Design Parameters. Span 1. Span 2. All Spans. Assume. County: Any Hwy: Any Design: BRG Date: 6/2010. Rectangular Bent Cap Design Example

Transcription

1 County: Any Hwy: Any Design: BRG Date: 6/2010 Rectangular Bent Cap Design Example Design example is in accordance with the AASHTO LRFD Bridge Design Specifications, 5th Ed. (2010) as prescribed by TxDOT Bridge Design Manual - LRFD (May 2009). Design Parameters "AASHTO LRFD" refers to the AASHTO LRFD Bridge Design Specification, 5th Ed. (2010) Span 1 Span 1 Span 2 100' Type Tx54 Girders (0.851 k / ft ) 5 Girders 8.50' with 3' overhangs "BDM-LRFD" refers to the TxDOT Bridge Design Manual - LRFD (May 2009) "TxSP" refers to TxDOT guidance, recommendations, and standard practice. Span 2 120' Type Tx54 Girders (0.851 k / ft ) 6 Girders 6.80' with 3' overhangs All Spans Deck is 40ft wide Type T551 Rail (0.382k/ft) 8" Thick Slab (0.100 ksf) Assume 2" 140 pcf (0.023 ksf) Use Class "C" Concrete f' c =3.60 ksi w c =150 pcf (for weight) w c =145 pcf (for Modulus of Elasticity calculation) Grade 60 Reinforcing F y =60 ksi The basic bridge geometry can be found on the Bridge Layout (in the Appendices). (TxSP) (BDM-LRFD, Ch. 4, Sect. 5, Materials) (BDM-LRFD, Ch. 4, Sect. 5, Materials) Assume 3'-6" X 3'-6" Cap 3~36" Columns 15'-0" Cap will be modeled as a continuous beam with simple supports using TxDOT's CAP18 program. 4' 15' 15' 4' TxDOT does not consider frame action for typical multi-column bents. (BDM-LRFD, Ch. 4, Sect. 4, Structural Analysis) LRFD Rectangular Bent Cap Design Example 1 June 2010

2 Design Parameters (Con't) Define Variables Back Span Forward Span Span1 GdrSpa1 100ft Span2 120ft 8.5ft GdrSpa2 6.8ft GdrNo1 5 GdrNo2 6 GdrWt klf GdrWt klf Span Length Girder Spacing Number of Girders in Span Weight of Girder Bridge RailWt 0.382klf Weight of Rail SlabThk 8in Thickness of Bridge Slab OverlayThk 2in Thickness of Overlay w c 0.150kcf Unit Weight of Concrete for Loads w Olay 0.140kcf Unit Weight of Overlay Other Variables station 0.5ft Station increment for CAP18. IM 33% Cap Dimentions: Dynamic load allowance, (AASHTO LRFD Table ) CapWidth 3ft 6in CapWidth 42.00in CapDepth 3ft 6in CapDepth 42.00in cover 2.25in Measured from Center of stirrup. Material Properties: f c 3.60ksi Concrete Strength w ce 0.145kcf Unit Weight of Concrete for E c 1.5 E c = w ce f c E c 3457ksi E s 29000ksi Modulus of Elasticity of Concrete, (AASHTO LRFD Eq ) Modulus of Elasticity of Steel LRFD Rectangular Bent Cap Design Example 2 June 2010

3 Cap Analysis Cap Model The circled numbers are the stations that will be used in the CAP 18 input file. One station is 0.5ft in the direction perpendicular to the pgl, not parallel to the bent. Dead Load SPAN 1 Rail1 Slab1 Span1 2RailWt 2 kip Rail min( GdrNo1 6) girder Span1 kip w c GdrSpa1SlabThk 1.10 Slab girder Rail weight is distributed evenly among stringers, up to 3 stringers per rail. (TxSP) Increase slab DL by 10% to account for haunch and thickened slab ends. Girder1 GdrWt1 Span1 kip Girder girder kip DLRxn1 Rail1 Slab1 Girder1 DLRxn girder Span1 kip Overlay1 w Olay GdrSpa1OverlayThk Overlay girder Overlay is calculated separately, because it can have a different load factor than the rest of the dead loads. Design for future overlay. LRFD Rectangular Bent Cap Design Example 3 June 2010

4 Cap Analysis (Con't) Dead Load (Con't) SPAN 2 Rail2 Slab2 Span2 2RailWt 2 kip Rail min( GdrNo2 6) girder Span2 kip w c GdrSpa2SlabThk 1.10 Slab girder Girder2 GdrWt2 Span2 kip Girder girder kip DLRxn2 Rail2 Slab2 Girder2 DLRxn girder Overlay2 Span2 kip w Olay GdrSpa2OverlayThk Overlay girder CAP A g CapWidthCapDepth A g 1764in 2 Gross Area of Cap Cap w c A g kip * ft 0.5ft station kip = Cap station Dead Load of Cap 1 I g 12 CapWidth CapDepth3 I g in 4 Gross Moment of Inertia E c ksi From Pg. 2 E c I g kipin 2 / 12 in ft Live Load (AASHTO LRFD and ) 2 = E c I g kipft 2 Bending Stiffness of Cap LongSpan ShortSpan max( Span1 Span2) min( Span1 Span2) LongSpan ft ShortSpan ft IM 0.33 LRFD Rectangular Bent Cap Design Example 4 June 2010

