.3 kips/ft - Portland Cement Associationcement.org/buildings/Timesaving-MomentRedistribution-IA.pdf · TIME SAVING DESIGN AID Page 1 of 23 Moment Redistribution A 3-span continuous

TIME SAVING DESIGN AID

Page 12 of 23

Moment Redistribution

pcaBeam v2.00 © Portland Cement Association 05-04-2007, 09:55:25 AMLicensed to: PCA, License ID: 12345-1234567-4-2D2DE-2C8D0 C:\Data\Time Saving Design Aid\Moment redistribution example.slb Page 3

2 SELF 0 0 3 SELF 0 0 4 SELF 0 0 1 Live 0 0 2 Live 0 0 3 Live 0 0 4 Live 0 0 Lateral Load Effects - M (k-ft): Span Case Mleft Mright ---- -------- ------------ ------------ 1 EQ 0 0 2 EQ 0 0 3 EQ 0 0 1 Wind 0 0 2 Wind 0 0 3 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 #9 #9 #3 #5 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 1.50 1.50 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============================================================================================= Moment Redistribution Factors:============================== Units: Org.Mu (k-ft) ____________Calculated_____________ __User__ _Applied_ Supp Side Org.Mu Iter.# EpsilonT Factor[%] Limit[%] Factor[%] ---- ------ -------- ------ -------- --------- -------- --------- 1 Right 388.10 3 0.02384 20.00 0.00 0.00 2 Left 676.69 5 0.00994 9.94 20.00 9.94 2 Right 638.55 5 0.01099 10.99 20.00 10.99 3 Left 638.55 5 0.01099 10.99 20.00 10.99 3 Right 676.69 5 0.00994 9.94 20.00 9.94 4 Left 388.10 3 0.02384 20.00 0.00 0.00 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 0.00 386.19 0.833 1.729 9.369 4.789 3.520 4-#9 Middle 0.00 0.00 15.000 0.000 9.369 0.000 0.000 --- Right 0.00 599.46 29.167 1.729 9.369 2.873 5.686 6-#9

2 Left 0.00 555.98 0.833 1.729 9.369 2.873 5.229 6-#9 Middle 0.00 0.00 15.000 0.000 9.369 0.000 0.000 --- Right 0.00 555.98 29.167 1.729 9.369 2.873 5.229 6-#9

3 Left 0.00 599.46 0.833 1.729 9.369 2.873 5.686 6-#9 Middle 0.00 0.00 15.000 0.000 9.369 0.000 0.000 --- Right 0.00 386.19 29.167 1.729 9.369 4.789 3.520 4-#9

Top Bar Details:================ Units: Length (ft) _____________Left______________ ___Continuous__ _____________Right_____________ Span Bars Length Bars Length Bars Length Bars Length Bars Length ---- ------- ------- ------- ------- ------- ------- ------- ------- ------- ------- 1 2-#9 6.68 2-#9 5.02 --- 3-#9 9.51 3-#9 7.30

2 3-#9 9.23 3-#9 6.78 --- 3-#9 9.23 3-#9 6.78

3 3-#9 9.51 3-#9 7.30 --- 2-#9 6.68 2-#9 5.02

Page 13: 9.3 kips/ft - Portland Cement Associationcement.org/buildings/Timesaving-MomentRedistribution-IA.pdf · TIME SAVING DESIGN AID Page 1 of 23 Moment Redistribution A 3-span continuous

TIME SAVING DESIGN AID

Page 13 of 23

Moment Redistribution

pcaBeam v2.00 © Portland Cement Association 05-04-2007, 09:55:25 AMLicensed to: PCA, License ID: 12345-1234567-4-2D2DE-2C8D0 C:\Data\Time Saving Design Aid\Moment redistribution example.slb Page 4

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 1.67 487.21 14.433 1.729 9.369 3.592 4.522 5-#9

2 1.67 461.84 15.000 1.729 9.369 3.592 4.267 5-#9

3 1.67 487.21 15.567 1.729 9.369 3.592 4.522 5-#9

Bottom Bar Details:=================== Units: Start (ft), Length (ft) _______Long Bars_______ ______Short Bars_______ Span Bars Start Length Bars Start Length ---- ------- ------- ------- ------- ------- ------- 1 3-#9 0.00 30.00 2-#9 4.97 19.14

2 3-#9 0.00 30.00 2-#9 6.14 17.72

3 3-#9 0.00 30.00 2-#9 5.89 19.14

Flexural Capacity:================== Units: x (ft), As (in^2), PhiMn (k-ft) Span x AsTop AsBot PhiMn- PhiMn+ ---- --------- ----- ----- ------------ ------------ 1 0.000 4.00 3.00 -435.08 332.27 0.833 4.00 3.00 -435.08 332.27 0.834 4.00 3.00 -435.08 332.27 2.497 3.20 3.00 -353.64 332.27 4.966 0.84 3.00 -96.96 332.27 5.015 0.80 3.03 -91.57 335.01 6.678 0.00 3.90 0.00 425.11 8.765 0.00 5.00 0.00 533.93 10.750 0.00 5.00 0.00 533.93 15.000 0.00 5.00 0.00 533.93 19.250 0.00 5.00 0.00 533.93 20.311 0.00 5.00 0.00 533.93 20.489 0.00 4.91 0.00 524.84 22.696 1.02 3.74 -117.38 409.19 24.110 2.34 3.00 -261.73 332.27 26.958 4.98 3.00 -531.65 332.27 29.166 6.00 3.00 -628.80 332.27 29.167 6.00 3.00 -628.80 332.27 30.000 6.00 3.00 -628.80 332.27

2 0.000 6.00 3.00 -628.80 332.27 0.833 6.00 3.00 -628.80 332.27 0.834 6.00 3.00 -628.80 332.27 3.279 4.77 3.00 -511.28 332.27 6.138 1.88 3.00 -212.80 332.27 6.784 1.23 3.36 -140.85 369.75 9.228 0.00 4.72 0.00 507.03 9.723 0.00 5.00 0.00 533.93 10.750 0.00 5.00 0.00 533.93 15.000 0.00 5.00 0.00 533.93 19.250 0.00 5.00 0.00 533.93 20.277 0.00 5.00 0.00 533.93 20.772 0.00 4.72 0.00 507.03 23.216 1.23 3.36 -140.85 369.75 23.862 1.88 3.00 -212.80 332.27 26.721 4.77 3.00 -511.28 332.27 29.166 6.00 3.00 -628.80 332.27 29.167 6.00 3.00 -628.80 332.27 30.000 6.00 3.00 -628.80 332.27

3 0.000 6.00 3.00 -628.80 332.27 0.833 6.00 3.00 -628.80 332.27 0.834 6.00 3.00 -628.80 332.27 3.042 4.98 3.00 -531.65 332.27 5.890 2.34 3.00 -261.73 332.27 7.304 1.02 3.74 -117.38 409.19 9.511 0.00 4.91 0.00 524.84 9.689 0.00 5.00 0.00 533.93 10.750 0.00 5.00 0.00 533.93 15.000 0.00 5.00 0.00 533.93 19.250 0.00 5.00 0.00 533.93 21.235 0.00 5.00 0.00 533.93 23.322 0.00 3.90 0.00 425.11 24.985 0.80 3.03 -91.56 335.01 25.034 0.84 3.00 -96.96 332.27 27.503 3.20 3.00 -353.64 332.27 29.166 4.00 3.00 -435.08 332.27 29.167 4.00 3.00 -435.08 332.27 30.000 4.00 3.00 -435.08 332.27

Page 14: 9.3 kips/ft - Portland Cement Associationcement.org/buildings/Timesaving-MomentRedistribution-IA.pdf · TIME SAVING DESIGN AID Page 1 of 23 Moment Redistribution A 3-span continuous

TIME SAVING DESIGN AID

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Moment Redistribution

pcaBeam v2.00 © Portland Cement Association 05-04-2007, 09:55:25 AMLicensed to: PCA, License ID: 12345-1234567-4-2D2DE-2C8D0 C:\Data\Time Saving Design Aid\Moment redistribution example.slb Page 5

Longitudinal Beam Shear Reinforcement Required:=============================================== Units: d (in), Start, End, Xu (ft), PhiVc, Vu (kip), Av/s (in^2/in) Span d PhiVc Start End Vu Xu Av/s ---- -------- -------- -------- -------- -------- -------- -------- 1 25.94 49.21 2.995 6.425 107.36 2.995 0.0498 6.425 9.855 75.46 6.425 0.0225 9.855 13.285 43.56 9.855 0.0167 13.285 16.715 24.67 16.715 0.0167 16.715 20.145 56.57 20.145 0.0167 20.145 23.575 88.47 23.575 0.0336 23.575 27.005 120.37 27.005 0.0610

