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DESCRIPTION
East San Diego Pedestrian Bridge Design.
Citation preview
1
East San Diego Pedestrian Bridge
SE 151A
Concrete Mechanics and Design Department of Structural Engineering
University of California, San Diego
Jose Restrepo
Alvin Aguelo
Luke Robinson
Term Project
Fall 2010
2
TABLE OF CONTENTS
I. References ........................................................................................................................................................................ 5
II. Dimensions & Section Properties ............................................................................................................................... 6
III. Design Loads ................................................................................................................................................................ 8
IV. Structural Analysis ........................................................................................................................................................ 9
V. Slab Design ................................................................................................................................................................... 19
VI. Girder Design ............................................................................................................................................................. 20
VII. Development of Longitudinal and Miscellaneous Requirements ..................................................................... 21
VIII. Column Design ....................................................................................................................................................... 22
IX. Drawings ..................................................................................................................................................................... 28
X. Appendix ....................................................................................................................................................................... 33
Appendix 1.1: Calculations for Ag,slab ,Ixx,slab and Se,slab ........................................................................................... 36
Appendix 1.2: Calculations for Ag,column, Ixx,column and Se,column. .............................................................................. 36
Appendix 1.3: Calculations for yb, yt, Ag,girder, Ixx,girder and Se,girder. ......................................................................... 37
Appendix 1.4: Calculations for Slab Design Loads................................................................................................. 38
Appendix 1.5: Calculations for Girder Design Loads. ........................................................................................... 38
Appendix 1.6: Calculations for the Slab Design ...................................................................................................... 39
Appendix 1.7: Calculations for the Positive Girder Design .................................................................................. 41
Appendix 1.8: Calculations for the Negative Girder Design ................................................................................ 44
Appendix 1.9: Calculations for the Shear Design – Slab Section ......................................................................... 47
Appendix 2.0: Calculations for the Shear Design – Girder Section ..................................................................... 48
Appendix 2.1: Bar Development Girder Calculations ........................................................................................... 50
Appendix 2.2 : Column Design Sample Calculation .............................................................................................. 53
Appendix 2.3: MATLAB Program used for Linear Interpolation ....................................................................... 55
XI. Hours Spent per Student .......................................................................................................................................... 56
3
DESIGN PROCESS
ARCHITECTURAL
RENDERINGS
|01
|02
|03
4
5
I. REFERENCES
PURPOSE:
The proposed bridge is designed as a connecting two-span pedestrian path for a park located in
East San Diego County. The proposed geometric layout requires a crossing of a 5 lane low-
volume roadway designed for frequent loading (due to pedestrians). As stated, the bridge will
account for multiple loading cases that are designed to assure public safety (reference accordance
with the American Association of Highway and Transportation Officials (AASHTO)). The
permanent load cases are defined as follows: dead load of structural components (DC, AASHTO
3.3.2) and dead load of wearing surfaces and utilities (DW, AASHTO 3.3.2). Transient loading
are also accounted for and defined as: pedestrian live load (PL, AASHTO 3.3.2).
The preliminary design for the bridge was originally a T-shaped girder cross section which was
re-designed to have a taper of 30 mm depth. This design was primarily chosen for aesthetic basis
and as well as safety purposes. In addition, the slab and overhanging girder depth are designed
with consideration of the minimum code requirements (with specifications from the
client). Column size for the bridge was designed to have a side dimension of 850 mm.
Additional specification for the loading is as follows: the structure shall be designed to support
its own dead weight, the weight of a 50mm asphaltic concrete overlay (unit weight of asphaltic
concrete is 16 kN/m3, a 1 kN/m handrail load at the slab edges, and a live load per AASHTO
LRFD of 4.1 kN/m2. The normal weight of concrete are also considered and defined as 23.5
kN/m3 with a specified compressive strength of fc’ = 38 MPa. The average aggregate size used
in the concrete is 25 millimeters in diameter.