5 Cap Analysis Live Load (Con't) Lane 0.64klf (Con't) Lane kip lane LongSpan ShortSpan LongSpan 14ft Truck 32kip 32kip 8kip LongSpan Truck kip lane 2 ShortSpan 14ft ShortSpan Use HL-93 Live Load. For maximum reaction at interior bents, "Design Truck" will always govern over "Design Tandem". For the maximum reaction when the long span is less than twice as long as the short span, place the middle (32 kip) axle over the support, the front (8 kip) axle on the short span and the rear (32 kip) axle on the long span. LLRxn Lane Truck( 1 IM) LLRxn kip lane P 16.0kip( 1 IM) P 21.28kip W LLRxn ( 2P) 10ft W kip * ft 0.5ft kip W 5.86 station station Combine "Design Truck" and "Design Lane" loadings. (AASHTO LRFD ) Dynamic load allowance, IM, does not apply to "Design Lane." (AASHTO LRFD ) The Live Load is applied to the slab by two 16 kip wheel loads increased by the dynamic load allowance with the remainder of the live load distributed over a 10 ft (AASHTO LRFD ) design lane width. (TxSP) The Live Load applied to the slab is distributed to the beams assuming the slab is hinged at each beam except the outside beam. (BDM-LRFD, Ch. 4, Sect. 4, Structural Analysis) Cap 18 Input Multiple Presence Factors, m (AASHTO LRFD Table ) Input "Multiple Presence Factors" into Cap18 as "Load Reduction Factors". No. of Lanes Factor "m" > Limit States (AASHTO LRFD 3.4.1) The cap design need only consider Strength I Live Load and Dynamic Load Allowance LL + IM = 1.75 Dead Load Components DC = 1.25 Dead Load Wearing Surface (Overlay) DW = 1.5 Strength I, Service I, and Service I with DL. (TxSP) TxDOT allows the Overlay Factor to be reduced to 1.25 (TxSP), since overlay is typically used in design only to increase the safety factor, but in this example we will use DW = LRFD Rectangular Bent Cap Design Example 5 June 2010

6 Cap Analysis Cap 18 Input (Con't) Limit States (Con't) Service I Live Load and Dynamic Load Allowance LL + IM = 1.00 Dead Load and Wearing Surface DC & DW = 1.00 Dead Load (Con't) TxDOT considers Service level Dead Load only with a limit reinforcement stress of 22 ksi to minimize cracking. (BDM-LRFD, Chapter 4, Section 5, Design Criteria) The Cap 18 input file is located in the appendixes. For bents with different girder spacings forward and back, TXDOT standard design procedure requires two CAP18 problems as follows: Problem 1, Table 3 describes stringers for SPAN 1 only. Problem 2, same as problem 1 except hold envelopes from problem 1 and on Table 3 describe stringers for SPAN 2 only. Use problem 2 results. Cap 18 Output Max +M Max -M Dead Load posdl 407.6kipft negdl 625.8kipft Service posserv 796.7kipft negserv 935.7kipft Ultimate posult kipft negult kipft These loads are the maximum loads from the Cap 18 Output File located in the appendices. Flexural Reinforcement M dl max( posdl negdl ) M dl 625.8kipft M s max( posserv negserv ) M s 935.7kipft M u max( posult negult ) M u kipft Minimum Flexural Reinforcement (AASHTO LRFD ) Factored Flexural Resistance, M r, must be greater than or equal to the lesser of 1.2 M cr (Cracking Moment) or 1.33 Mu (Ultimate Moment) I g in 4 From Pg. 4 f r = 0.24 f c f r 0.455ksi 1 y t 2 CapDepth y t 21.00in I g S S in 3 y t Modulus of Rupture (BDM-LRFD, Ch. 4, Sect. 5, Design Criteria) Distance from Center of Gravity to extreme tension fiber Section Modulus M cr 1ft Sf r M 12in cr kipft Cracking Moment (AASHTO LRFD Eq ) LRFD Rectangular Bent Cap Design Example 6 June 2010