2 25.94 49.21 2.995 6.425 115.73 2.995 0.0570 6.425 9.855 83.83 6.425 0.0297 9.855 13.285 51.93 9.855 0.0167 13.285 16.715 20.03 13.285 0.0000 16.715 20.145 51.93 20.145 0.0167 20.145 23.575 83.83 23.575 0.0297 23.575 27.005 115.73 27.005 0.0570

3 25.94 49.21 2.995 6.425 120.37 2.995 0.0610 6.425 9.855 88.47 6.425 0.0336 9.855 13.285 56.57 9.855 0.0167 13.285 16.715 24.67 13.285 0.0167 16.715 20.145 43.56 20.145 0.0167 20.145 23.575 75.46 23.575 0.0225 23.575 27.005 107.36 27.005 0.0498

Longitudinal Beam Shear Reinforcement Details:============================================== Units: spacing & distance (in). Span Size Stirrups (2 legs each unless otherwise noted) ---- ---- --------------------------------------------- 1 #3 10 @ 6.4 [3L] + 5 @ 8.2 + 10 @ 12.3 + 7 @ 5.9 + 13 @ 5.3 [3L] 2 #3 12 @ 5.3 [3L] + 6 @ 6.9 + 5 @ 10.3 + <-- 41.2 --> + 4 @ 10.3 + 6 @ 6.9 + 13 @ 5.3 [3L] 3 #3 12 @ 5.3 [3L] + 7 @ 5.9 + 10 @ 12.3 + 5 @ 8.2 + 11 @ 6.4 [3L]

Beam Shear Capacity:==================== Units: d, Sp (in), Start, End, Xu (ft), PhiVc, PhiVn, Vu (kip), Av/s (in^2/in) Span d PhiVc Start End Av/s Sp PhiVn Vu Xu ---- -------- -------- -------- -------- -------- -------- -------- -------- -------- 1 25.94 49.21 0.000 1.083 ----- ----- 109.30 135.21 0.000 1.083 6.425 0.0515 6.4 109.30 107.36 2.995 6.425 9.855 0.0267 8.2 80.40 75.46 6.425 9.855 20.145 0.0178 12.3 70.00 56.57 20.145 20.145 23.575 0.0374 5.9 92.88 88.47 23.575 23.575 28.917 0.0618 5.3 121.32 120.37 27.005 28.917 30.000 ----- ----- 121.32 148.22 30.000

2 25.94 49.21 0.000 1.083 ----- ----- 121.32 143.58 0.000 1.083 6.425 0.0618 5.3 121.32 115.73 2.995 6.425 9.855 0.0321 6.9 86.64 83.83 6.425 9.855 13.285 0.0214 10.3 74.16 51.93 9.855 13.285 16.715 ----- ----- 24.61 20.03 13.285 16.715 20.145 0.0214 10.3 74.16 51.93 20.145 20.145 23.575 0.0321 6.9 86.64 83.83 23.575 23.575 28.917 0.0618 5.3 121.32 115.73 27.005 28.917 30.000 ----- ----- 121.32 143.58 30.000

3 25.94 49.21 0.000 1.083 ----- ----- 121.32 148.22 0.000 1.083 6.425 0.0618 5.3 121.32 120.37 2.995 6.425 9.855 0.0374 5.9 92.88 88.47 6.425 9.855 20.145 0.0178 12.3 70.00 56.57 9.855 20.145 23.575 0.0267 8.2 80.40 75.46 23.575 23.575 28.917 0.0515 6.4 109.30 107.36 27.005 28.917 30.000 ----- ----- 109.30 135.21 30.000

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 ---

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

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Moment Redistribution

pcaBeam v2.00 © Portland Cement Association 05-04-2007, 09:55:25 AMLicensed to: PCA, License ID: 12345-1234567-4-2D2DE-2C8D0 C:\Data\Time Saving Design Aid\Moment redistribution example.slb Page 6

________Ie,avg_________ _________Dead_______ ______Dead+Live_____ Span Dead Dead+Live Zone Ig Icr Mcr Mmax Ie Mmax Ie ---- ----------- ----------- ------ ----------- ----------- -------- -------- ----------- -------- ----------- 1 18341 16434 Middle 36587 15572 103.30 203.93 18303 341.26 16154 Right 36587 17869 103.30 -310.90 18555 -520.28 18015 2 19355 16921 Left 36587 17869 103.30 -280.07 18808 -468.69 18069 Middle 36587 15572 103.30 179.30 19590 300.06 16429 Right 36587 17869 103.30 -280.07 18808 -468.69 18069 3 18341 16434 Left 36587 17869 103.30 -310.90 18555 -520.28 18015 Middle 36587 15572 103.30 203.93 18303 341.26 16154 Maximum Instantaneous Deflections --------------------------------- Units: D (in) Span Ddead Dlive Dtotal ---- -------- -------- -------- 1 0.245 0.199 0.444 2 0.171 0.155 0.326 3 0.245 0.199 0.444 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 0.245 2.000 0.490 0.689 0.689 0.934 2 0.171 2.000 0.343 0.498 0.498 0.669 3 0.245 2.000 0.490 0.689 0.689 0.934 Material Takeoff:================= Reinforcement in the Direction of Analysis ------------------------------------------ Top Bars: 828.7 lb <=> 9.21 lb/ft <=> 5.525 lb/ft^2 Bottom Bars: 1298.9 lb <=> 14.43 lb/ft <=> 8.659 lb/ft^2 Stirrups: 1354.2 lb <=> 15.05 lb/ft <=> 9.028 lb/ft^2 Total Steel: 3481.8 lb <=> 38.69 lb/ft <=> 23.212 lb/ft^2 Concrete: 350.0 ft^3 <=> 3.89 ft^3/ft <=> 2.333 ft^3/ft^2

=============================================================================================[6] REDISTRIBUTED SEGMENTAL MOMENT AND SHEAR - ENVELOPES============================================================================================= Span x (ft) M- (k-ft) Comb M+ (k-ft) Comb V- (kip) Comb V+ (kip) Comb ---- -------- ------------ ---- ------------ ---- ------------ ---- ------------ ---- 1 0.000 -495.63 U1 0.00 U1 0.00 U1 135.21 U1 0.208 -467.67 U1 0.00 U1 0.00 U1 133.27 U1 0.417 -440.10 U1 0.00 U1 0.00 U1 131.34 U1 0.625 -412.94 U1 0.00 U1 0.00 U1 129.40 U1 0.833 -386.19 U1 0.00 U1 0.00 U1 127.46 U1 0.833 -386.19 U1 0.00 U1 0.00 U1 127.46 U1 1.117 -350.45 U1 0.00 U1 0.00 U1 124.83 U1 1.400 -315.45 U1 0.00 U1 0.00 U1 122.19 U1 1.683 -281.21 U1 0.00 U1 0.00 U1 119.56 U1 1.967 -247.70 U1 0.00 U1 0.00 U1 116.92 U1 2.250 -214.95 U1 0.00 U1 0.00 U1 114.29 U1 2.533 -182.94 U1 0.00 U1 0.00 U1 111.65 U1 2.817 -151.68 U1 0.00 U1 0.00 U1 109.02 U1 3.100 -121.17 U1 0.00 U1 0.00 U1 106.38 U1 3.383 -91.40 U1 0.00 U1 0.00 U1 103.75 U1 3.667 -62.38 U1 0.00 U1 0.00 U1 101.11 U1 3.950 -34.10 U1 8.87 U1 0.00 U1 98.48 U1 4.233 -6.58 U1 21.69 U1 0.00 U1 95.84 U1 4.517 0.00 U1 37.72 U1 0.00 U1 93.21 U1 4.800 0.00 U1 62.50 U1 0.00 U1 90.57 U1 5.083 0.00 U1 86.53 U1 0.00 U1 87.94 U1 5.367 0.00 U1 109.82 U1 0.00 U1 85.30 U1 5.650 0.00 U1 132.36 U1 0.00 U1 82.67 U1 5.933 0.00 U1 154.15 U1 0.00 U1 80.03 U1 6.217 0.00 U1 175.19 U1 0.00 U1 77.40 U1 6.500 0.00 U1 195.49 U1 0.00 U1 74.76 U1 6.783 0.00 U1 215.05 U1 0.00 U1 72.13 U1 7.067 0.00 U1 233.85 U1 0.00 U1 69.49 U1 7.350 0.00 U1 251.91 U1 0.00 U1 66.86 U1 7.633 0.00 U1 269.23 U1 0.00 U1 64.22 U1 7.917 0.00 U1 285.79 U1 0.00 U1 61.59 U1 8.200 0.00 U1 301.61 U1 0.00 U1 58.95 U1 8.483 0.00 U1 316.75 U1 0.00 U1 56.32 U1 8.767 0.00 U1 332.34 U1 0.00 U1 53.68 U1 9.050 0.00 U1 347.17 U1 0.00 U1 51.05 U1 9.333 0.00 U1 361.26 U1 0.00 U1 48.41 U1 9.617 0.00 U1 374.61 U1 0.00 U1 45.78 U1 9.900 0.00 U1 387.20 U1 0.00 U1 43.14 U1 10.183 0.00 U1 399.05 U1 0.00 U1 40.51 U1

