LRFD Inverted Tee Bent Cap Design Example

88 Pages·2010·0.75 MB·English

County: Any Hwy: Any Design: BRG Date: 6/2010
Inverted Tee 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
Span 1 "AASHTO LRFD" refers to the
AASHTO LRFD Bridge Design
54' Type TX54 Girders (0.851k/ )
ft Specification, 5th Ed. (2010)
6 Girders Spaced @ 8.00' with 3' overhangs
2" Haunch "BDM-LRFD" refers to the TxDOT
Bridge Design Manual - LRFD (May
Span 2 2009)
112' Type TX54 Girders (0.851k/ft) "TxSP" refers to TxDOT guidance,
6 Girders Spaced @ 8.00' with 3' overhangs recommendations, and standard
3.75" Haunch practice.
"Furlong & Mirza" refers to "Strength
Span 3
and Servicability of Inverted T-Beam
54' Type TX54 Girders (0.851k/ ) Bent Caps Subject to Combined
ft
Flexure, Shear, and Torsion", Center
6 Girders Spaced @ 8.00' with 3' overhangs
for Highway Research Research
2" Haunch
Report No. 153-1F, The University of
Texas at Austin, August 1974
All Spans
The basic bridge geometry can be
Deck is 46ft wide
found on the Bridge Layout located in
Type T551 Rail (0.382k/ft)
the Appendices.
8" Thick Slab (0.100 ksf)
Assume 2" Overlay @ 140 pcf (0.023 ksf) (TxSP)
Use Class "C" Concrete
f' =3.60 ksi (BDM-LRFD, Ch. 4, Sect. 5, Materials)
c
w =150 pcf (for weight)
c
w =145 pcf (for Modulus of Elasticity calculation)
c
Grade 60 Reinforcing
F =60 ksi (BDM-LRFD, Ch. 4, Sect. 5, Materials)
y
Bents
Use 36" Diameter Columns (Typical for Type TX54 Girders)
LRFDInvertedTeeBentCapDesignExample 1 June2010
Design Parameters (Con't)
Define Variables
Back Span Forward Span
Span1 (cid:2) 54ft Span2 (cid:2) 112ft Span Length
GdrSpa1 (cid:2) 8ft GdrSpa2 (cid:2) 8ft Girder Spacing
GdrNo1 (cid:2) 6 GdrNo2 (cid:2) 6 Number of Girders in Span
GdrWt1 (cid:2) 0.851klf GdrWt2 (cid:2) 0.851klf Weight of Girder
Haunch1 (cid:2) 2in Haunch2 (cid:2) 3.75in Size of Haunch
Bridge
Skew (cid:2) 0deg Skew of Bents
BridgeW (cid:2) 46ft Width of Bridge Deck
RdwyW (cid:2) 44ft Width of Roadway
GirderD (cid:2) 54in Depth of Type TX54 Girder
BrgSeat (cid:2) 1.5in Bearing Seat Buildup
BrgPad (cid:2) 2.75in Bearing Pad Thickness
SlabThk (cid:2) 8in Thickness of Bridge Slab
OverlayThk (cid:2) 2in Thickness of Overlay
RailWt (cid:2) 0.382klf Weight of Rail
w (cid:2) 0.150kcf Unit Weight of Concrete for Loads
c
W (cid:2) 0.140kcf Unit Weight of Overlay
Olay
Bents
f (cid:2) 3.60ksi Concrete Strength
c
w (cid:2) 0.145kcf Unit Weight of Concrete for E
cE c
1.5
E = 33(cid:4)(cid:5)000(cid:3)w (cid:3) f E (cid:2) 3457(cid:3)ksi Modulus of Elasticity of Concrete,
c cE c c
(AASHTO LRFD Eq. 5.4.2.4-1)
f (cid:2) 60ksi Yield Strength of reinforcement
y
E (cid:2) 29000ksi Modulus of Elasticity of Steel
s
D (cid:2) 36in Diameter of Columns
column
Other Variables
Dynamic load allowance,
IM (cid:2) 33%
(AASHTO LRFD Table 3.6.2.1-1)
LRFDInvertedTeeBentCapDesignExample 2 June2010
Determine Cap Dimensions
Stem Width The stem is typically at least 3" wider
than the Diameter of the Column
b (cid:2) D (cid:6) 3in b (cid:2) 39(cid:3)in (36") to allow for the extension of the
stem column stem
column reinforcement into the Cap.