7 Flexural Reinforcement (Con't) Minimum Flexural Reinforcement (Con't) M f = minimum of: 1.2M cr 562.3kipft 1.33M u kipft Thus, M r must be greater than M f 562.3kipft Design for the lesser of 1.2M cr or 1.33Mu when determining minimum area of steel required. Moment Capacity Design (AASHTO LRFD ) Try, 7 #11's Top & Bottom BarNo 7 Number of bars in tension. d bar 1.41in Diameter of main reinforcing bars. A bar 1.56in 2 Area of one main reinforcing bar. A s ( BarNo) A bar A s 10.92in 2 Area of steel in tension. d stirrup 0.625in 1 d s CapDepth cover 2 d 1 stirrup 2 d bar d s 38.73in b CapWidth b 42in f c 3.60ksi Diameter of shear reinforcing bars (#5). "cover" is measured to center of shear reinforcement. Compressive Strength of Concrete f y 60ksi Compressive Strength of Concrete β 1 = f c 4ksi (AASHTO LRFD ) Bounded by: 0.65 β β c A s f y c 6.00in 0.85f c β 1 b Depth of Cross Section under Compression under Ultimate Load (AASHTO LRFD Eq ) a cβ 1 a 5.10in a 1ft M n A s f y d s 2 12in M n kipft d s c ε s c ε s Depth of Equivalent Stress Block (AASHTO LRFD ) Nominal Flexural Resistance (AASHTO LRFD Eq ) Strain in Reinforcing at Ultimate ε s > FlexureBehavior "Tension Controlled" (AASHTO LRFD ) ϕ M 0.90 (AASHTO LRFD ) M r ϕ M M n M r kipft Factored Flexural Resistance (AASHTO LRFD Eq ) M f kipft < M r MinReinfChk "OK!" M u kipft < M r UltimateMom "OK!" LRFD Rectangular Bent Cap Design Example 7 June 2010

8 Flexural Reinforcement (Con't) Check Serviceability (AASHTO LRFD ) To find s max : 1 d c cover 2 d 1 stirrup 2 d bar d c 3.27in h CapDepth h 42.00in "cover" is measured to center of shear reinforcement. For service loads, the stress on the cross-section is located as drawn: Modular Ratio: n E s n 8.39 E c Tension Reinforcement Ratio: ρ A s bd s ρ k ( 2ρn) ( ρn) 2 ( ρn) k k j 1 j M s 12in f ss f A s j d s 1ft ss 29.32ksi f a 0.6f y f a 36.00ksi f ss < f a ServiceStress "OK!" Exposure Condition Factor: γ e 1.00 d c β s 1 β 0.7 h d s 1.12 c For simplicity one can take j=0.9 for "typical" rectangular bent caps. Service Load Bending Stress in outer layer of the reinforcing Allowable Bending Stress in the outer layer of the reinforcing (BDM-LRFD Ch. 4, Sect. 4, Design Criteria) For class 1 exposure conditions. For areas where deicing chenicals are frequently used, design for Class 2 Exposure ( e = 0.75). (BDM-LRFD, Ch. 4, Sect. 5, Design Criteria) s max = minimum of: & 700γ e 2d β s f c ss 12in 14.77in s max 12.00in 1 b 2cover 2 d stirrup s Actual BarNo d bar (AASHTO LRFD Eq ) A good practice is to place a bar every 12in along each surface of the bent. (TxSP) s Actual 5.91in < s max ServiceabilityCheck "OK!" LRFD Rectangular Bent Cap Design Example 8 June 2010

9 Flexural Reinforcement (Con't) Check Dead Load Check allowable M dl : f dl 22ksi BDM-LRFD, Chapter 4, Section 4, Design Criteria 1ft M a A s d s j f dl M 12in a kipft TXDOT limits dead load stress to 22 ksi. This is due to observed cracking under dead load. Allowable Dead Load Moment M dl kipft < M a DeadLoadMom "OK!" Flexural Steel Summary: Use 7~#11 Bars (Top & Bottom) TXDOT typically uses the same reinforcement top and bottom for simplicity. Shear Design (AASHTO LRFD 5.8) Shear Capacity Design V u (Ultimate Shear) must be less than V r (Shear Resistance) V u V r (AASHTO LRFD Eq ) V r = ϕ v V n (AASHTO LRFD Eq ) ϕ v 0.9 (AASHTO LRFD ) V n is the lesser of V n1 and V n2 Where, V n1 = 0.25 f c b v d v + V p (AASHTO LRFD Eq ) V n2 = V c + V s + V p (AASHTO LRFD Eq ) V c is the Shear Resistance of the Concrete V c = β f c b v d v (AASHTO LRFD Eq ) V s is the Shear Resistance of the Transverse Steel V s = A v f y d v cot( θ) s (AASHTO LRFD Eq. C ) V p is the Vertical Component of the Prestress Force V p 0kip There is no prestressing steel in this cap. Since shear is dependent on location, let's look at STA 12: V u M u N u 354.1kip 705.0kipft 0kip LRFD Rectangular Bent Cap Design Example 9 June 2010