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Moment Redistribution

pcaBeam v2.00 © Portland Cement Association 05-04-2007, 09:55:25 AMLicensed to: PCA, License ID: 12345-1234567-4-2D2DE-2C8D0 C:\Data\Time Saving Design Aid\Moment redistribution example.slb Page 7

10.467 0.00 U1 410.16 U1 0.00 U1 37.87 U1 10.750 0.00 U1 420.51 U1 0.00 U1 35.24 U1 11.033 0.00 U1 430.12 U1 0.00 U1 32.60 U1 11.317 0.00 U1 438.99 U1 0.00 U1 29.97 U1 11.600 0.00 U1 447.10 U1 0.00 U1 27.33 U1 11.883 0.00 U1 454.47 U1 0.00 U1 24.70 U1 12.167 0.00 U1 461.10 U1 0.00 U1 22.06 U1 12.450 0.00 U1 466.97 U1 0.00 U1 19.43 U1 12.733 0.00 U1 472.10 U1 0.00 U1 16.79 U1 13.017 0.00 U1 476.49 U1 0.00 U1 14.16 U1 13.300 0.00 U1 480.12 U1 0.00 U1 11.52 U1 13.583 0.00 U1 483.02 U1 -1.26 U1 8.89 U1 13.867 0.00 U1 485.16 U1 -2.65 U1 6.25 U1 14.150 0.00 U1 486.56 U1 -4.04 U1 3.62 U1 14.433 0.00 U1 487.21 U1 -5.42 U1 0.98 U1 14.717 0.00 U1 487.11 U1 -6.81 U1 0.00 U1 15.000 0.00 U1 486.27 U1 -8.72 U1 0.00 U1 15.283 0.00 U1 484.68 U1 -11.36 U1 0.00 U1 15.567 0.00 U1 482.35 U1 -13.99 U1 0.00 U1 15.850 0.00 U1 479.26 U1 -16.63 U1 0.00 U1 16.133 0.00 U1 475.44 U1 -19.26 U1 0.00 U1 16.417 0.00 U1 470.86 U1 -21.90 U1 0.00 U1 16.700 0.00 U1 465.54 U1 -24.53 U1 0.00 U1 16.983 0.00 U1 459.47 U1 -27.17 U1 0.00 U1 17.267 0.00 U1 452.66 U1 -29.80 U1 0.00 U1 17.550 0.00 U1 445.09 U1 -32.44 U1 0.00 U1 17.833 0.00 U1 436.79 U1 -35.07 U1 0.00 U1 18.117 0.00 U1 427.73 U1 -37.71 U1 0.00 U1 18.400 0.00 U1 417.93 U1 -40.34 U1 0.00 U1 18.683 0.00 U1 407.38 U1 -42.98 U1 0.00 U1 18.967 0.00 U1 396.09 U1 -45.61 U1 0.00 U1 19.250 0.00 U1 384.05 U1 -48.25 U1 0.00 U1 19.533 0.00 U1 371.26 U1 -50.88 U1 0.00 U1 19.817 0.00 U1 357.73 U1 -53.52 U1 0.00 U1 20.100 0.00 U1 343.44 U1 -56.15 U1 0.00 U1 20.383 0.00 U1 328.42 U1 -58.79 U1 0.00 U1 20.667 0.00 U1 312.64 U1 -61.42 U1 0.00 U1 20.950 0.00 U1 296.12 U1 -64.06 U1 0.00 U1 21.233 0.00 U1 278.86 U1 -66.69 U1 0.00 U1 21.517 0.00 U1 260.84 U1 -69.33 U1 0.00 U1 21.800 0.00 U1 242.08 U1 -71.96 U1 0.00 U1 22.083 0.00 U1 222.58 U1 -74.60 U1 0.00 U1 22.367 0.00 U1 202.32 U1 -77.23 U1 0.00 U1 22.650 0.00 U1 181.32 U1 -79.87 U1 0.00 U1 22.933 -1.85 U1 159.58 U1 -82.50 U1 0.00 U1 23.217 -15.38 U1 137.08 U1 -85.14 U1 0.00 U1 23.500 -29.31 U1 113.84 U1 -87.77 U1 0.00 U1 23.783 -43.63 U1 89.86 U1 -90.41 U1 0.00 U1 24.067 -58.35 U1 65.12 U1 -93.04 U1 0.00 U1 24.350 -73.45 U1 39.64 U1 -95.68 U1 0.00 U1 24.633 -88.96 U1 13.42 U1 -98.31 U1 0.00 U1 24.917 -104.85 U1 0.00 U1 -100.95 U1 0.00 U1 25.200 -121.14 U1 0.00 U1 -103.58 U1 0.00 U1 25.483 -145.14 U1 0.00 U1 -106.22 U1 0.00 U1 25.767 -175.61 U1 0.00 U1 -108.85 U1 0.00 U1 26.050 -206.82 U1 0.00 U1 -111.49 U1 0.00 U1 26.333 -238.78 U1 0.00 U1 -114.12 U1 0.00 U1 26.617 -271.49 U1 0.00 U1 -116.76 U1 0.00 U1 26.900 -304.95 U1 0.00 U1 -119.39 U1 0.00 U1 27.183 -339.15 U1 0.00 U1 -122.03 U1 0.00 U1 27.467 -374.09 U1 0.00 U1 -124.66 U1 0.00 U1 27.750 -409.79 U1 0.00 U1 -127.30 U1 0.00 U1 28.033 -446.23 U1 0.00 U1 -129.93 U1 0.00 U1 28.317 -483.42 U1 0.00 U1 -132.57 U1 0.00 U1 28.600 -521.35 U1 0.00 U1 -135.20 U1 0.00 U1 28.883 -560.03 U1 0.00 U1 -137.84 U1 0.00 U1 29.167 -599.46 U1 0.00 U1 -140.47 U1 0.00 U1 29.167 -599.46 U1 0.00 U1 -140.47 U1 0.00 U1 29.375 -628.92 U1 0.00 U1 -142.41 U1 0.00 U1 29.583 -658.79 U1 0.00 U1 -144.35 U1 0.00 U1 29.792 -689.06 U1 0.00 U1 -146.28 U1 0.00 U1 30.000 -719.74 U1 0.00 U1 -148.22 U1 0.00 U1

2 0.000 -672.40 U1 0.00 U1 0.00 U1 143.58 U1 0.208 -642.69 U1 0.00 U1 0.00 U1 141.65 U1 0.417 -613.38 U1 0.00 U1 0.00 U1 139.71 U1 0.625 -584.48 U1 0.00 U1 0.00 U1 137.77 U1 0.833 -555.98 U1 0.00 U1 0.00 U1 135.83 U1 0.833 -555.98 U1 0.00 U1 0.00 U1 135.83 U1 1.117 -517.87 U1 0.00 U1 0.00 U1 133.20 U1 1.400 -480.50 U1 0.00 U1 0.00 U1 130.56 U1 1.683 -443.88 U1 0.00 U1 0.00 U1 127.93 U1 1.967 -408.01 U1 0.00 U1 0.00 U1 125.29 U1 2.250 -372.88 U1 0.00 U1 0.00 U1 122.66 U1 2.533 -338.50 U1 0.00 U1 0.00 U1 120.02 U1 2.817 -304.87 U1 0.00 U1 0.00 U1 117.39 U1 3.100 -271.98 U1 0.00 U1 0.00 U1 114.75 U1