Figure1: Elevation View of Proposed Bridge (Dimensions in mm)
6
Figure 2: Preliminary Cross-Sectional View of Proposed Bridge (Dimensions in mm).
II. DIMENSIONS & SECTION PROPERTIES
A.) Deck Slab:
Analysis of the decking slab and determination of the slab depth was based on idealizing
the T-section as a solid one way cantilevered beam. Checking against ACI Code in Table
9.5(a), to avoid calculating deflections the minimum depth of the fixed end of the
cantilever must be 0.19m or larger. For the proposed bridge a slab depth of 0.20m was
chosen for simplicity.
Figure 3: Cross-Sectional Measurements: Decking Slab measurement in mm.
The proposed slab has the following sectional properties:
Cross-Sectional Properties:
Decking Slab
Ag,slab 0.2 m2
Ixx,slab 6.667e-4 m4
Se,slab 6.667e-3 m3
Table 1: Sectional Properties of Decking Slab (For Calculation See Appendix 1.1)
7
B) Girder:
Analysis of the girder and determination of the girder depth was based on ACI Code for
non-pre-stressed beams. Checking against ACI Code in Table 9.5(a), to avoid calculating
deflections the minimum depth of the non-pre-stressed beam with one end continuous
must be a minimum if 0.95m. For the design proposed a depth of 1m was chosen for
calculation purposes.
Figure 4: Cross-Sectional Measurements: Girder measurement in meters.
The proposed girder has the following sectional properties:
Cross-Sectional Properties:
Decking Girder
Ag,girder 1.510 m2
yb 0.701 m
yt 0.299 m
Ixx,girder 0.1254 m4
Sb,girder 0.1788 m3
St,girder 0.420 m3
Table 2: Sectional Properties of Girder (For Calculation See Appendix 1.2)
C) Column:
The design of the column is allowed to be 850mm, 900mm, 950mm. For the proposed
bridge, a slanted square cross section has been chosen with a width of 850mm. The
thinner column has a more aesthetic quality to it and gives an overall more transparent
appearance to the bridge. Should it be found later that the bridge needs a larger column, it
can always be increased easily.
8
The proposed column has the following sectional properties:
Cross-Sectional Properties:
Column
Ag,column 0.723 m2
Ixx,column 0.0435 m4
Se,column 0.1024 m3
Table 3: Sectional Properties of Girder (For Calculation See Appendix 1.1)
III. DESIGN LOADS
A) Deck Slab Design Loads: The design loads for the deck slab were determined to be:
Design Loads: Deck Slab
Design Factor
Final Load
Design with
Factors
WDC1,slab 4.70 kN/m 1.25 5.875 kN/m
PDC2,slab 1.00 kN 1.25 1.25 kN
WPL,slab 4.10 kN/m 1.75 7.175 kN/m
WDW,slab 0.80 kN/m 1.50 1.20 kN/m
Table 4: Design Loads for Deck Slab Cantilever (For Calculation See Appendix 1.3)
B) Girder Design Loads:
The design loads for the girder were determined to be:
Design Loads: Girder
WDC1,girder 35.49 kN/m
WDC2,girder 2.000 kN/m
WPL,girder 18.655 kN/m
WDW,girder 3.640 kN/m
Table 5: Design Loads for Deck Slab Cantilever (For Calculation See Appendix 1.4)
9
Table: 6The shear and the moment values for the loads are calculated through SAP and yield:
IV. STRUCTURAL ANALYSIS
A) Slab:
i) Model:
Figure 5: Cross-Sectional View of the idealized model for transverse bending and shear in the slab.
ii) Load Factors and Combinations:
Using ASSHTO Code for structural analysis, limit states STRENGTH I and
STRENGTH III recommend a load factor of 1.75 for pedestrian live loads in Table
3.4.1-1. Referring to Table 3.4.1-2, ASSHTO Code recommends a minimum load
factor of 1.25 for DC Components and 1.50 for DW wearing surfaces. The following
load factors are incorporated in the Design Envelope.
iii & iv) Bending Moment Diagrams & Shear Force Diagrams:
NOTE: The following shear and moment diagrams were modeled for a solid fixed
end one-way cantilever of length 1.9m. The design loads used were according to
Table 4 of this document and did not use ASSHTO design load factors.
