STRESS CHECK AND REBAR VERIFICATION

Transcription

1 Structural Concrete Software System TN180_stress_check_ 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 through 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 ). In both instances, the sections selected do not meet the requirements of the design code (ACI ). This is indicated by the broken lines (shown in violet in color prints) in Fig Note: Units are in ft and in. FIGURE 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. support@adaptsoft.com 1733 Woodside Road, Suite 220, Redwood City, California, 94061, USA, Tel: (650) Fax (650)

2 FIGURE THREE-DIMENSIONAL VIEW OF THE STRUCTURE FIGURE DESIGN STRIPS IN X-DIRECTION 2

3 FIGURE 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 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 Design section geometry as identified by the program, and idealized if need be. Data Table 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 GEOMETRY OF DESIGN SECTIONS 3

4 AUTOMATICALLY GENERATED DESIGN SECTIONS Design Strip: Support Line 1 Design Section b1 d1 b2 d2 b3 d3 ft ft ft ft ft ft Design Strip: Support Line 2 Design Section b1 d1 b2 d2 b3 d3 ft ft ft ft ft ft TABLE SECTION PROPERTIES AUTOMATICALLY GENERATED DESIGN SECTIONS Design Strip: Support Line 1 Design Section Start(x,y) End(x,y) Centroid Area I Ytop Ybot (local x,z) Ft ft Ft in2 in4 in in 1204 (65.20,36.50) (65.20,18.25) (9.13,9.60) (68.25,36.50) (68.25,18.25) (7.50,9.60) (71.30,36.50) (71.30,18.25) (9.13,9.60) Design Strip: Support Line 2 Design Section Start(x,y) End(x,y) Centroid Area I Ytop Ybot (local x,z) Ft ft Ft in2 in4 in in 2201 (56.80,18.25) (56.80,0.00) (9.13,9.47) (60.60,18.25) (60.60,0.00) (9.13,9.47) (64.40,18.25) (64.40,0.00) (9.13,9.47)

5 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 the actual length of the design section is given by: b = [(X2 X1) 2 + (Y2 Y1) 2 ] 0.5 = [( ) 2 + ( ) 2 ] 0.5 = ft However, since 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 in 2 OK Moment of inertia (I) = (15* /12)*12 4 = in 4, OK (From Table I = in 4 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) 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 The dimensions of the section are: Section width b1 = ft Section depth d1 = 2.5 ft Flange thickness d2 = 0.79 ft Web thickness b2 = 1.00 ft FIGURE GEOMETRY OF DESIGN SECTION The distance 3.25 ft was measured from on the plan using the measure tool of the program and the appropriate snap tools 5

6 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*( ) = 2322 in 2 (From Table in 2 OK) Moment of inertia I = in 4 (From Table I = in 4 OK) Distance of centroid to bottom = in. (From Table Ybot = in. OK) Distance of centroid to top = 6.33 in. (From Table Ytop = 6.34 in. OK) 2.3 DESIGN ACTIONS The integral of the calculated actions (moments, shears, axial) are listed in report Table 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 DESIGN VALUES DESIGN ACTIONS FOR AUTOMATICALLY GENERATED SECTIONS Load Combination:Service(Sustained Load) Design Strip: Support Line 1 Design section Moment Shear Axial Torsion Top Bottom Centroid k-ft k k k-ft psi psi psi Design Strip: Support Line 2 Design section Moment Shear Axial Torsion Top Bottom Centroid k-ft k k k-ft psi psi psi Load Combination:Strength(Dead and Live) 6

7 Design Strip: Support Line 1 Design section Moment Shear Axial Torsion k-ft k K k-ft Design Strip: Support Line 2 Design section Moment Shear Axial Torsion k-ft k K k-ft STRESS CHECK Consider section 2202 through the beam for verification of stresses reported. Geometry (from Table 2.2-2) o Area = in. o Moment of inertia = in 4 o Distance to bottom fiber = in. Actions (from Table 2.3-1) o Moment o Axial = k-ft (tension at bottom) = k (compression) at bottom is given by: f b = P/A + M*Y b /I = ( / ( *12)*23.66 / )*1000 = = psi (tension) (ADAPT -> 783 psi from Table OK) at centroid (precompression) f centroid = P/A = / = psi (compression) (ADAPT -> 161 psi from Table OK) 2.5 REINFORCEMENT VALUES Reinforcement is provided for service condition and strength. The results are reported in Table Herein, the reinforcement required for strength condition of design section 1205 is verified. 7