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Moment Redistribution

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3.383 -239.84 U1 0.00 U1 0.00 U1 112.12 U1 3.667 -208.45 U1 0.00 U1 0.00 U1 109.48 U1 3.950 -177.80 U1 0.00 U1 0.00 U1 106.85 U1 4.233 -147.90 U1 0.00 U1 0.00 U1 104.21 U1 4.517 -123.00 U1 0.00 U1 0.00 U1 101.58 U1 4.800 -107.44 U1 0.00 U1 0.00 U1 98.94 U1 5.083 -92.28 U1 18.32 U1 0.00 U1 96.31 U1 5.367 -77.51 U1 42.92 U1 0.00 U1 93.67 U1 5.650 -63.14 U1 66.78 U1 0.00 U1 91.04 U1 5.933 -49.16 U1 89.88 U1 0.00 U1 88.40 U1 6.217 -35.57 U1 112.24 U1 0.00 U1 85.77 U1 6.500 -22.37 U1 133.86 U1 0.00 U1 83.13 U1 6.783 -9.57 U1 154.72 U1 0.00 U1 80.50 U1 7.067 0.00 U1 174.84 U1 0.00 U1 77.86 U1 7.350 0.00 U1 194.22 U1 0.00 U1 75.23 U1 7.633 0.00 U1 212.85 U1 0.00 U1 72.59 U1 7.917 0.00 U1 230.73 U1 0.00 U1 69.96 U1 8.200 0.00 U1 247.86 U1 0.00 U1 67.32 U1 8.483 0.00 U1 264.37 U1 0.00 U1 64.69 U1 8.767 0.00 U1 281.17 U1 0.00 U1 62.05 U1 9.050 0.00 U1 297.22 U1 0.00 U1 59.42 U1 9.333 0.00 U1 312.52 U1 0.00 U1 56.78 U1 9.617 0.00 U1 327.08 U1 0.00 U1 54.15 U1 9.900 0.00 U1 340.89 U1 0.00 U1 51.51 U1 10.183 0.00 U1 353.96 U1 0.00 U1 48.88 U1 10.467 0.00 U1 366.28 U1 0.00 U1 46.24 U1 10.750 0.00 U1 377.85 U1 0.00 U1 43.61 U1 11.033 0.00 U1 388.68 U1 0.00 U1 40.97 U1 11.317 0.00 U1 398.76 U1 0.00 U1 38.34 U1 11.600 0.00 U1 408.09 U1 0.00 U1 35.70 U1 11.883 0.00 U1 416.67 U1 0.00 U1 33.07 U1 12.167 0.00 U1 424.51 U1 0.00 U1 30.43 U1 12.450 0.00 U1 431.61 U1 0.00 U1 27.80 U1 12.733 0.00 U1 437.95 U1 0.00 U1 25.16 U1 13.017 0.00 U1 443.55 U1 0.00 U1 22.53 U1 13.300 0.00 U1 448.40 U1 0.00 U1 19.89 U1 13.583 0.00 U1 452.51 U1 0.00 U1 17.26 U1 13.867 0.00 U1 455.87 U1 0.00 U1 14.62 U1 14.150 0.00 U1 458.48 U1 -0.06 U1 11.99 U1 14.433 0.00 U1 460.35 U1 -1.45 U1 9.35 U1 14.717 0.00 U1 461.47 U1 -2.84 U1 6.72 U1 15.000 0.00 U1 461.84 U1 -4.23 U1 4.23 U1 15.283 0.00 U1 461.47 U1 -6.72 U1 2.84 U1 15.567 0.00 U1 460.35 U1 -9.35 U1 1.45 U1 15.850 0.00 U1 458.48 U1 -11.99 U1 0.06 U1 16.133 0.00 U1 455.87 U1 -14.62 U1 0.00 U1 16.417 0.00 U1 452.51 U1 -17.26 U1 0.00 U1 16.700 0.00 U1 448.40 U1 -19.89 U1 0.00 U1 16.983 0.00 U1 443.55 U1 -22.53 U1 0.00 U1 17.267 0.00 U1 437.95 U1 -25.16 U1 0.00 U1 17.550 0.00 U1 431.61 U1 -27.80 U1 0.00 U1 17.833 0.00 U1 424.51 U1 -30.43 U1 0.00 U1 18.117 0.00 U1 416.67 U1 -33.07 U1 0.00 U1 18.400 0.00 U1 408.09 U1 -35.70 U1 0.00 U1 18.683 0.00 U1 398.76 U1 -38.34 U1 0.00 U1 18.967 0.00 U1 388.68 U1 -40.97 U1 0.00 U1 19.250 0.00 U1 377.85 U1 -43.61 U1 0.00 U1 19.533 0.00 U1 366.28 U1 -46.24 U1 0.00 U1 19.817 0.00 U1 353.96 U1 -48.88 U1 0.00 U1 20.100 0.00 U1 340.89 U1 -51.51 U1 0.00 U1 20.383 0.00 U1 327.08 U1 -54.15 U1 0.00 U1 20.667 0.00 U1 312.52 U1 -56.78 U1 0.00 U1 20.950 0.00 U1 297.22 U1 -59.42 U1 0.00 U1 21.233 0.00 U1 281.17 U1 -62.05 U1 0.00 U1 21.517 0.00 U1 264.37 U1 -64.69 U1 0.00 U1 21.800 0.00 U1 247.86 U1 -67.32 U1 0.00 U1 22.083 0.00 U1 230.73 U1 -69.96 U1 0.00 U1 22.367 0.00 U1 212.85 U1 -72.59 U1 0.00 U1 22.650 0.00 U1 194.22 U1 -75.23 U1 0.00 U1 22.933 0.00 U1 174.84 U1 -77.86 U1 0.00 U1 23.217 -9.57 U1 154.72 U1 -80.50 U1 0.00 U1 23.500 -22.37 U1 133.86 U1 -83.13 U1 0.00 U1 23.783 -35.57 U1 112.24 U1 -85.77 U1 0.00 U1 24.067 -49.16 U1 89.88 U1 -88.40 U1 0.00 U1 24.350 -63.14 U1 66.78 U1 -91.04 U1 0.00 U1 24.633 -77.51 U1 42.92 U1 -93.67 U1 0.00 U1 24.917 -92.28 U1 18.32 U1 -96.31 U1 0.00 U1 25.200 -107.44 U1 0.00 U1 -98.94 U1 0.00 U1 25.483 -123.00 U1 0.00 U1 -101.58 U1 0.00 U1 25.767 -147.90 U1 0.00 U1 -104.21 U1 0.00 U1 26.050 -177.80 U1 0.00 U1 -106.85 U1 0.00 U1 26.333 -208.45 U1 0.00 U1 -109.48 U1 0.00 U1 26.617 -239.84 U1 0.00 U1 -112.12 U1 0.00 U1 26.900 -271.98 U1 0.00 U1 -114.75 U1 0.00 U1 27.183 -304.87 U1 0.00 U1 -117.39 U1 0.00 U1 27.467 -338.50 U1 0.00 U1 -120.02 U1 0.00 U1 27.750 -372.88 U1 0.00 U1 -122.66 U1 0.00 U1

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Moment Redistribution

pcaBeam v2.00 © Portland Cement Association 05-04-2007, 09:55:25 AMLicensed to: PCA, License ID: 12345-1234567-4-2D2DE-2C8D0 C:\Data\Time Saving Design Aid\Moment redistribution example.slb Page 9

28.033 -408.01 U1 0.00 U1 -125.29 U1 0.00 U1 28.317 -443.88 U1 0.00 U1 -127.93 U1 0.00 U1 28.600 -480.50 U1 0.00 U1 -130.56 U1 0.00 U1 28.883 -517.87 U1 0.00 U1 -133.20 U1 0.00 U1 29.167 -555.98 U1 0.00 U1 -135.83 U1 0.00 U1 29.167 -555.98 U1 0.00 U1 -135.83 U1 0.00 U1 29.375 -584.48 U1 0.00 U1 -137.77 U1 0.00 U1 29.583 -613.38 U1 0.00 U1 -139.71 U1 0.00 U1 29.792 -642.69 U1 0.00 U1 -141.65 U1 0.00 U1 30.000 -672.40 U1 0.00 U1 -143.58 U1 0.00 U1