10 Shear Design (Con't) Shear Capacity Design (Con't) Recall, f c 3.60ksi f y 60.00ksi From Pg. 1 b v CapWidth b v 42.00in Find d v : M n kipft w/ 7~#11's (Top & Bottom) From to page 7 A ps f ps d p A s f y d s d e d A ps f ps A s f e 38.73in (AASHTO LRFD Eq ) y d v need not be less than the greater of 0.9d e and 0.72h: (AASHTO LRFD ) d v = maximum of: A s f y M n A ps f ps 36.18in (AASHTO LRFD Eq. C ) d v 0.9d e 0.72h 36.18in 34.86in 30.24in Since V n must be the lesser of V n1 and V n2 (as per AASHTO LRFD ), then V u must be less than both V n1 and V n2. V n1 is dependent on the section properties and the flexural reinforcement. V n2 is dependent on the section properties, the flexural reinforcement, and the shear reinforcement. V n1 is independent of the shear steel, therefore if V u is greater than V n1 the cap fails in shear regardless of the transverse steel. V n1 0.25f c b v d v V p V n kip (AASHTO LRFD Eq ) V r1 must be greater than V u V u kip V r1 ϕ v V n1 (AASHTO LRFD Eq ) V r kip > V u Vr1check "OK!" If V r1 is greater than V u1, then use a LARGER cap depth in order to satisfy shear requirements. The method for calculating and used in this design example are from AASHTO LRFD Appendix B5. The method from AASHTO LRFD may be used instead. The method from is based on the method from Appendix B5; however, it is less accurate and more conservative (often excessively conservative). The method from Apendix B5 is preferred because it is more accurate, but it requires iterating to a solution. The method from can be used when doing calculations by hand. LRFD Rectangular Bent Cap Design Example 10 June 2010

11 Shear Design (Con't) Shear Capacity Design (Con't) Determine and : V u ϕ v V p v u v ϕ v b v d u 0.26ksi v Shear Stress on the Concrete (AASHTO LRFD Eq ) ε x v u 0.07 f c Using Table B5.2-1 with θ M u d v where, M u 36.4 deg and β N u 0.5 V u V p 2 E s A s E p A ps v u 0.07 and ε f x c cot( θ) kipft Must be > V u V p ε x in in A ps f po d v kipft Determining and is an iterative process, therefore, assume initial shear strain value x of per LRFD B5.2 and then verify that the assumption was valid. Strain halfway between the compressive and tensile resultants (AASHTO LRFD Eq. B5.2-1) If x < 0, then use equation B5.2-3 and re-solve for x. Using Table B5.2-1 with θ 36.4 deg and β 2.23 v u 0.07 and ε f x c The table values for and can be applied over a range, thus, no interpolation is required. (*Note: Shear spreadsheet will automatically interpolate and values so results will slightly vary from hand calculations.) and have not changed from the assumed values, therefore no more iterations are required. V c = β f c b v d v V c kip (AASHTO LRFD Eq ) Assuming #5 stirrups at s 8.5in spacing, TxDOT limits transverse reinforcement spacing to a maximum A of 12" and a minimum of 4". v 2( 0.31) in 2 A v 0.62in 2 (BDM-LRFD, Ch. 4, Sect. 4, Detailing) Trial and error is used to determine the stirrup spacing required for the section. V s A v f y d v cot( θ) V s s kip The transverse reinforcement, "A v ", is a closed stirrup. The failure surface intersects two legs of the stirrup, therefore the area of the shear steel is two times the stirrup bar's area (0.31in 2 ). See the sketch of the failure plane to the left. (AASHTO LRFD Eq. C ) V p 0kip "V p " is zero as there is no prestressing. LRFD Rectangular Bent Cap Design Example 11 June 2010

12 Shear Design (Con't) Shear Capacity Design (Con't) V n = minimum of: V c V s V p kip (AASHTO LRFD Eq ) V n 0.25f c kip b v d v V p kip (AASHTO LRFD Eq ) V r ϕ v V n V r kip (AASHTO LRFD Eq ) V u kip < V r ShearResistance "OK!" Check Minimum Transverse Reinforcement A v_min = f c b v s A f v_min 0.36in 2 (AASHTO LRFD Eq ) y A v 0.62in 2 > A v_min MinimumSteelCheck "OK!" Check Maximum Spacing of Transverse Reinforcement (AASHTO LRFD ) Shear Stress V u ϕ v V p v u v ϕ v b v d u 0.259ksi (AASHTO LRFD Eq ) v 0.125f c 0.450ksi if v u 0.125f c, s max = minimum of: (AASHTO LRFD Eq ) 0.8d v & 24in 28.95in if v u 0.125f c, s max = minimum of: (AASHTO LRFD Eq ) 0.4d v & 12in Since v u < 0.125*f c, s max 24.00in 14.47in TxDOT limits the maximum transverse reinforcement spacing to 12", therefore: (BDM-LRFD, Ch. 4, Sect. 4, Detailing) s s max 12.00in 8.50in < s max SpacingCheck "OK!" Shear capacity and checks should be repeated at ALL points of critical shear. The Concrete Section Shear Capacity spreadsheet can be used in lieu of hand calculations. Note: in the overhangs, the stirrups need to be 5in because the shear is higher. Similarly the stirrups need to be 5in near the center column. (See the Shear Spreadsheet in the appendicies). When the spacing needed is less than 4in, use double stirrups. (BDM-LRFD, Ch. 4, Sect. 4, Detailing) When using double stirrups, A v is four times the stirrup bar's area. LRFD Rectangular Bent Cap Design Example 12 June 2010