8 TABLE SUMMARY OF REQUIRED AND PROVIDED REINFORCEMENT DESIGN SECTION REBAR FOR AUTOMATICALLY GENERATED SECTIONS Load Combination: Service(Sustained Load) Design Strip: Support Line 1 Design Criteria: SERVICE_SUSTAINED_LOAD <Bending rebar> Design section As top As bot Top bar Bottom bar In2 in #5 8# #5 8# #5 9#8 Design Strip: Support Line 2 Design Criteria: SERVICE_SUSTAINED_LOAD <Bending rebar> Design section As top As bot Top bar Bottom bar In2 in #3 0# #3 0# #3 0# #3 26#3 Load Combination: Strength(Dead and Live) Design Strip: Support Line 1 Design Criteria: STRENGTH <Bending rebar> Design section As top As bot Top bar Bottom bar in2 in #5 10# #5 11# #5 11#8 Design Strip: Support Line 2 Design Criteria: STRENGTH <Bending rebar> <Shear rebar> Design section As top As bot Top bar Bottom bar Av U-Strip spacing in2 in2 in2/ft in #3 23# #3 20# #3 18# Reinforcement reported by ADAPT is 8.04 in 2 at bottom for design section 1205 Geometry of section b = 15 (ft) * 12 = 180 in. h = 9.50 in. Material 8

9 Concrete PT Rebar Rebar cover Rebar size f c = 5000 psi fpu = 270 ksi fse = 26.7*1000/0.153 = 175 ksi 3 CGS = 1.08 in. 60 ksi 1.50 in. #8 (1 in. diameter) Reinforcement PT = 9 strands * = in 2 (from input data ) Rebar = 8.04 in 2 (from report of Table 2.5-1) Design moment M u = k-ft 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 f ps = f se f c /(300 ρ p ) < f se + 30 (Eqn 18-5 of ACI-318) ρ p = A ps /b*d p d p = = 8.42 in. ρ p = A ps /b*d p = / (180 * 8.42) = 9.09x10-4 f ps = /( 300 * 9.09x10-4 ) = ksi < = 205 ksi OK Total tension = * * 60 = = k Depth of compression zone: a = /(0.85*5*180) = in. Depth of neutral axis: c = / 0.80 = 1.25 in. Distance to farthest reinforcement: d t = *1 = 7.50 in. c/d t = 1.25/7.5 = < 0.375, hence φ = 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. 9

10 Design capacity ( φm n ) is given by: φm n = 0.90[279.99( /2) ( /2)]/12 = k-ft The design moment (Mu) is k-ft. The difference between the hand calculation (419.66) and the required value from the program ( ) 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 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. 10

11 SUPPORT LINE 1 Diagrams Project: General name / Support Line 1 / Load Case: Service(Sustained Load) 1.00 x Selfweight x Dead load x Live load x Prestressing Tensile Positive Diagrams Project: General name / Support Line 1 / Load Case: Service(Sustained Load) 1.00 x Selfweight x Dead load x Live load x Prestressing Tensile Positive Top Allowable es Bottom Allowable es [psi] [psi] Span 1 Span 2 Span 3 Span 1 Span 2 Span 3 (a) Max tension 64.8 psi, Allowable psi (b) Max tension psi, Allowable psi Max compression psi, Allowable psi Max compression psi, Allowable 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 x Dead load x Live load x Hyperstatic Moment Drawn on Tension Side Moment [k-ft] Span 1 Span 2 Span 3 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 Provided Top Rebar Required Bottom Rebar Provided Bottom Rebar [in²] Span 1 Span 2 Span 3 DESIGN STRIP REINFORCEMENT REQUIRED AND PROVIDED 11