WDW, slab
WPL, slab
WDC1, slab
WDC2, slab
Wcomb1, slab
Shear Value 2.28 kN 13.63 kN 11.16 kN 1.25 kN 28.33 kN
Moment Value 2.17 kN-m 12.95 kN-m 10.6 kN-m 2.25 kN-m 27.97 kN-m
10
1) Dead Load WDC1,slab (Dead Load due to Concrete)
Figure 6: Shear Force Diagram (Max Shear: 11.16 kN)
Figure 7: Moment Diagram (Max Moment: -10.60 kN*m)
2) Superimposed Dead Load WDW,slab (due to Overlay)
Figure 8: Shear Force Diagram (Max Shear: 2.28 kN)
Figure 9: Moment Diagram (Max Moment: -2.17 kN*m)
3) Handrail Road WDC2,slab (due to handrail)
Figure 10: Shear Force Diagram (Max Shear: 1.25 kN)
Figure 11: Moment Diagram (Max Moment: -2.25 kN*m)
4) Pedestrian Live Load WPL,slab
Figure 12: Shear Force Diagram (Max Shear: 13.63 kN)
Figure 13: Moment Diagram (Max Moment: -12.95 kN*m)
11
5) Design Envelope: ASSHTO load factors considered.
Figure 14: Shear Force Diagram (Max Shear: 28.33 kN)
Figure 15: Moment Diagram (Max Moment: -27.97 kN*m)
B.) Girder:
i.) Model:
Figure 16: First-order SAP Model of the proposed bridge. All dimensions are in mm.
12
ii.) Load Combinations and Factors:
The un-factored loads used in the girder design can be found in Table 5. Five load
cases were considered for the proposed bridge to account for moving live loads and
variability in specific gravity of materials used in the construction of Pollo Gigante
Pedestrian Bridge.
Figure 17: Load Case 1 – Live load across entire bridge span with max load factors used in dead weight of
construction materials.
Figure 18: Load Case 2&3 – Live load across half bridge span with min. load factors used in dead weight of
construction materials.
13
Figure 19: Load Case 4&5 – Live load across half bridge span with max load factors used in dead weight of
construction materials.
Design Loads: Girder
Load Case 1 Load Case 2 Load Case 3
Load LF
(γp)
Design Load
(kN/m) Load
LF (γp)
Design Load
(kN/m) Load
LF (γp)
Design Load
(kN/m)
WDC1,girder 1.25 44.36 WDC1,girder 0.9 31.94 WDC1,girder 0.9 31.94
WDC2,girder 1.25 2.500 WDC2,girder 0.9 1.800 WDC2,girder 0.9 1.800
WPL,girder 1.75 32.65 WPL,girder 1.75 32.65 WPL,girder 1.75 32.65
WDW,girder 1.5 5.460 WDW,girder 0.65 2.366 WDW,girder 0.65 2.366
Load Case 4 Load Case 5
Load LF
(γp)
Design Load
(kN/m) Load
LF (γp)
Design Load
(kN/m)
WDC1,girder 1.25 44.36 WDC1,girder 1.25 44.36
WDC2,girder 1.25 2.500 WDC2,girder 1.25 2.500
WPL,girder 1.75 32.65 WPL,girder 1.75 32.65
WDW,girder 1.5 5.46 WDW,girder 1.5 5.46
Table 7: Design Loads and Load factors used for Girder analysis.
Load Case 1 is considered to account for the possibility of the bridge being
completely loaded with pedestrians, LC 1 yields a maximum negative moment in the
girder near the column and in the top of the column and also yields maximum shear in the
girders and column. Load Cases 2, 3 were considered for possible maximum positive
bending in the girder, but was not large enough to control the design. Load cases 4 and 5
were also considered to determine maximum positive bending moments in the left and
14
right side of the girder and did control the design. The design loads for the load cases
used in analysis are as follows.
iii.) Bending Moment Diagrams:
Figure 20: Moment Diagram for Load Combination 1 with Max Values units in kN-m.