(TxSP)
Stem Height
Distance From Top of Slab to Top of Ledge
D (cid:2) SlabThk (cid:6) Haunch2(cid:6) GirderD (cid:6) BrgPad (cid:6) BrgSeat Haunch 2 is the larger of the two
Slab_to_Ledge
haunches.
D (cid:2) 70.00(cid:3)in
Slab_to_Ledge
StemHaunch (cid:2) 3.75(cid:3)in The top of the stem must be 2.5" below the bottom of the slab.
(BDM-LRFD, Ch. 4, Sect. 5, Geometric Constraints)
Accounting for the 1/2" of bituminus fiber, the top of the stem
must have at least 2" of haunch on it, but the haunch should
not be less than either of the haunches of the adjacent spans.
d (cid:2) D (cid:7) SlabThk (cid:7) StemHaunch (cid:7) 0.5in The stem must accommodate 1/2" of
stem Slab_to_Ledge
bituminous fiber.
d (cid:2) 57.75(cid:3)in
stem
Use: d (cid:2) 57(cid:3)in Round the Stem Height down to the
stem
nearest 1". (TxSP)
LRFDInvertedTeeBentCapDesignExample 3 June2010
Determine Cap Dimensions (Con't)
Ledge Width
The Ledge Width must be adequate
for Bar M to develop fully. 26" is
typically used for TX54 girders, as it is
adequate to develop a # 6 bar with
the typical 2.5" cover. If the cover is
increased to 3", allowing for a
modification factor of 0.7, a 24" Ledge
is adequate to develop a # 7 bar.
I-Beams have 9.5" from the face of
the cap to the CL of Bearing. The
typical ledge width for these bridges
is 23".
"L " must be greater than or
dh,prov
equal to "L " for bar M.
dh,req
"cover" is measured from the center
cover (cid:2) 2.5in
of the transverse bars.
"L" is the length of the Bearing Pad
L (cid:2) 8in
along the girder. A typical type TX54
bearing pad is 8"x21" as shown in the
Determine the Required Development Length of Bar M: IGEB standard.
Try # 6 Bar for Bar M.
d (cid:2) 0.750in
bar_M
2
A (cid:2) 0.44in
bar_M
Basic Development Length
38.0(cid:3)d
bar_M
L = L (cid:2) 15.02(cid:3)in (AASHTO LRFD Eq. 5.11.2.4.1-1)
dh dh
f
c
Modification Factors for L (AASHTO LRFD 5.11.2.4.2)
dh:
Is Top Cover greater than or equal to 2.5", and Side Cover greater than or equal to 2"?
d
bar_M "Side Cover" and "Top Cover" are
SideCover (cid:2) cover (cid:7) SideCover (cid:2) 2.13(cid:3)in
the clear cover on the side and top
2
of the hook respectively. The
dbar_M dimension "cover" is measured
TopCover (cid:2) cover (cid:7) TopCover(cid:2) 2.13(cid:3)in from the center of Bar M.