3 0.000 -719.74 U1 0.00 U1 0.00 U1 148.22 U1 0.208 -689.06 U1 0.00 U1 0.00 U1 146.28 U1 0.417 -658.79 U1 0.00 U1 0.00 U1 144.35 U1 0.625 -628.92 U1 0.00 U1 0.00 U1 142.41 U1 0.833 -599.46 U1 0.00 U1 0.00 U1 140.47 U1 0.833 -599.46 U1 0.00 U1 0.00 U1 140.47 U1 1.117 -560.03 U1 0.00 U1 0.00 U1 137.84 U1 1.400 -521.35 U1 0.00 U1 0.00 U1 135.20 U1 1.683 -483.42 U1 0.00 U1 0.00 U1 132.57 U1 1.967 -446.23 U1 0.00 U1 0.00 U1 129.93 U1 2.250 -409.79 U1 0.00 U1 0.00 U1 127.30 U1 2.533 -374.09 U1 0.00 U1 0.00 U1 124.66 U1 2.817 -339.15 U1 0.00 U1 0.00 U1 122.03 U1 3.100 -304.95 U1 0.00 U1 0.00 U1 119.39 U1 3.383 -271.49 U1 0.00 U1 0.00 U1 116.76 U1 3.667 -238.78 U1 0.00 U1 0.00 U1 114.12 U1 3.950 -206.82 U1 0.00 U1 0.00 U1 111.49 U1 4.233 -175.61 U1 0.00 U1 0.00 U1 108.85 U1 4.517 -145.14 U1 0.00 U1 0.00 U1 106.22 U1 4.800 -121.14 U1 0.00 U1 0.00 U1 103.58 U1 5.083 -104.85 U1 0.00 U1 0.00 U1 100.95 U1 5.367 -88.96 U1 13.42 U1 0.00 U1 98.31 U1 5.650 -73.45 U1 39.64 U1 0.00 U1 95.68 U1 5.933 -58.35 U1 65.12 U1 0.00 U1 93.04 U1 6.217 -43.63 U1 89.86 U1 0.00 U1 90.41 U1 6.500 -29.31 U1 113.84 U1 0.00 U1 87.77 U1 6.783 -15.38 U1 137.08 U1 0.00 U1 85.14 U1 7.067 -1.85 U1 159.58 U1 0.00 U1 82.50 U1 7.350 0.00 U1 181.32 U1 0.00 U1 79.87 U1 7.633 0.00 U1 202.32 U1 0.00 U1 77.23 U1 7.917 0.00 U1 222.58 U1 0.00 U1 74.60 U1 8.200 0.00 U1 242.08 U1 0.00 U1 71.96 U1 8.483 0.00 U1 260.84 U1 0.00 U1 69.33 U1 8.767 0.00 U1 278.86 U1 0.00 U1 66.69 U1 9.050 0.00 U1 296.12 U1 0.00 U1 64.06 U1 9.333 0.00 U1 312.64 U1 0.00 U1 61.42 U1 9.617 0.00 U1 328.42 U1 0.00 U1 58.79 U1 9.900 0.00 U1 343.45 U1 0.00 U1 56.15 U1 10.183 0.00 U1 357.73 U1 0.00 U1 53.52 U1 10.467 0.00 U1 371.26 U1 0.00 U1 50.88 U1 10.750 0.00 U1 384.05 U1 0.00 U1 48.25 U1 11.033 0.00 U1 396.09 U1 0.00 U1 45.61 U1 11.317 0.00 U1 407.38 U1 0.00 U1 42.98 U1 11.600 0.00 U1 417.93 U1 0.00 U1 40.34 U1 11.883 0.00 U1 427.73 U1 0.00 U1 37.71 U1 12.167 0.00 U1 436.79 U1 0.00 U1 35.07 U1 12.450 0.00 U1 445.09 U1 0.00 U1 32.44 U1 12.733 0.00 U1 452.66 U1 0.00 U1 29.80 U1 13.017 0.00 U1 459.47 U1 0.00 U1 27.17 U1 13.300 0.00 U1 465.54 U1 0.00 U1 24.53 U1 13.583 0.00 U1 470.86 U1 0.00 U1 21.90 U1 13.867 0.00 U1 475.44 U1 0.00 U1 19.26 U1 14.150 0.00 U1 479.26 U1 0.00 U1 16.63 U1 14.433 0.00 U1 482.35 U1 0.00 U1 13.99 U1 14.717 0.00 U1 484.68 U1 0.00 U1 11.36 U1 15.000 0.00 U1 486.27 U1 0.00 U1 8.72 U1 15.283 0.00 U1 487.11 U1 0.00 U1 6.81 U1 15.567 0.00 U1 487.21 U1 -0.98 U1 5.42 U1 15.850 0.00 U1 486.56 U1 -3.62 U1 4.04 U1 16.133 0.00 U1 485.16 U1 -6.25 U1 2.65 U1 16.417 0.00 U1 483.02 U1 -8.89 U1 1.26 U1 16.700 0.00 U1 480.12 U1 -11.52 U1 0.00 U1 16.983 0.00 U1 476.49 U1 -14.16 U1 0.00 U1 17.267 0.00 U1 472.10 U1 -16.79 U1 0.00 U1 17.550 0.00 U1 466.97 U1 -19.43 U1 0.00 U1 17.833 0.00 U1 461.10 U1 -22.06 U1 0.00 U1 18.117 0.00 U1 454.47 U1 -24.70 U1 0.00 U1 18.400 0.00 U1 447.10 U1 -27.33 U1 0.00 U1 18.683 0.00 U1 438.98 U1 -29.97 U1 0.00 U1 18.967 0.00 U1 430.12 U1 -32.60 U1 0.00 U1 19.250 0.00 U1 420.51 U1 -35.24 U1 0.00 U1 19.533 0.00 U1 410.15 U1 -37.87 U1 0.00 U1 19.817 0.00 U1 399.05 U1 -40.51 U1 0.00 U1 20.100 0.00 U1 387.20 U1 -43.14 U1 0.00 U1 20.383 0.00 U1 374.60 U1 -45.78 U1 0.00 U1 20.667 0.00 U1 361.26 U1 -48.41 U1 0.00 U1

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pcaBeam v2.00 © Portland Cement Association 05-04-2007, 09:55:25 AMLicensed to: PCA, License ID: 12345-1234567-4-2D2DE-2C8D0 C:\Data\Time Saving Design Aid\Moment redistribution example.slb Page 10

20.950 0.00 U1 347.17 U1 -51.05 U1 0.00 U1 21.233 0.00 U1 332.34 U1 -53.68 U1 0.00 U1 21.517 0.00 U1 316.75 U1 -56.32 U1 0.00 U1 21.800 0.00 U1 301.61 U1 -58.95 U1 0.00 U1 22.083 0.00 U1 285.79 U1 -61.59 U1 0.00 U1 22.367 0.00 U1 269.23 U1 -64.22 U1 0.00 U1 22.650 0.00 U1 251.91 U1 -66.86 U1 0.00 U1 22.933 0.00 U1 233.85 U1 -69.49 U1 0.00 U1 23.217 0.00 U1 215.05 U1 -72.13 U1 0.00 U1 23.500 0.00 U1 195.49 U1 -74.76 U1 0.00 U1 23.783 0.00 U1 175.19 U1 -77.40 U1 0.00 U1 24.067 0.00 U1 154.15 U1 -80.03 U1 0.00 U1 24.350 0.00 U1 132.35 U1 -82.67 U1 0.00 U1 24.633 0.00 U1 109.81 U1 -85.30 U1 0.00 U1 24.917 0.00 U1 86.53 U1 -87.94 U1 0.00 U1 25.200 0.00 U1 62.49 U1 -90.57 U1 0.00 U1 25.483 0.00 U1 37.71 U1 -93.21 U1 0.00 U1 25.767 -6.58 U1 21.69 U1 -95.84 U1 0.00 U1 26.050 -34.11 U1 8.87 U1 -98.48 U1 0.00 U1 26.333 -62.38 U1 0.00 U1 -101.11 U1 0.00 U1 26.617 -91.40 U1 0.00 U1 -103.75 U1 0.00 U1 26.900 -121.17 U1 0.00 U1 -106.38 U1 0.00 U1 27.183 -151.68 U1 0.00 U1 -109.02 U1 0.00 U1 27.467 -182.95 U1 0.00 U1 -111.65 U1 0.00 U1 27.750 -214.95 U1 0.00 U1 -114.29 U1 0.00 U1 28.033 -247.71 U1 0.00 U1 -116.92 U1 0.00 U1 28.317 -281.21 U1 0.00 U1 -119.56 U1 0.00 U1 28.600 -315.46 U1 0.00 U1 -122.19 U1 0.00 U1 28.883 -350.45 U1 0.00 U1 -124.83 U1 0.00 U1 29.167 -386.19 U1 0.00 U1 -127.46 U1 0.00 U1 29.167 -386.19 U1 0.00 U1 -127.46 U1 0.00 U1 29.375 -412.95 U1 0.00 U1 -129.40 U1 0.00 U1 29.583 -440.10 U1 0.00 U1 -131.34 U1 0.00 U1 29.792 -467.67 U1 0.00 U1 -133.27 U1 0.00 U1 30.000 -495.63 U1 0.00 U1 -135.21 U1 0.00 U1