13 Shear Design (Con't) A c b h 2 A c 882.0in 2 Shear Reinforcement Summary: (AASHTO LRFD B5.2) "A c " is the area of concrete on the flexural tension side of the cap, from the extreme tension fiber to one half the cap depth. "A c " is needed if AASHTO LRFD Eq. B5.2-1 is negative. Use single #5 8.5" maximum spacing Skin Reinforcement (Bars T) Try 5~#5 bars on each side Actual Area of Skin Reinforcement: A Tbar 0.31in 2 (# 5) NoTBars 5 A Tbar NoTBars A sk A 2 sk 0.78in 2 Required Area of Skin Reinforcement: d s h skin h 2 skin 1.61ft Area of skin reinforcement on one side face of the flexural tension side of the section Depth of the member on the flexural tension side of the section over which the skin reinforcement should be applied A sk_req = minimum of: (AASHTO LRFD Eq ) d s 30 A s in 2 h skin 0.17in 2 A sk_req 0.17in 2 < A sk SkinReinforcement "OK!" Actual Spacing of Skin Reinforcement: 1 h 2 cover 2 d 1 stirrup 2 d bar s sk s NoTBars 1 sk 5.91in "cover" is measured to center of shear reinforcement. Required Spacing of Skin Reinforcement: s sk_req = minimum of: (AASHTO LRFD ) & s sk_req d s 6 12in 6.46in 6.46in s sk < s sk_req SkinSpacing "OK!" Skin Reinforcement Summary: Use 5~# 5 on each side of bent. See the Bent Cap Detail Sheet in the Appendixes for the resulting design of these calculations. LRFD Rectangular Bent Cap Design Example 13 June 2010

14 Appendices Bridge Layout... pg 15 CAP 18 Input File CAP 18 Output File pg 16 pg 17 Concrete Section Shear Capacity Spreadsheet... pg 53 Bent Cap Details... pg 54 LRFD Rectangular Bent Cap Design Example 14 June 2010

15 LRFD Rectangular Bent Cap Design Example 15 June 2010

16 00001 County Highwy Pro# BRG Comment CAP18 Version 6.10 LRFD Example input file. Rectangular Bent, Skew = E Span 1 (L=100', Type TX54 8.5', 8" Slab, 2" O'lay) Table Table E Table (Lane Left) (Lane Right) (Stringers) (Supports) (Mom CP) (Mom CP) 70 (Shear CP) Table 4 (Cap) E (DL Span1, Bm1) (DL Span1, Bm2) (DL Span1, Bm3) (DL Span1, Bm4) (DL Span1, Bm5) (DL Span2, Bm1) (DL Span2, Bm2) (DL Span2, Bm3) (DL Span2, Bm4) (DL Span2, Bm5) (DL Span2, Bm6) (Dist. Lane Ld) (Conc. Lane Ld) (Conc. Lane Ld) E Span 2 (L=120', Type TX54 6.8', 8" Slab, 2" O'lay)-Hold Envp Table E+00 Table (Lane Left) (Lane Right) (Stringers) (Supports) (Mom CP) (Mom CP) 70 (Shear CP) LRFD Rectangular Bent Cap Design Example 16 June 2010

17 APR 27, 2010 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 1 PSF HIGHWAY PD- CONTROL- CODED NO COUNTY NO IPE SECTION-JOB BY DATE County Highwy Pro# BRG APR 27, 2010 Comment CAP18 Version 6.10 LRFD Example input file. Rectangular Bent, Skew = 0.00 PROB 1 Span 1 (L=100', Type TX54 8.5', 8" Slab, 2" O'lay) ENGLISH SYSTEM UNITS TABLE 1. CONTROL DATA ENVELOPES TABLE NUMBER OF MAXIMUMS KEEP FROM PRECEDING PROBLEM (1=YES) CARDS INPUT THIS PROBLEM 15 OPTION TO CLEAR ENVELOPES BEFORE LANE LOADINGS (1=YES) 0 OPTION TO OMIT PRINT (-1=TABLE 4A, -2=TABLE 5, -3=BOTH) 0 SKEW ANGLE, DEGREES TABLE 2. CONSTANTS NUMBER OF INCREMENTS FOR SLAB AND CAP 80 INCREMENT LENGTH, FT NUMBER OF INCREMENTS FOR MOVABLE LOAD 20 START POSITION OF MOVABLE-LOAD STA ZERO 2 STOP POSITION OF MOVABLE-LOAD STA ZERO 58 NUMBER OF INCREMENTS BETWEEN EACH POSITION OF MOVABLE LOAD 1 ANALYSIS OPTION (1=WORKING STRESS, 2=LOAD FACTOR, 3=BOTH) 3 LOAD FACTOR FOR DEAD LOAD 1.25 LOAD FACTOR FOR OVERLAY LOAD 1.25 LOAD FACTOR FOR LIVE LOAD 1.75 MAXIMUM NUMBER OF LANES TO BE LOADED SIMULTANEOUSLY 3 LIST OF LOAD COEFFICIENTS CORRESPONDING TO NUMBER OF LANES LOADED LRFD Rectangular Bent Cap Design Example 17 June 2010