2
No, Factor = 1.0
LRFDInvertedTeeBentCapDesignExample 4 June2010
Determine Cap Dimensions (Con't)
The Required Development Length is the larger of the following: (AASHTO LRFD 5.11.2.4.1)
L (cid:3)Factor (cid:2) 15.02(cid:3)in
dh
8(cid:3)d (cid:2) 6.00(cid:3)in
bar_M
6in
Therefore,
L (cid:2) 15.02(cid:3)in
dh_req
L The distance from the face of
b (cid:2) L (cid:6) cover (cid:6) 12in(cid:7) b (cid:2) 25.52(cid:3)in
ledge_min dh_req ledge_min the stem to the center of bearing
2
is 12" for TxGirders. (IGEB)
Use:
b (cid:2) 26(cid:3)in
ledge
Width of Bottom Flange
b (cid:2) 2(cid:3)b (cid:6) b b (cid:2) 91(cid:3)in
f ledge stem f
Ledge Depth
As a general rule of thumb Ledge
Use a Ledge Depth of 28"
Depth is greater than or equal to 2'-3".
This is the depth at which a bent from
d (cid:2) 28in
ledge a typical bridge will pass the
punching shear check (calculations
found on Pg. 21).
Total Depth of Cap
h (cid:2) d (cid:6) d h (cid:2) 85(cid:3)in
cap stem ledge cap
Summary of Cross Sectional Dimensions
b (cid:2) 39(cid:3)in From Pg. 3
stem
d (cid:2) 57(cid:3)in From Pg. 3
stem
b (cid:2) 26(cid:3)in
ledge
d (cid:2) 28(cid:3)in
ledge
h (cid:2) 85(cid:3)in
cap
LRFDInvertedTeeBentCapDesignExample 5 June2010
Determine Cap Dimensions (Con't)
Length of Cap
First define Girder Spacing and End Distance:
S (cid:2) 8ft Girder Spacing
"c" is the distance from the Center
c (cid:2) 2ft
Line of the Exterior Girder to the
Edge of the Cap measured along
the Cap.
L (cid:2) S(cid:3)(GdrNo1 (cid:7) 1) (cid:6) 2(cid:3)c L (cid:2) 44ft Length of Cap
Cap Cap
TxDOT policy is as follows, "The edge distance between the exterior bearing pad and the end of the inverted
T-beam shall not be less than 12in." (BDM-LRFD, Ch. 4, Sect. 5, Design Criteria) replacing the statement in
AASHTO LRFD 5.13.2.5.5 stating it shall not be less than d . Preferably, the stem should extend at least 3"
f
beyond the edge of the bearing seat.
Bearing Pad Dimensions (IGEB standard)
L(cid:2) 8(cid:3)in Length of Bearing Pad
W (cid:2) 21in Width of Bearing Pad
Cross Sectional Properties of Cap
2
A (cid:2) d (cid:3)b (cid:6) d (cid:3)b A (cid:2) 4771(cid:3)in
g ledge f stem stem g
(cid:8)1 (cid:11) (cid:8) 1 (cid:11)
d (cid:3)b (cid:3)(cid:9) (cid:3)d (cid:12) (cid:6) d (cid:3)b (cid:3)(cid:9)d (cid:6) (cid:3)d (cid:12)
ledge f (cid:10)2 ledge(cid:13) stem stem (cid:10) ledge 2 stem(cid:13) Distance from bottom of cap to the
ybar (cid:2)
center of gravity of the cap
A
g
ybar(cid:2) 33.80(cid:3)in
3
bf(cid:3)dledge (cid:8) 1 (cid:11)2
I (cid:2) (cid:6) b (cid:3)d (cid:3)(cid:9)ybar(cid:7) (cid:3)d (cid:12) (cid:20)(cid:20)(cid:20)
g 12 f ledge (cid:10) 2 ledge(cid:13)
3
bstem(cid:3)dstem (cid:14) (cid:8) 1 (cid:11)(cid:17)2
(cid:6) (cid:6) b (cid:3)d (cid:3)(cid:15)ybar(cid:7) (cid:9)d (cid:6) (cid:3)d (cid:12)(cid:18)
12 stem stem (cid:16) (cid:10) ledge 2 stem(cid:13)(cid:19)
6 4
I (cid:2) 2.91(cid:21) 10 (cid:3)in
g
LRFDInvertedTeeBentCapDesignExample 6 June2010
Cap Analysis
Cap Model
Assume:
4 Columns Spaced @ 12'-0"
The cap will be modeled as a continuous beam with simple supports using TxDOT's CAP18 program.