=============================================================================================[6a] NON-REDISTRIBUTED SEGMENTAL MOMENT AND SHEAR - ENVELOPES============================================================================================= Span x (ft) M- (k-ft) Comb M+ (k-ft) Comb V- (kip) Comb V+ (kip) Comb ---- -------- ------------ ---- ------------ ---- ------------ ---- ------------ ---- 1 0.000 -495.63 U1 0.00 U1 0.00 U1 132.91 U1 0.208 -468.14 U1 0.00 U1 0.00 U1 130.98 U1 0.417 -441.06 U1 0.00 U1 0.00 U1 129.04 U1 0.625 -414.38 U1 0.00 U1 0.00 U1 127.10 U1 0.833 -388.10 U1 0.00 U1 0.00 U1 125.16 U1 0.833 -388.10 U1 0.00 U1 0.00 U1 125.16 U1 1.117 -353.01 U1 0.00 U1 0.00 U1 122.53 U1 1.400 -318.67 U1 0.00 U1 0.00 U1 119.89 U1 1.683 -285.07 U1 0.00 U1 0.00 U1 117.26 U1 1.967 -252.22 U1 0.00 U1 0.00 U1 114.62 U1 2.250 -220.12 U1 0.00 U1 0.00 U1 111.99 U1 2.533 -188.76 U1 0.00 U1 0.00 U1 109.35 U1 2.817 -158.15 U1 0.00 U1 0.00 U1 106.72 U1 3.100 -128.29 U1 0.00 U1 0.00 U1 104.08 U1 3.383 -99.17 U1 0.00 U1 0.00 U1 101.45 U1 3.667 -70.80 U1 0.00 U1 0.00 U1 98.81 U1 3.950 -43.18 U1 2.23 U1 0.00 U1 96.18 U1 4.233 -16.30 U1 14.58 U1 0.00 U1 93.54 U1 4.517 0.00 U1 26.53 U1 0.00 U1 90.91 U1 4.800 0.00 U1 49.79 U1 0.00 U1 88.27 U1 5.083 0.00 U1 73.07 U1 0.00 U1 85.64 U1 5.367 0.00 U1 95.61 U1 0.00 U1 83.00 U1 5.650 0.00 U1 117.39 U1 0.00 U1 80.37 U1 5.933 0.00 U1 138.44 U1 0.00 U1 77.73 U1 6.217 0.00 U1 158.73 U1 0.00 U1 75.10 U1 6.500 0.00 U1 178.28 U1 0.00 U1 72.46 U1 6.783 0.00 U1 197.09 U1 0.00 U1 69.83 U1 7.067 0.00 U1 215.14 U1 0.00 U1 67.19 U1 7.350 0.00 U1 232.45 U1 0.00 U1 64.56 U1 7.633 0.00 U1 249.02 U1 0.00 U1 61.92 U1 7.917 0.00 U1 265.17 U1 0.00 U1 59.29 U1 8.200 0.00 U1 281.59 U1 0.00 U1 56.65 U1 8.483 0.00 U1 297.27 U1 0.00 U1 54.02 U1 8.767 0.00 U1 312.20 U1 0.00 U1 51.38 U1 9.050 0.00 U1 326.39 U1 0.00 U1 48.75 U1 9.333 0.00 U1 339.83 U1 0.00 U1 46.11 U1 9.617 0.00 U1 352.52 U1 0.00 U1 43.48 U1 9.900 0.00 U1 364.46 U1 0.00 U1 40.84 U1 10.183 0.00 U1 375.66 U1 0.00 U1 38.21 U1 10.467 0.00 U1 386.12 U1 0.00 U1 35.57 U1 10.750 0.00 U1 395.82 U1 0.00 U1 32.94 U1 11.033 0.00 U1 404.78 U1 0.00 U1 30.30 U1 11.317 0.00 U1 412.99 U1 0.00 U1 27.67 U1 11.600 0.00 U1 420.46 U1 0.00 U1 25.03 U1

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pcaBeam v2.00 © Portland Cement Association 05-04-2007, 09:55:25 AMLicensed to: PCA, License ID: 12345-1234567-4-2D2DE-2C8D0 C:\Data\Time Saving Design Aid\Moment redistribution example.slb Page 11

11.883 0.00 U1 427.18 U1 0.00 U1 22.40 U1 12.167 0.00 U1 433.15 U1 0.00 U1 19.76 U1 12.450 0.00 U1 438.38 U1 0.00 U1 17.13 U1 12.733 0.00 U1 442.86 U1 0.00 U1 14.49 U1 13.017 0.00 U1 446.59 U1 -0.16 U1 11.86 U1 13.300 0.00 U1 449.58 U1 -1.55 U1 9.22 U1 13.583 0.00 U1 451.82 U1 -2.94 U1 6.59 U1 13.867 0.00 U1 453.31 U1 -4.33 U1 3.95 U1 14.150 0.00 U1 454.06 U1 -5.72 U1 1.32 U1 14.433 0.00 U1 454.06 U1 -7.10 U1 0.00 U1 14.717 0.00 U1 453.31 U1 -8.73 U1 0.00 U1 15.000 0.00 U1 451.82 U1 -11.37 U1 0.00 U1 15.283 0.00 U1 449.58 U1 -14.00 U1 0.00 U1 15.567 0.00 U1 446.59 U1 -16.64 U1 0.00 U1 15.850 0.00 U1 442.86 U1 -19.27 U1 0.00 U1 16.133 0.00 U1 438.38 U1 -21.91 U1 0.00 U1 16.417 0.00 U1 433.15 U1 -24.54 U1 0.00 U1 16.700 0.00 U1 427.18 U1 -27.18 U1 0.00 U1 16.983 0.00 U1 420.46 U1 -29.81 U1 0.00 U1 17.267 0.00 U1 413.00 U1 -32.45 U1 0.00 U1 17.550 0.00 U1 404.79 U1 -35.08 U1 0.00 U1 17.833 0.00 U1 395.83 U1 -37.72 U1 0.00 U1 18.117 0.00 U1 386.12 U1 -40.35 U1 0.00 U1 18.400 0.00 U1 375.67 U1 -42.99 U1 0.00 U1 18.683 0.00 U1 364.47 U1 -45.62 U1 0.00 U1 18.967 0.00 U1 352.53 U1 -48.26 U1 0.00 U1 19.250 0.00 U1 339.83 U1 -50.89 U1 0.00 U1 19.533 0.00 U1 326.40 U1 -53.53 U1 0.00 U1 19.817 0.00 U1 312.21 U1 -56.16 U1 0.00 U1 20.100 0.00 U1 297.28 U1 -58.80 U1 0.00 U1 20.383 0.00 U1 281.60 U1 -61.43 U1 0.00 U1 20.667 0.00 U1 265.18 U1 -64.07 U1 0.00 U1 20.950 0.00 U1 248.00 U1 -66.70 U1 0.00 U1 21.233 0.00 U1 230.09 U1 -69.34 U1 0.00 U1 21.517 0.00 U1 211.42 U1 -71.97 U1 0.00 U1 21.800 0.00 U1 192.01 U1 -74.61 U1 0.00 U1 22.083 -0.72 U1 171.85 U1 -77.24 U1 0.00 U1 22.367 -13.55 U1 150.95 U1 -79.88 U1 0.00 U1 22.650 -26.78 U1 129.30 U1 -82.51 U1 0.00 U1 22.933 -40.39 U1 106.90 U1 -85.15 U1 0.00 U1 23.217 -54.40 U1 83.76 U1 -87.78 U1 0.00 U1 23.500 -68.81 U1 59.87 U1 -90.42 U1 0.00 U1 23.783 -83.60 U1 35.23 U1 -93.05 U1 0.00 U1 24.067 -98.80 U1 9.85 U1 -95.69 U1 0.00 U1 24.350 -114.38 U1 0.00 U1 -98.32 U1 0.00 U1 24.633 -130.36 U1 0.00 U1 -100.96 U1 0.00 U1 24.917 -152.42 U1 0.00 U1 -103.59 U1 0.00 U1 25.200 -182.14 U1 0.00 U1 -106.23 U1 0.00 U1 25.483 -212.62 U1 0.00 U1 -108.86 U1 0.00 U1 25.767 -243.83 U1 0.00 U1 -111.50 U1 0.00 U1 26.050 -275.80 U1 0.00 U1 -114.13 U1 0.00 U1 26.333 -308.51 U1 0.00 U1 -116.77 U1 0.00 U1 26.617 -341.97 U1 0.00 U1 -119.40 U1 0.00 U1 26.900 -376.17 U1 0.00 U1 -122.04 U1 0.00 U1 27.183 -411.12 U1 0.00 U1 -124.67 U1 0.00 U1 27.467 -446.82 U1 0.00 U1 -127.31 U1 0.00 U1 27.750 -483.27 U1 0.00 U1 -129.94 U1 0.00 U1 28.033 -520.46 U1 0.00 U1 -132.58 U1 0.00 U1 28.317 -558.39 U1 0.00 U1 -135.21 U1 0.00 U1 28.600 -597.08 U1 0.00 U1 -137.85 U1 0.00 U1 28.883 -636.51 U1 0.00 U1 -140.48 U1 0.00 U1 29.167 -676.69 U1 0.00 U1 -143.12 U1 0.00 U1 29.167 -676.69 U1 0.00 U1 -143.12 U1 0.00 U1 29.375 -706.70 U1 0.00 U1 -145.06 U1 0.00 U1 29.583 -737.12 U1 0.00 U1 -146.99 U1 0.00 U1 29.792 -767.95 U1 0.00 U1 -148.93 U1 0.00 U1 30.000 -799.18 U1 0.00 U1 -150.87 U1 0.00 U1