18 APR 27, 2010 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 2 PROB 1 Span 1 (L=100', Type TX54 8.5', 8" Slab, 2" O'lay) TABLE 3. LISTS OF STATIONS NUM OF NUM OF NUM OF NUM MOM NUM SHEAR LANES STRINGERS SUPPORTS CONTR PTS CONTR PTS TOTAL LANE LEFT LANE RIGHT STRINGERS SUPPORTS MOM CONTR SHEAR CONTR TABLE 4. STIFFNESS AND LOAD DATA - FIXED-OR-MOVABLE FIXED-POSITION DATA MOVABLE- STA STA CONTD CAP BENDING SIDEWALK, STRINGER, OVERLAY POSITION FROM TO IF=1 STIFFNESS SLAB LOADS CAP LOADS LOADS SLAB LOADS ( K-FT*FT ) ( K ) ( K ) ( K ) ( K ) LRFD Rectangular Bent Cap Design Example 18 June 2010

19 APR 27, 2010 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 3 PROB 1 Span 1 (L=100', Type TX54 8.5', 8" Slab, 2" O'lay) TABLE 4A. DEAD LOAD RESULTS ( WORKING STRESS ) STA DIST X (FT) DEFLECTION (FT) MOMENT (K-FT) SHEAR (K) LRFD Rectangular Bent Cap Design Example 19 June 2010

20 APR 27, 2010 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 4 PROB 1 Span 1 (L=100', Type TX54 8.5', 8" Slab, 2" O'lay) TABLE 4A. DEAD LOAD RESULTS ( WORKING STRESS ) STA DIST X (FT) DEFLECTION (FT) MOMENT (K-FT) SHEAR (K) LRFD Rectangular Bent Cap Design Example 20 June 2010

21 APR 27, 2010 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 5 PROB 1 Span 1 (L=100', Type TX54 8.5', 8" Slab, 2" O'lay) TABLE 5. MULTI-LANE LOADING SUMMARY ( WORKING STRESS ) ( *--CRITICAL NUMBER OF LANE LOADS) MOMENT ( FT-K ) AT DEAD LD LANE POSITIVE LOAD AT LANE NEGATIVE LOAD AT STA EFFECT ORDER MAXIMUM LANE STA ORDER MAXIMUM LANE STA * 3* LRFD Rectangular Bent Cap Design Example 21 June 2010

22 APR 27, 2010 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 6 PROB 1 Span 1 (L=100', Type TX54 8.5', 8" Slab, 2" O'lay) MOMENT ( FT-K ) AT DEAD LD LANE POSITIVE LOAD AT LANE NEGATIVE LOAD AT STA EFFECT ORDER MAXIMUM LANE STA ORDER MAXIMUM LANE STA LRFD Rectangular Bent Cap Design Example 22 June 2010

23 APR 27, 2010 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 7 PROB 1 Span 1 (L=100', Type TX54 8.5', 8" Slab, 2" O'lay) SHEAR ( K ) AT DEAD LD LANE POSITIVE LOAD AT LANE NEGATIVE LOAD AT STA EFFECT ORDER MAXIMUM LANE STA ORDER MAXIMUM LANE STA * 0* * 2* LRFD Rectangular Bent Cap Design Example 23 June 2010

24 APR 27, 2010 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 8 PROB 1 Span 1 (L=100', Type TX54 8.5', 8" Slab, 2" O'lay) REACTION ( K ) AT DEAD LD LANE POSITIVE LOAD AT LANE NEGATIVE LOAD AT STA EFFECT ORDER MAXIMUM LANE STA ORDER MAXIMUM LANE STA * 0* LRFD Rectangular Bent Cap Design Example 24 June 2010

25 APR 27, 2010 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 9 PROB 1 Span 1 (L=100', Type TX54 8.5', 8" Slab, 2" O'lay) TABLE 6. ENVELOPES OF MAXIMUM VALUES ( WORKING STRESS ) STA DIST X MAX + MOM MAX - MOM MAX + SHEAR MAX - SHEAR ( FT ) ( FT-K ) ( FT-K ) ( K ) ( K ) LRFD Rectangular Bent Cap Design Example 25 June 2010

26 APR 27, 2010 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 10 PROB 1 Span 1 (L=100', Type TX54 8.5', 8" Slab, 2" O'lay) TABLE 6. ENVELOPES OF MAXIMUM VALUES ( WORKING STRESS ) STA DIST X MAX + MOM MAX - MOM MAX + SHEAR MAX - SHEAR ( FT ) ( FT-K ) ( FT-K ) ( K ) ( K ) LRFD Rectangular Bent Cap Design Example 26 June 2010

27 APR 27, 2010 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 11 PROB 1 Span 1 (L=100', Type TX54 8.5', 8" Slab, 2" O'lay) TABLE 7. MAXIMUM SUPPORT REACTIONS ( WORKING STRESS ) STA DIST X MAX + REACT MAX - REACT ( FT ) ( K ) ( K ) LRFD Rectangular Bent Cap Design Example 27 June 2010

