Tn 180 Stress Check And Rebar Verification Us

Technical Note Structural Concrete Software System TN180_stress_check_12 102905

STRESS CHECK AND REBAR VERIFICATION

1.0 OBJECTIVE This example illustrates how you can verify the stresses and other design values reported by Floor-Pro. It presents the input data and the results obtained from a column supported floor system, followed by steps to take for their verification. 2.1 GEOMETRY AND STRUCTURE DEFINITION The plan view and other characteristics of the floor system selected are shown in Figs. 2.1-1 through 2.1-3. Two design sections are selected for verification. One is through a region of the slab that includes the opening (design section 1205) 1. The other is through the beam (design section 2202). Results of the following two sections are verified (Fig. 2.1-4). In both instances, the sections selected do not meet the requirements of the design code (ACI-318-02). This is indicated by the broken lines (shown in violet in color prints) in Fig. 2.1-4.

Note: Units are in ft and in.

FIGURE 2.1-1 PLAN VIEW 1

Note the convention used for definition of design sections. The first digit refers to the support line, the second to the span and the last two to the design section from the beginning of the span. For example, design section 3412 means the third support line, fourth span and the twelfth section. E-Mail [email protected] 1733 Woodside Road, Suite 220, Redwood City, California, 94061, USA, Tel: (650) 306-2400 Fax (650) 306 2401

Technical Note

FIGURE 2.1-2 THREE-DIMENSIONAL VIEW OF THE STRUCTURE

FIGURE 2.1-3 DESIGN STRIPS IN X-DIRECTION

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Technical Note

FIGURE 2.1-4 DESIGN SECTION IDENTIFICATION NUMBERS IN X-DIRECTION

2.2 SECTION PROPERTIES The section properties of the design sections are reported in two input data tables (Tables 2.2-1 and 2.2-2). These tables can be viewed, printed or appended to your compiled report. The tables included in this writing are truncated by removing the rows that are not relevant to the current verification. The tables are: • •

Data Table 153.2 Design section geometry as identified by the program, and idealized if need be. Data Table 152.2 This table reports the properties of the section, such as centroid, area, and moment of inertia as calculated and used by the program. The program calculates the centroid of the design section and determines the section properties with respect to the calculated centroid, where applicable.

TABLE 2.2-1 GEOMETRY OF DESIGN SECTIONS 3

Technical Note

153.20 AUTOMATICALLY GENERATED DESIGN SECTIONS Design Strip: Support Line 1 Design Section b1 d1 b2 d2 ft ft ft ft 1204 18.25 0.79 0.00 0.00 1205 15.00 0.79 0.00 0.00 1206 18.25 0.79 0.00 0.00

b3 ft 0.00 0.00 0.00

d3 ft 0.00 0.00 0.00

Design Strip: Support Line 2 Design Section b1 ft 2201 18.25 2202 18.25 2203 18.25

b3 ft 0.00 0.00 0.00

d3 ft 0.00 0.00 0.00

d1 ft 2.50 2.50 2.50

b2 ft 1.00 1.00 1.00

d2 ft 0.79 0.79 0.79

TABLE 2.2-2 SECTION PROPERTIES 152.20 AUTOMATICALLY GENERATED DESIGN SECTIONS Design Strip: Support Line 1 Design Section Start(x,y) End(x,y) Centroid Area (local x,z) Ft ft Ft in2 1204 (65.20,36.50) (65.20,18.25) (9.13,9.60) 2080.52 1205 (68.25,36.50) (68.25,18.25) (7.50,9.60) 1709.92 1206 (71.30,36.50) (71.30,18.25) (9.13,9.60) 2080.52 Design Strip: Support Line 2 Design Section Start(x,y) 2201 2202 2203

Ft (56.80,18.25) (60.60,18.25) (64.40,18.25)

End(x,y) ft (56.80,0.00) (60.60,0.00) (64.40,0.00)

Centroid (local x,z) Ft (9.13,9.47) (9.13,9.47) (9.13,9.47)