2 0.000 -755.39 U1 0.00 U1 0.00 U1 144.09 U1 0.208 -725.58 U1 0.00 U1 0.00 U1 142.15 U1 0.417 -696.17 U1 0.00 U1 0.00 U1 140.21 U1 0.625 -667.16 U1 0.00 U1 0.00 U1 138.28 U1 0.833 -638.55 U1 0.00 U1 0.00 U1 136.34 U1 0.833 -638.55 U1 0.00 U1 0.00 U1 136.34 U1 1.117 -600.30 U1 0.00 U1 0.00 U1 133.70 U1 1.400 -562.79 U1 0.00 U1 0.00 U1 131.07 U1 1.683 -526.03 U1 0.00 U1 0.00 U1 128.43 U1 1.967 -490.01 U1 0.00 U1 0.00 U1 125.80 U1 2.250 -454.74 U1 0.00 U1 0.00 U1 123.16 U1 2.533 -420.22 U1 0.00 U1 0.00 U1 120.53 U1 2.817 -386.44 U1 0.00 U1 0.00 U1 117.89 U1 3.100 -353.41 U1 0.00 U1 0.00 U1 115.26 U1 3.383 -321.13 U1 0.00 U1 0.00 U1 112.62 U1 3.667 -289.59 U1 0.00 U1 0.00 U1 109.99 U1 3.950 -258.80 U1 0.00 U1 0.00 U1 107.35 U1 4.233 -228.76 U1 0.00 U1 0.00 U1 104.72 U1 4.517 -199.46 U1 0.00 U1 0.00 U1 102.08 U1

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Moment Redistribution

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4.800 -170.91 U1 0.00 U1 0.00 U1 99.45 U1 5.083 -143.11 U1 0.00 U1 0.00 U1 96.81 U1 5.367 -127.91 U1 0.00 U1 0.00 U1 94.18 U1 5.650 -113.43 U1 0.00 U1 0.00 U1 91.54 U1 5.933 -99.35 U1 19.02 U1 0.00 U1 88.91 U1 6.217 -85.66 U1 41.24 U1 0.00 U1 86.27 U1 6.500 -72.36 U1 62.71 U1 0.00 U1 83.64 U1 6.783 -59.46 U1 83.43 U1 0.00 U1 81.00 U1 7.067 -46.95 U1 103.41 U1 0.00 U1 78.37 U1 7.350 -34.83 U1 122.64 U1 0.00 U1 75.73 U1 7.633 -23.11 U1 141.13 U1 0.00 U1 73.10 U1 7.917 -11.78 U1 158.86 U1 0.00 U1 70.46 U1 8.200 -0.84 U1 175.86 U1 0.00 U1 67.83 U1 8.483 0.00 U1 192.24 U1 0.00 U1 65.19 U1 8.767 0.00 U1 209.04 U1 0.00 U1 62.56 U1 9.050 0.00 U1 225.09 U1 0.00 U1 59.92 U1 9.333 0.00 U1 240.39 U1 0.00 U1 57.29 U1 9.617 0.00 U1 254.95 U1 0.00 U1 54.65 U1 9.900 0.00 U1 268.76 U1 0.00 U1 52.02 U1 10.183 0.00 U1 281.83 U1 0.00 U1 49.38 U1 10.467 0.00 U1 294.15 U1 0.00 U1 46.75 U1 10.750 0.00 U1 305.72 U1 0.00 U1 44.11 U1 11.033 0.00 U1 316.54 U1 0.00 U1 41.48 U1 11.317 0.00 U1 326.62 U1 0.00 U1 38.84 U1 11.600 0.00 U1 335.96 U1 0.00 U1 36.21 U1 11.883 0.00 U1 344.54 U1 0.00 U1 33.57 U1 12.167 0.00 U1 352.38 U1 0.00 U1 30.94 U1 12.450 0.00 U1 359.47 U1 0.00 U1 28.30 U1 12.733 0.00 U1 365.82 U1 0.00 U1 25.67 U1 13.017 0.00 U1 371.42 U1 0.00 U1 23.03 U1 13.300 0.00 U1 376.27 U1 0.00 U1 20.40 U1 13.583 0.00 U1 380.38 U1 0.00 U1 17.76 U1 13.867 0.00 U1 383.74 U1 0.00 U1 15.13 U1 14.150 0.00 U1 386.35 U1 -0.42 U1 12.49 U1 14.433 0.00 U1 388.22 U1 -1.81 U1 9.86 U1 14.717 0.00 U1 389.34 U1 -3.20 U1 7.22 U1 15.000 0.00 U1 389.71 U1 -4.59 U1 4.59 U1 15.283 0.00 U1 389.34 U1 -7.22 U1 3.20 U1 15.567 0.00 U1 388.22 U1 -9.86 U1 1.81 U1 15.850 0.00 U1 386.35 U1 -12.49 U1 0.42 U1 16.133 0.00 U1 383.74 U1 -15.13 U1 0.00 U1 16.417 0.00 U1 380.38 U1 -17.76 U1 0.00 U1 16.700 0.00 U1 376.27 U1 -20.40 U1 0.00 U1 16.983 0.00 U1 371.42 U1 -23.03 U1 0.00 U1 17.267 0.00 U1 365.82 U1 -25.67 U1 0.00 U1 17.550 0.00 U1 359.47 U1 -28.30 U1 0.00 U1 17.833 0.00 U1 352.38 U1 -30.94 U1 0.00 U1 18.117 0.00 U1 344.54 U1 -33.57 U1 0.00 U1 18.400 0.00 U1 335.96 U1 -36.21 U1 0.00 U1 18.683 0.00 U1 326.62 U1 -38.84 U1 0.00 U1 18.967 0.00 U1 316.54 U1 -41.48 U1 0.00 U1 19.250 0.00 U1 305.72 U1 -44.11 U1 0.00 U1 19.533 0.00 U1 294.15 U1 -46.75 U1 0.00 U1 19.817 0.00 U1 281.83 U1 -49.38 U1 0.00 U1 20.100 0.00 U1 268.76 U1 -52.02 U1 0.00 U1 20.383 0.00 U1 254.95 U1 -54.65 U1 0.00 U1 20.667 0.00 U1 240.39 U1 -57.29 U1 0.00 U1 20.950 0.00 U1 225.09 U1 -59.92 U1 0.00 U1 21.233 0.00 U1 209.04 U1 -62.56 U1 0.00 U1 21.517 0.00 U1 192.24 U1 -65.19 U1 0.00 U1 21.800 -0.84 U1 175.86 U1 -67.83 U1 0.00 U1 22.083 -11.78 U1 158.86 U1 -70.46 U1 0.00 U1 22.367 -23.11 U1 141.13 U1 -73.10 U1 0.00 U1 22.650 -34.83 U1 122.64 U1 -75.73 U1 0.00 U1 22.933 -46.95 U1 103.41 U1 -78.37 U1 0.00 U1 23.217 -59.46 U1 83.43 U1 -81.00 U1 0.00 U1 23.500 -72.36 U1 62.71 U1 -83.64 U1 0.00 U1 23.783 -85.66 U1 41.24 U1 -86.27 U1 0.00 U1 24.067 -99.35 U1 19.02 U1 -88.91 U1 0.00 U1 24.350 -113.43 U1 0.00 U1 -91.54 U1 0.00 U1 24.633 -127.91 U1 0.00 U1 -94.18 U1 0.00 U1 24.917 -143.11 U1 0.00 U1 -96.81 U1 0.00 U1 25.200 -170.91 U1 0.00 U1 -99.45 U1 0.00 U1 25.483 -199.46 U1 0.00 U1 -102.08 U1 0.00 U1 25.767 -228.76 U1 0.00 U1 -104.72 U1 0.00 U1 26.050 -258.80 U1 0.00 U1 -107.35 U1 0.00 U1 26.333 -289.59 U1 0.00 U1 -109.99 U1 0.00 U1 26.617 -321.13 U1 0.00 U1 -112.62 U1 0.00 U1 26.900 -353.41 U1 0.00 U1 -115.26 U1 0.00 U1 27.183 -386.44 U1 0.00 U1 -117.89 U1 0.00 U1 27.467 -420.22 U1 0.00 U1 -120.53 U1 0.00 U1 27.750 -454.74 U1 0.00 U1 -123.16 U1 0.00 U1 28.033 -490.01 U1 0.00 U1 -125.80 U1 0.00 U1 28.317 -526.03 U1 0.00 U1 -128.43 U1 0.00 U1 28.600 -562.79 U1 0.00 U1 -131.07 U1 0.00 U1 28.883 -600.30 U1 0.00 U1 -133.70 U1 0.00 U1 29.167 -638.55 U1 0.00 U1 -136.34 U1 0.00 U1

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Moment Redistribution

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29.167 -638.55 U1 0.00 U1 -136.34 U1 0.00 U1 29.375 -667.16 U1 0.00 U1 -138.28 U1 0.00 U1 29.583 -696.17 U1 0.00 U1 -140.21 U1 0.00 U1 29.792 -725.58 U1 0.00 U1 -142.15 U1 0.00 U1 30.000 -755.39 U1 0.00 U1 -144.09 U1 0.00 U1