Figure 21: Moment Diagram for Load Combination 2 with Max Values units in kN-m.
Figure 22: Moment Diagram for Load Combination 3 with Max Values units in kN-m.
15
Figure 23: Moment Diagram for Load Combination 4 with Max Values units in kN-m.
Figure 24: Moment Diagram for Load Combination 5 with Max Values units in kN-m.
iv.) Shear Force Diagrams:
Figure 25: Shear Diagram for Load Combination 1 with Max Values units in kN.
16
Figure 26: Shear Diagram for Load Combination 2 with Max Values units in kN.
Figure 27: Shear Diagram for Load Combination 3 with Max Values units in kN.
Figure 28: Shear Diagram for Load Combination 4 with Max Values units in kN.
Figure 29: Shear Diagram for Load Combination 5 with Max Values units in kN.
17
v.) Shear and Bending Moment Design Envelopes:
Figure 30: Moment Design Envelope. All Load Combinations with Max Values in kN-m
Figure 31: Shear Design Envelope with All Load Combinations with Max Values in kN
vi.) Girder Analysis Result Table:
The results for the Girder Analysis are shown below. These results are consistent with
those found from the values in the Moment and Shear Diagrams. From the table, we
check for possible design loads:
1. Shear Analysis (Left Girder): The highest positive shear on the left girder (from
nodes 2 & 3) is 918 kN and the highest negative shear to design for is -567 kN.
2. Shear Analyis (Right Girder): The highest positive shear on the right girder
(from nodes 5 & 6) is 629 kN and the highest positive shear to design for is -848
kN.
18
Girder Analysis
Element Nodes 2-3: Girder Left
Pos. M (kN*m)
Loc. (m)
Neg. M (kN*m) Loc.
Pos. V (kN) Loc.
Neg. V (kN) Loc.
LC 1 1664 6.1 -3295 Col. 918 Col. -532 Sup.
LC 2 1576 6.7 -2069 Col. 708 Col. -466 Sup.
LC 3 503 5.5 -2000 Col. 425 Col. -191 Sup.
LC 4 1892 6.7 -2699 Col. 883 Col. -567 Sup.
LC 5 815 5.5 -2630 Col. 599 Col. -293 Sup.
Element Nodes 5-6: Girder Right
Pos. M (kN*m)
Loc. (m)
Neg. M (kN*m) Loc.
Pos. V (kN) Loc.
Neg. V (kN) Loc.
LC 1 2130 9.8 -2102 Col. 602 Sup. -848 Col.
LC 2 741 10.4 -1304 Col. 232 Sup. -384 Col.
LC 3 1901 9.8 -1285 Col. 512 Sup. -662 Col.
LC 4 1147 10.4 -1703 Col. 347 Sup. -546 Col.
LC 5 2309 9.8 -1684 Col. 629 Sup. -824 Col.
Element Nodes 8-9: Column
Pos. M (kN*m) Loc.
Neg. M (kN*m) Loc.
Pos. V (kN) Loc.
Neg. V (kN) Loc.
LC 1 1222 Girder -1863 Ft. 458 Ft. 425 Girder
LC 2 905 Girder -1016 Ft. 287 Ft. 262 Girder
LC 3 611 Girder -1302 Ft. 286 Ft. 262 Girder
LC 4 1142 Girder -1381 Ft. 378 Ft. 344 Girder
LC 5 848 Girder -1667 Ft. 343 Ft. 377 Girder
Table 8: Tabular results of load case analysis. Listed are the maximum and minimum moments and shears
for each load case and their locations on the girder and column. (Col. – Column/Girder Node [3 or 5], Sup. –
Support/Girder Node [2 or 6], Ft. – Footing/Column Node [9], Girder – Column/Girder Node [8]) If Location
is in meters, it is the distance from the left node [2 or 5] of the girder element analyzed.)