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I

Ytop

Ybot

in4 15646.54 12860.25 15646.54

in 4.75 4.75 4.75

in 4.75 4.75 4.75

Area

I

Ytop

Ybot

in2 2326.50 2326.50 2326.50

in4 73772.68 73772.68 73772.68

in 6.34 6.34 6.34

in 23.66 23.66 23.66

Technical Note The “Start” and “End” columns list the coordinates of the beginning and end of a design section. The “Centroid” column gives the distance of the centroid of the design section along its length from the start of the section. The following is the verification of the properties of the two sections selected: •

Section 1205 This is a rectangular section with the following dimensions: b = 15 ft d1 = 0.79 ft (9.5 in.) From Table 2.2-2 the actual length of the design section is given by: b = [(X2 – X1)2 + (Y2 – Y1)2]0.5 = [(68.25 –68.25)2 + (18.25 – 36.5)2]0.5 = 18.25 ft However, since 3.252 ft of the design section falls within an opening, the “idealized” section is only 15 ft. The cross-sectional area and other properties of the section are determined using the solid part of the cross-section. Area = 15*0.79*144 = 1706 in2 OK Moment of inertia (I) = (15*0.793/12)*124 = 12779 in4 , OK (From Table 2.2-2 I = 12860 in4 the difference is due to using only two decimal points in the hand calculation.) Distance from the centroid to the top and bottom = (0.79/2)*12 = 4.74 in. (From Table 2.2-2, distance = 4.75 in. OK)

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Section 2202 Using the section display tool of the program and an exaggerated vertical scale the geometry of the design section is shown in Fig. 2.2-1. The dimensions of the section are: Section width b1 = 18.25 ft Section depth d1 = 2.5 ft Flange thickness d2 = 0.79 ft Web thickness b2 = 1.00 ft

FIGURE 2.2-1 GEOMETRY OF DESIGN SECTION 2202

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The distance 3.25 ft was measured from on the plan using the “measure” tool of the program and the appropriate snap tools

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Technical Note From the above dimensions, the following values are obtained. The minor discrepancy is due to the report and the hand calculation using two decimal points only. Area = (18.25*79) + 1*( 2 – 0.79) = 2322 in2 (From Table 2.2-2 2326.50 in2 OK) Moment of inertia I = 73777 in4 (From Table 2.2-2 I = 73773 in4 OK) Distance of centroid to bottom = 23.67 in. (From Table 2.2-2 Ybot = 23.66 in. OK) Distance of centroid to top = 6.33 in. (From Table 2.2-2 Ytop = 6.34 in. OK)

2.3 DESIGN ACTIONS The integral of the calculated actions (moments, shears, axial) are listed in report Table 2.3-1 for load combinations selected by you. In this case, the following load combinations were selected: Sustained Load, and Strength. For each design section the program calculates three forces and three moments referenced to the centroid of the design section. However, the table lists only the four primary actions used in design of the section. The six actions are reported elsewhere.

TABLE 2.3-1 DESIGN VALUES 154.20 DESIGN ACTIONS FOR AUTOMATICALLY GENERATED SECTIONS Load Combination:Service(Sustained Load) Design Strip: Support Line 1 Design section Moment

Shear

Axial

Torsion

k-ft 153.270 151.508 159.761

k 0.479 0.901 -2.820

k -224.848 -216.685 -234.673

k-ft 59.259 17.256 -26.614

Design Strip: Support Line 2 Design section Moment

Shear

Axial

Torsion

k 16.032 -24.266 -18.686

k -375.862 -375.623 -379.291

k-ft 14.117 134.143 90.957

1204 1205 1206

2201 2202 2203

k-ft 310.513 245.456 166.307

Load Combination:Strength(Dead and Live)

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Top Stress psi -666 -798 -695

Bottom Stress psi 450 545 469

Centroid Stress psi -108 -127 -113

Top Stress psi -481 -414 -334

Bottom Stress psi 1033 783 477

Centroid Stress psi -162 -161 -163

Technical Note Design Strip: Support Line 1 Design section Moment k-ft 1204 416.976 1205 434.766 1206 458.207