28 APR 27, 2010 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 12 PROB 1 Span 1 (L=100', Type TX54 8.5', 8" Slab, 2" O'lay) TABLE 5. MULTI-LANE LOADING SUMMARY ( LOAD FACTOR) ( *--CRITICAL NUMBER OF LANE LOADS) MOMENT ( FT-K ) AT DEAD LD LANE POSITIVE LOAD AT LANE NEGATIVE LOAD AT STA EFFECT ORDER MAXIMUM LANE STA ORDER MAXIMUM LANE STA * 3* LRFD Rectangular Bent Cap Design Example 28 June 2010

29 APR 27, 2010 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 13 PROB 1 Span 1 (L=100', Type TX54 8.5', 8" Slab, 2" O'lay) MOMENT ( FT-K ) AT DEAD LD LANE POSITIVE LOAD AT LANE NEGATIVE LOAD AT STA EFFECT ORDER MAXIMUM LANE STA ORDER MAXIMUM LANE STA LRFD Rectangular Bent Cap Design Example 29 June 2010

30 APR 27, 2010 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 14 PROB 1 Span 1 (L=100', Type TX54 8.5', 8" Slab, 2" O'lay) SHEAR ( K ) AT DEAD LD LANE POSITIVE LOAD AT LANE NEGATIVE LOAD AT STA EFFECT ORDER MAXIMUM LANE STA ORDER MAXIMUM LANE STA * 0* * 2* LRFD Rectangular Bent Cap Design Example 30 June 2010

31 APR 27, 2010 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 15 PROB 1 Span 1 (L=100', Type TX54 8.5', 8" Slab, 2" O'lay) REACTION ( K ) AT DEAD LD LANE POSITIVE LOAD AT LANE NEGATIVE LOAD AT STA EFFECT ORDER MAXIMUM LANE STA ORDER MAXIMUM LANE STA * 0* LRFD Rectangular Bent Cap Design Example 31 June 2010

32 APR 27, 2010 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 16 PROB 1 Span 1 (L=100', Type TX54 8.5', 8" Slab, 2" O'lay) TABLE 6. ENVELOPES OF MAXIMUM VALUES ( LOAD FACTOR ) STA DIST X MAX + MOM MAX - MOM MAX + SHEAR MAX - SHEAR ( FT ) ( FT-K ) ( FT-K ) ( K ) ( K ) LRFD Rectangular Bent Cap Design Example 32 June 2010

33 APR 27, 2010 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 17 PROB 1 Span 1 (L=100', Type TX54 8.5', 8" Slab, 2" O'lay) TABLE 6. ENVELOPES OF MAXIMUM VALUES ( LOAD FACTOR ) STA DIST X MAX + MOM MAX - MOM MAX + SHEAR MAX - SHEAR ( FT ) ( FT-K ) ( FT-K ) ( K ) ( K ) LRFD Rectangular Bent Cap Design Example 33 June 2010

34 APR 27, 2010 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 18 PROB 1 Span 1 (L=100', Type TX54 8.5', 8" Slab, 2" O'lay) TABLE 7. MAXIMUM SUPPORT REACTIONS ( LOAD FACTOR ) STA DIST X MAX + REACT MAX - REACT ( FT ) ( K ) ( K ) LRFD Rectangular Bent Cap Design Example 34 June 2010

35 APR 27, 2010 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 19 PSF HIGHWAY PD- CONTROL- CODED NO COUNTY NO IPE SECTION-JOB BY DATE County Highwy Pro# BRG APR 27, 2010 Comment CAP18 Version 6.10 LRFD Example input file. Rectangular Bent, Skew = 0.00 PROB 2 Span 2 (L=120', Type TX54 6.8', 8" Slab, 2" O'lay)-Hold ENGLISH SYSTEM UNITS TABLE 1. CONTROL DATA ENVELOPES TABLE NUMBER OF MAXIMUMS KEEP FROM PRECEDING PROBLEM (1=YES) CARDS INPUT THIS PROBLEM 0 OPTION TO CLEAR ENVELOPES BEFORE LANE LOADINGS (1=YES) 0 OPTION TO OMIT PRINT (-1=TABLE 4A, -2=TABLE 5, -3=BOTH) 0 SKEW ANGLE, DEGREES TABLE 2. CONSTANTS USING DATA FROM THE PREVIOUS PROBLEM LRFD Rectangular Bent Cap Design Example 35 June 2010

36 APR 27, 2010 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 20 PROB 2 Span 2 (L=120', Type TX54 6.8', 8" Slab, 2" O'lay)-Hold TABLE 3. LISTS OF STATIONS NUM OF NUM OF NUM OF NUM MOM NUM SHEAR LANES STRINGERS SUPPORTS CONTR PTS CONTR PTS TOTAL LANE LEFT LANE RIGHT STRINGERS SUPPORTS MOM CONTR SHEAR CONTR TABLE 4. STIFFNESS AND LOAD DATA USING DATA FROM THE PREVIOUS PROBLEM PLUS NONE LRFD Rectangular Bent Cap Design Example 36 June 2010