3 0.000 -799.18 U1 0.00 U1 0.00 U1 150.87 U1 0.208 -767.95 U1 0.00 U1 0.00 U1 148.93 U1 0.417 -737.12 U1 0.00 U1 0.00 U1 146.99 U1 0.625 -706.70 U1 0.00 U1 0.00 U1 145.06 U1 0.833 -676.69 U1 0.00 U1 0.00 U1 143.12 U1 0.833 -676.69 U1 0.00 U1 0.00 U1 143.12 U1 1.117 -636.51 U1 0.00 U1 0.00 U1 140.48 U1 1.400 -597.08 U1 0.00 U1 0.00 U1 137.85 U1 1.683 -558.39 U1 0.00 U1 0.00 U1 135.21 U1 1.967 -520.46 U1 0.00 U1 0.00 U1 132.58 U1 2.250 -483.27 U1 0.00 U1 0.00 U1 129.94 U1 2.533 -446.82 U1 0.00 U1 0.00 U1 127.31 U1 2.817 -411.12 U1 0.00 U1 0.00 U1 124.67 U1 3.100 -376.17 U1 0.00 U1 0.00 U1 122.04 U1 3.383 -341.97 U1 0.00 U1 0.00 U1 119.40 U1 3.667 -308.51 U1 0.00 U1 0.00 U1 116.77 U1 3.950 -275.80 U1 0.00 U1 0.00 U1 114.13 U1 4.233 -243.83 U1 0.00 U1 0.00 U1 111.50 U1 4.517 -212.61 U1 0.00 U1 0.00 U1 108.86 U1 4.800 -182.14 U1 0.00 U1 0.00 U1 106.23 U1 5.083 -152.42 U1 0.00 U1 0.00 U1 103.59 U1 5.367 -130.36 U1 0.00 U1 0.00 U1 100.96 U1 5.650 -114.38 U1 0.00 U1 0.00 U1 98.32 U1 5.933 -98.80 U1 9.85 U1 0.00 U1 95.69 U1 6.217 -83.60 U1 35.23 U1 0.00 U1 93.05 U1 6.500 -68.81 U1 59.87 U1 0.00 U1 90.42 U1 6.783 -54.40 U1 83.76 U1 0.00 U1 87.78 U1 7.067 -40.39 U1 106.90 U1 0.00 U1 85.15 U1 7.350 -26.78 U1 129.30 U1 0.00 U1 82.51 U1 7.633 -13.55 U1 150.95 U1 0.00 U1 79.88 U1 7.917 -0.72 U1 171.85 U1 0.00 U1 77.24 U1 8.200 0.00 U1 192.01 U1 0.00 U1 74.61 U1 8.483 0.00 U1 211.42 U1 0.00 U1 71.97 U1 8.767 0.00 U1 230.09 U1 0.00 U1 69.34 U1 9.050 0.00 U1 248.01 U1 0.00 U1 66.70 U1 9.333 0.00 U1 265.18 U1 0.00 U1 64.07 U1 9.617 0.00 U1 281.60 U1 0.00 U1 61.43 U1 9.900 0.00 U1 297.28 U1 0.00 U1 58.80 U1 10.183 0.00 U1 312.21 U1 0.00 U1 56.16 U1 10.467 0.00 U1 326.40 U1 0.00 U1 53.53 U1 10.750 0.00 U1 339.83 U1 0.00 U1 50.89 U1 11.033 0.00 U1 352.53 U1 0.00 U1 48.26 U1 11.317 0.00 U1 364.47 U1 0.00 U1 45.62 U1 11.600 0.00 U1 375.67 U1 0.00 U1 42.99 U1 11.883 0.00 U1 386.12 U1 0.00 U1 40.35 U1 12.167 0.00 U1 395.83 U1 0.00 U1 37.72 U1 12.450 0.00 U1 404.79 U1 0.00 U1 35.08 U1 12.733 0.00 U1 413.00 U1 0.00 U1 32.45 U1 13.017 0.00 U1 420.46 U1 0.00 U1 29.81 U1 13.300 0.00 U1 427.18 U1 0.00 U1 27.18 U1 13.583 0.00 U1 433.15 U1 0.00 U1 24.54 U1 13.867 0.00 U1 438.38 U1 0.00 U1 21.91 U1 14.150 0.00 U1 442.86 U1 0.00 U1 19.27 U1 14.433 0.00 U1 446.59 U1 0.00 U1 16.64 U1 14.717 0.00 U1 449.58 U1 0.00 U1 14.00 U1 15.000 0.00 U1 451.82 U1 0.00 U1 11.37 U1 15.283 0.00 U1 453.31 U1 0.00 U1 8.73 U1 15.567 0.00 U1 454.06 U1 0.00 U1 7.10 U1 15.850 0.00 U1 454.06 U1 -1.32 U1 5.72 U1 16.133 0.00 U1 453.31 U1 -3.95 U1 4.33 U1 16.417 0.00 U1 451.82 U1 -6.59 U1 2.94 U1 16.700 0.00 U1 449.58 U1 -9.22 U1 1.55 U1 16.983 0.00 U1 446.59 U1 -11.86 U1 0.16 U1 17.267 0.00 U1 442.86 U1 -14.49 U1 0.00 U1 17.550 0.00 U1 438.38 U1 -17.13 U1 0.00 U1 17.833 0.00 U1 433.15 U1 -19.76 U1 0.00 U1 18.117 0.00 U1 427.18 U1 -22.40 U1 0.00 U1 18.400 0.00 U1 420.46 U1 -25.03 U1 0.00 U1 18.683 0.00 U1 412.99 U1 -27.67 U1 0.00 U1 18.967 0.00 U1 404.78 U1 -30.30 U1 0.00 U1 19.250 0.00 U1 395.82 U1 -32.94 U1 0.00 U1 19.533 0.00 U1 386.11 U1 -35.57 U1 0.00 U1 19.817 0.00 U1 375.66 U1 -38.21 U1 0.00 U1 20.100 0.00 U1 364.46 U1 -40.84 U1 0.00 U1 20.383 0.00 U1 352.52 U1 -43.48 U1 0.00 U1 20.667 0.00 U1 339.83 U1 -46.11 U1 0.00 U1 20.950 0.00 U1 326.39 U1 -48.75 U1 0.00 U1 21.233 0.00 U1 312.20 U1 -51.38 U1 0.00 U1 21.517 0.00 U1 297.27 U1 -54.02 U1 0.00 U1 21.800 0.00 U1 281.59 U1 -56.65 U1 0.00 U1 22.083 0.00 U1 265.17 U1 -59.29 U1 0.00 U1

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Moment Redistribution

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22.367 0.00 U1 249.01 U1 -61.92 U1 0.00 U1 22.650 0.00 U1 232.45 U1 -64.56 U1 0.00 U1 22.933 0.00 U1 215.14 U1 -67.19 U1 0.00 U1 23.217 0.00 U1 197.08 U1 -69.83 U1 0.00 U1 23.500 0.00 U1 178.28 U1 -72.46 U1 0.00 U1 23.783 0.00 U1 158.73 U1 -75.10 U1 0.00 U1 24.067 0.00 U1 138.44 U1 -77.73 U1 0.00 U1 24.350 0.00 U1 117.39 U1 -80.37 U1 0.00 U1 24.633 0.00 U1 95.60 U1 -83.00 U1 0.00 U1 24.917 0.00 U1 73.07 U1 -85.64 U1 0.00 U1 25.200 0.00 U1 49.78 U1 -88.27 U1 0.00 U1 25.483 0.00 U1 26.53 U1 -90.91 U1 0.00 U1 25.767 -16.30 U1 14.58 U1 -93.54 U1 0.00 U1 26.050 -43.18 U1 2.23 U1 -96.18 U1 0.00 U1 26.333 -70.80 U1 0.00 U1 -98.81 U1 0.00 U1 26.617 -99.17 U1 0.00 U1 -101.45 U1 0.00 U1 26.900 -128.29 U1 0.00 U1 -104.08 U1 0.00 U1 27.183 -158.15 U1 0.00 U1 -106.72 U1 0.00 U1 27.467 -188.76 U1 0.00 U1 -109.35 U1 0.00 U1 27.750 -220.12 U1 0.00 U1 -111.99 U1 0.00 U1 28.033 -252.23 U1 0.00 U1 -114.62 U1 0.00 U1 28.317 -285.08 U1 0.00 U1 -117.26 U1 0.00 U1 28.600 -318.67 U1 0.00 U1 -119.89 U1 0.00 U1 28.883 -353.02 U1 0.00 U1 -122.53 U1 0.00 U1 29.167 -388.10 U1 0.00 U1 -125.16 U1 0.00 U1 29.167 -388.10 U1 0.00 U1 -125.16 U1 0.00 U1 29.375 -414.38 U1 0.00 U1 -127.10 U1 0.00 U1 29.583 -441.06 U1 0.00 U1 -129.04 U1 0.00 U1 29.792 -468.15 U1 0.00 U1 -130.98 U1 0.00 U1 30.000 -495.63 U1 0.00 U1 -132.91 U1 0.00 U1