Shear k 12.003 2.805 -9.094

Axial K 24.072 28.452 21.604

Torsion k-ft 130.438 0.562 -101.495

Design Strip: Support Line 2 Design section Moment k-ft 2201 389.410 2202 735.385 2203 988.670

Shear k 105.771 74.912 52.693

Axial K -8.000 -15.472 -20.506

Torsion k-ft -261.872 -205.871 -140.362

2.4 STRESS CHECK Consider section 2202 through the beam for verification of stresses reported. •

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Geometry (from Table 2.2-2) o Area o Moment of inertia o Distance to bottom fiber

= 2326.50 in. = 73772.68 in4 = 23.66 in.

Actions (from Table 2.3-1) o Moment o Axial

= 245.456 k-ft (tension at bottom) = -375.623 k (compression)

Stress at bottom is given by: fb = P/A + M*Yb/I = (-375.623/2326.50 + (245.456*12)*23.66 / 73772.68)*1000 = -161.45 + 944.66 = 783.21 psi (tension) (ADAPT -> 783 psi from Table 2.3-1 OK) Stress at centroid (precompression) fcentroid = P/A = -375.623/2326.5 = -161.45 psi (compression) (ADAPT -> 161 psi from Table 2.3-1 OK)

2.5 REINFORCEMENT VALUES Reinforcement is provided for service condition and strength. The results are reported in Table 2.5-1. Herein, the reinforcement required for strength condition of design section 1205 is verified.

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Technical Note

TABLE 2.5-1 SUMMARY OF REQUIRED AND PROVIDED REINFORCEMENT 156.20 DESIGN SECTION REBAR FOR AUTOMATICALLY GENERATED SECTIONS Load Combination: Service(Sustained Load) Design Strip: Support Line 1 Design Criteria: SERVICE_SUSTAINED_LOAD Design section As top As bot Top bar Bottom bar In2 in2 1204 0.00 6.30 0#5 8#8 1205 0.00 6.30 0#5 8#8 1206 0.00 6.56 0#5 9#8 Design Strip: Support Line 2 Design Criteria: SERVICE_SUSTAINED_LOAD Design section As top As bot Top bar Bottom bar In2 in2 2201 4.46 0.00 41#3 0#3 2202 0.00 0.00 0#3 0#3 2203 0.00 0.00 0#3 0#3 2204 0.00 2.76 0#3 26#3

Load Combination: Strength(Dead and Live) Design Strip: Support Line 1 Design Criteria: STRENGTH Design section As top As bot Top bar Bottom bar in2 in2 1204 0.00 7.39 0#5 10#8 1205 0.00 8.04 0#5 11#8 1206 0.00 8.33 0#5 11#8 Design Strip: Support Line 2 Design Criteria: STRENGTH Design section As top As bot Top bar Bottom bar in2 in2 2201 0.00 2.45 0#3 23#3 2202 0.00 2.15 0#3 20#3 2203 0.00 1.91 0#3 18#3

<Shear rebar> Av U-Strip spacing in2/ft in 0.15 17.87 0.20 13.21 0.16 16.82

Reinforcement reported by ADAPT is 8.04 in2 at bottom for design section 1205 •

Geometry of section b = 15 (ft) * 12 = 180 in. h = 9.50 in.

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Material

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Technical Note Concrete PT

f’c = 5000 psi fpu = 270 ksi fse = 26.7*1000/0.153 = 175 ksi CGS = 1.08 in. 3 60 ksi 1.50 in. #8 (1 in. diameter)

Rebar Rebar cover Rebar size •

Reinforcement PT = 9 strands * 0.153 = 1.377 in2 (from input data ) Rebar = 8.04 in2 (from report of Table 2.5-1)

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Design moment = 434.766 k-ft Mu

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Verification o Determine ultimate stress in prestressing (fps) Span 33 ft Depth 9.5 in. (0.79 ft) Span/depth ration = 33/0.79 = 41 > 35, hence use fps = fse + 10 + f’c/(300 ρp) < fse + 30 (Eqn 18-5 of ACI-318)

ρp = Aps/b*dp dp = 9.5 – 1.08 = 8.42 in.