37 APR 27, 2010 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 21 PROB 2 Span 2 (L=120', Type TX54 6.8', 8" Slab, 2" O'lay)-Hold TABLE 4A. DEAD LOAD RESULTS ( WORKING STRESS ) STA DIST X (FT) DEFLECTION (FT) MOMENT (K-FT) SHEAR (K) LRFD Rectangular Bent Cap Design Example 37 June 2010

38 APR 27, 2010 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 22 PROB 2 Span 2 (L=120', Type TX54 6.8', 8" Slab, 2" O'lay)-Hold TABLE 4A. DEAD LOAD RESULTS ( WORKING STRESS ) STA DIST X (FT) DEFLECTION (FT) MOMENT (K-FT) SHEAR (K) LRFD Rectangular Bent Cap Design Example 38 June 2010

39 APR 27, 2010 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 23 PROB 2 Span 2 (L=120', Type TX54 6.8', 8" Slab, 2" O'lay)-Hold TABLE 5. MULTI-LANE LOADING SUMMARY ( WORKING STRESS ) ( *--CRITICAL NUMBER OF LANE LOADS) MOMENT ( FT-K ) AT DEAD LD LANE POSITIVE LOAD AT LANE NEGATIVE LOAD AT STA EFFECT ORDER MAXIMUM LANE STA ORDER MAXIMUM LANE STA * 3* LRFD Rectangular Bent Cap Design Example 39 June 2010

40 APR 27, 2010 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 24 PROB 2 Span 2 (L=120', Type TX54 6.8', 8" Slab, 2" O'lay)-Hold MOMENT ( FT-K ) AT DEAD LD LANE POSITIVE LOAD AT LANE NEGATIVE LOAD AT STA EFFECT ORDER MAXIMUM LANE STA ORDER MAXIMUM LANE STA * 2* LRFD Rectangular Bent Cap Design Example 40 June 2010

41 APR 27, 2010 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 25 PROB 2 Span 2 (L=120', Type TX54 6.8', 8" Slab, 2" O'lay)-Hold SHEAR ( K ) AT DEAD LD LANE POSITIVE LOAD AT LANE NEGATIVE LOAD AT STA EFFECT ORDER MAXIMUM LANE STA ORDER MAXIMUM LANE STA * 0* * 2* * 0* * 2* LRFD Rectangular Bent Cap Design Example 41 June 2010

42 APR 27, 2010 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 26 PROB 2 Span 2 (L=120', Type TX54 6.8', 8" Slab, 2" O'lay)-Hold REACTION ( K ) AT DEAD LD LANE POSITIVE LOAD AT LANE NEGATIVE LOAD AT STA EFFECT ORDER MAXIMUM LANE STA ORDER MAXIMUM LANE STA * 0* LRFD Rectangular Bent Cap Design Example 42 June 2010

43 APR 27, 2010 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 27 PROB 2 Span 2 (L=120', Type TX54 6.8', 8" Slab, 2" O'lay)-Hold TABLE 6. ENVELOPES OF MAXIMUM VALUES ( WORKING STRESS ) STA DIST X MAX + MOM MAX - MOM MAX + SHEAR MAX - SHEAR ( FT ) ( FT-K ) ( FT-K ) ( K ) ( K ) LRFD Rectangular Bent Cap Design Example 43 June 2010

44 APR 27, 2010 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 28 PROB 2 Span 2 (L=120', Type TX54 6.8', 8" Slab, 2" O'lay)-Hold TABLE 6. ENVELOPES OF MAXIMUM VALUES ( WORKING STRESS ) STA DIST X MAX + MOM MAX - MOM MAX + SHEAR MAX - SHEAR ( FT ) ( FT-K ) ( FT-K ) ( K ) ( K ) LRFD Rectangular Bent Cap Design Example 44 June 2010

45 APR 27, 2010 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 29 PROB 2 Span 2 (L=120', Type TX54 6.8', 8" Slab, 2" O'lay)-Hold TABLE 7. MAXIMUM SUPPORT REACTIONS ( WORKING STRESS ) STA DIST X MAX + REACT MAX - REACT ( FT ) ( K ) ( K ) LRFD Rectangular Bent Cap Design Example 45 June 2010

46 APR 27, 2010 TEXAS DEPARTMENT OF TRANSPORTATION (TxDOT) PAGE 30 PROB 2 Span 2 (L=120', Type TX54 6.8', 8" Slab, 2" O'lay)-Hold TABLE 5. MULTI-LANE LOADING SUMMARY ( LOAD FACTOR) ( *--CRITICAL NUMBER OF LANE LOADS) MOMENT ( FT-K ) AT DEAD LD LANE POSITIVE LOAD AT LANE NEGATIVE LOAD AT STA EFFECT ORDER MAXIMUM LANE STA ORDER MAXIMUM LANE STA * 3* LRFD Rectangular Bent Cap Design Example 46 June 2010