TxDOT does not consider frame action for typical multi-column bents.
(BDM-LRFD, Ch. 4, Sect. 5, Structural Analysis)
Cap 18 Model
Station = 0.5'
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.
station (cid:2) 0.5ft Station increment for CAP18
Recall:
6 4
E (cid:2) 3457.14(cid:3)ksi (Pg. 2) I (cid:2) 2.91(cid:21) 10 (cid:3)in (Pg.6)
c g
E (cid:3)I (cid:2) 1.01(cid:21) 1010(cid:3)kip(cid:3)in2 / (cid:8)(cid:9)12 in(cid:11)(cid:12)2 = E (cid:3)I (cid:2) 6.99(cid:21) 107(cid:3)kip(cid:3)ft2
c g (cid:10) ft(cid:13) c g
LRFDInvertedTeeBentCapDesignExample 7 June2010
Cap Analysis (Con't)
Dead Load
Values used in the following
SPAN 1
equations can be found on Pg. 2.
Span1
2(cid:3)RailWt(cid:3)
Rail weight is distributed evenly
2 kip
Rail1 (cid:2) Rail1 (cid:2) 3.44(cid:3) among stringers, up to 3 stringers
min(GdrNo1(cid:4)(cid:5)6) girder per rail. (TxSP)
Span1 kip Increase slab DL by 10% to
Slab1 (cid:2) w (cid:3)GdrSpa1(cid:3)SlabThk(cid:3) (cid:3)1.10 Slab1(cid:2) 23.76(cid:3)
c account for haunch and thickened
2 girder
slab ends.
Span1 kip
Girder1 (cid:2) GdrWt1(cid:3) Girder1 (cid:2) 22.98(cid:3)
2 girder
Overlay is calculated separately,
kip
DLRxn1 (cid:2) Rail1 (cid:6) Slab1(cid:6) Girder1 DLRxn1 (cid:2) 50.17(cid:3) because it has a different load
girder factor than the rest of the dead
loads.
Span1 kip
Overlay1 (cid:2) W (cid:3)GdrSpa1(cid:3)OverlayThk(cid:3) Overlay1(cid:2) 5.04(cid:3) Design for future overlay.
Olay
2 girder
SPAN 2
Span2
2(cid:3)RailWt(cid:3)
2 kip
Rail2 (cid:2) Rail2 (cid:2) 7.13(cid:3)
min(GdrNo2(cid:4)(cid:5)6) girder
Span2 kip
Slab2 (cid:2) w (cid:3)GdrSpa2(cid:3)SlabThk(cid:3) (cid:3)1.10 Slab2(cid:2) 49.28(cid:3)
c
2 girder
Span2 kip
Girder2 (cid:2) GdrWt2(cid:3) Girder2 (cid:2) 47.66(cid:3)
2 girder
kip
DLRxn2 (cid:2) Rail2 (cid:6) Slab2(cid:6) Girder2 DLRxn2 (cid:2) 104.07(cid:3)
girder
Span2 kip
Overlay2 (cid:2) W (cid:3)GdrSpa2(cid:3)OverlayThk(cid:3) Overlay2(cid:2) 10.45(cid:3)
Olay
2 girder
CAP
kip 0.5ft kip
Cap (cid:2) w (cid:3)A (cid:2) 4.970(cid:3) * = Cap (cid:2) 2.485(cid:3)
c g
ft station station
LRFDInvertedTeeBentCapDesignExample 8 June2010
Cap Analysis (Con't)
Live Load (AASHTO LRFD 3.6.1.2.2 and 3.6.1.2.4)
LongSpan (cid:2) max(Span1(cid:4)(cid:5)Span2)
ShortSpan (cid:2) min(Span1(cid:4)(cid:5)Span2)
LongSpan (cid:2) 112.00ft
ShortSpan (cid:2) 54.00ft
IM(cid:2) 0.33
(cid:8)LongSpan (cid:6) ShortSpan(cid:11) Use HL-93 Live Load. For maximum
Lane (cid:2) 0.64klf(cid:3)(cid:9) (cid:12) reaction at interior bents, "Design
(cid:10) 2 (cid:13) Truck" will always govern over
"Design Tandem". For the maximum
kip
Lane (cid:2) 53.12(cid:3) reaction when the long span is more
lane than twice as long as the short span,
place the rear (32 kip) axle over the
(cid:8)LongSpan (cid:7) 14ft(cid:11) (cid:8)LongSpan (cid:7) 28ft(cid:11) support and the middle (32 kip) and
Truck (cid:2) 32kip (cid:6) 32kip(cid:3)(cid:9) (cid:12) (cid:6) 8kip(cid:3)(cid:9) (cid:12) front (8 kip) axles on the long span.