ρp = Aps/b*dp = 1.377 / (180 * 8.42) = 9.09x10-4 fps = 175 + 10 + 5/( 300 * 9.09x10-4 ) = 203.34 ksi <175 + 30 = 205 ksi OK Total tension = 1.377 * 203.34 + 8.04 * 60 = 279.99 + 482.40 = 762.39 k Depth of compression zone: a = 762.39/(0.85*5*180) = 0.997 in. Depth of neutral axis: c = 0.997 / 0.80 = 1.25 in. Distance to farthest reinforcement: dt = 9.50 – 1.5 – 0.5*1 = 7.50 in. c/dt = 1.25/7.5 = 0.167 < 0.375 , hence

φ = 0.90

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The location of the strands are measured from the cross-sectional geometry of the design section using the “Create a Cut at Specified Location” and “Measure” tools of the program. The dimension is given in ft.

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Technical Note Design capacity ( φMn ) is given by:

φMn = 0.90[279.99(8.42 – 0.997/2) + 482.40 (7.50 – 0.997/2)]/12 = 419.66 k-ft The design moment (Mu) is 434.766 k-ft. The difference between the hand calculation (419.66) and the required value from the program (434.766) is 3.5%. The apparent discrepancy is due to the fact that the program’s computation is based on “strain compatibility,” whereas the above verification was carried out using the simple code formulas. Using strain compatibility, the stresses calculated for the prestressing strands are generally higher. This leads to a smaller value for the required rebar, as reported in Table 2.5-1.

2.6 SUMMARY REPORT The summary report generated for each of the design strips and shown as an example for design strip 1 lists the critical stresses, along with the envelope of the reinforcement required and provided.

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Technical Note SUPPORT LINE 1 Stress Diagrams

Stress Diagrams

Project: General name / Support Line 1 / Load Case: Service(Sustained Load) 1.00 x Selfweight + 1.00 x Dead load + 0.30 x Live load + 1.00 x Prestressing Tensile Stress Positive

Project: General name / Support Line 1 / Load Case: Service(Sustained Load) 1.00 x Selfweight + 1.00 x Dead load + 0.30 x Live load + 1.00 x Prestressing Tensile Stress Positive

Allowable Stresses

Bottom

Allowable Stresses

Top 0

500 -100

400 300

-300

Stress [psi]

Stress [psi]

-200

-400 -500

200 100

-600

0

-700

-100

-800

-200 Span 1

Span 2

Span 1

Span 3

Span 2

Span 3

(a) Max tension 64.8 psi, Allowable 530.1 psi (b) Max tension 888.8 psi, Allowable 530.1 psi Max compression -1136.7 psi, Allowable -2250.0 psi Max compression -289.6 psi, Allowable -2250.0 psi

DESIGN STRIP SERVICE COMBINATION STRESSES (Tension stress positive) Moment Diagrams Project: General name / Support Line 1 / Load Case: Strength(Dead and Live) 1.20 x Selfweight + 1.20 x Dead load + 1.60 x Live load + 1.00 x Hyperstatic Moment Drawn on Tension Side -100

Moment [k-ft]

0

100

200

300

400

500

Span 3

Span 2

Span 1

DESIGN STRIP "DESIGN MOMENT (Mu)" (Moment is drawn on the tension side) Rebar Diagrams Project: General name / Support Line 1 / Load Case: Envelope Rebar Required Top

Rebar Required Bottom

Rebar Provided Top

Rebar Provided Bottom

0.0

Rebar [in²]

-2.5

-5.0

-7.5

-10.0

-12.5

Span 1

Span 2

Span 3

DESIGN STRIP REINFORCEMENT REQUIRED AND PROVIDED

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