(cid:10) LongSpan (cid:13) (cid:10) LongSpan (cid:13) For the maximum reaction when the
long span is less than twice as long
kip
Truck (cid:2) 66.00(cid:3) as the short span, place the middle
lane (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 (cid:2) Lane (cid:6) Truck(cid:3)(1(cid:6) IM) Combine "Design Truck" and
"Design Lane" loadings.
kip
LLRxn (cid:2) 140.90(cid:3) (AASHTO LRFD 3.6.1.3)
lane
Dynamic load allowance, IM, does
not apply to "Design Lane."
(AASHTO LRFD 3.6.1.2.4)
P (cid:2) 16.0kip(cid:3)(1(cid:6) IM) The Live Load is applied to the slab
by two 16 kip wheel loads increased
P (cid:2) 21.28(cid:3)kip
by the dynamic load allowance with
the remainder of the live load
LLRxn (cid:7) (2(cid:3)P) distributed over a 10 ft (AASHTO
w (cid:2) LRFD 3.6.1.2.1) design lane width.
10ft
(TxSP)
kip 0.5ft
w(cid:2) 9.83(cid:3) * The Live Load applied to the slab is
ft station distributed to the beams assuming
the slab is hinged at each beam
kip
w(cid:2) 4.92(cid:3) except the outside beam.
station (BDM-LRFD, Ch. 4, Sect. 5, Structural
Analysis)
LRFDInvertedTeeBentCapDesignExample 9 June2010
Cap Analysis (Con't)
Cap 18 Input
Multiple Presence Factors, m (AASHTO LRFD Table 3.6.1.1.2-1) Input "Multiple Presence Factors" into
Cap18 as "Load Reduction Factors".
No. of Lanes Factor "m"
1 1.20
2 1.00
3 0.85
>3 0.65
Limit States (AASHTO LRFD 3.4.1) The cap design need only consider
Strength I, Service I, and Service I
Strength I
with DL. (TxSP)
Live Load and Dynamic Load Allowance LL + IM = 1.75
Dead Load Components DC = 1.25
Dead Load Wearing Surface (Overlay) DW = 1.50 TxDOT allows the Overlay Factor to
be reduced to 1.25 (TxSP), since
Service I overlay is typically used in design
only to increase the safety factor, but
Live Load and Dynamic Load Allowance LL + IM = 1.00
in this example we will use DW = 1.50.
Dead Load and Wearing Surface DC & DW = 1.00
Dead Load
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)
Cap 18 Output
Max +M Max -M
Dead Load: M (cid:2) 250.1kip(cid:3)ft M (cid:2) (cid:7)379.4kip(cid:3)ft These loads are the maximum loads
posDL negDL
from the Cap 18 Output File located in
Service Load: M (cid:2) 492.5kip(cid:3)ft M (cid:2) (cid:7)590.9kip(cid:3)ft the Appendices.
posServ negServ
Factored Load: M (cid:2) 741.7kip(cid:3)ft M (cid:2) (cid:7)852.1kip(cid:3)ft
posUlt negUlt
LRFDInvertedTeeBentCapDesignExample 10 June2010