19
V. SLAB DESIGN
i.) Slab Flexure
Slab Design – Single Layer Tensile Steel
Bar Size
No. Bars
db (mm) Ab (mm2) As (mm2) smin (mm) s (mm)
4 7 12.7 129 903 60 130.2
d (mm) c (mm) c/d Mn (kN-
m) Mcr (kN-
m) фMn (kN-m)
Mu (kN-m)
144 14.881 0.1 51.59 25.89 46.53 28
c/d<0.42 Mn > 1.85Mcr фMn > Mu
Table 9: This table lists the slab design for multiple spacing. It also includes the checks for each of the bars
recommended.
Figure32: Slab design with reinforcement. Unit in mm.
ii.) Slab Shear
From analysis of the load case for the slab sections, it was determined that the
concrete in the slab has a factored resistance of 79kN. The analysis listed a maximum
demand of 28kN at the base of the cantilevered section. Per ACI-318, when designing for
shear, no shear reinforcement is needed if the factored demand is less than half the
resistance of the concrete. With a factored resistance of more than 3x the demand, no
shear reinforcement was considered for the slab design.
20
VI. GIRDER DESIGN
i.) Girder Flexure Design:
Girder Design - 1 Layer (Critical Positive Moment)
Bar Size No. Bars
db (mm) Ab (mm2) As (mm2) smin (mm) s (mm)
11 7 35.81 1006 7042 50.8 62
d (mm) c (mm) c/d Mn (kN-m) Mcr (kN-m) фMn (kN-m) Mu (kN-m)
919 29.38 0.032 265 68 2383 2309
c/d<0.42 Mn > 1.85Mcr фMn > Mu
Girder Design - 1 Layer (Critical Negative Moment)
Bar Size No. Bars
db (mm) Ab (mm2) As (mm2) smin (mm) s (mm)
17 9 28.65 645 10965 50.8 varies
d (mm) c (mm) c/d Mn (kN-m) Mcr (kN-m) фMn (kN-m) Mu (kN-m)
923 240.44 0.26 3763 485 3387 3295
c/d<0.42 Mn > 1.85Mcr фMn > Mu
Table 10: This table provides the chosen design for the girder
Figure 33: Design of Girder cross section for the critical positive moment case. Units in mm.
Figure 34: Design of Girder cross section for the critical negative moment case. Units in mm.
21
II.) ii.) Girder Shear Design:
III.)
IV.) The shear Design was completed per ACI-318. All calculations may be found in
Appendix 2.0. It was found that the worst case shear dictated a large section of Case 2,
another Case 3 section near the columns and a small case 1 section at mid-span. Due to
seismic loading in California no unreinforced shear sections were designed for. Minimum
reinforcement was used in all sections of the girder up to section 3. Lastly even though
one side of the bridge experienced less loads per analysis, to be safe and make for easier
constructability, the worst case will be mirrored about the centerline at the column.
V.)
Range фVn (kN) Start (mm) End (mm) # sets Rebar Config. s (mm)
Case 4 Not Encountered
Case 3 3фVc<Vu<Vc 1600 50 4690 32 #4 4 leg 135
Case 2 фVc<Vu<0.5Vc 733 4875 17325 35 #3 4leg 400
Table11: design results from shear analysis.
Figure 35a: Shear design near the column. Case 3
Figure 35b: Shear design near mid-span to the supports. Case 2.
22
VII. DEVELOPMENT OF LONGITUDINAL AND MISCELLANEOUS
REQUIREMENTS
A.) Bar development per ACI-381
From the ACI code, all calculations passed the design checks. It was decided that
the negative reinforcement would be cut off from 17#9 bars to 6#9bars more than
3.27m from the column. Then cut off from 6#9 bars to 4#9 bars at more than 5.61m
from the column and continue till the support for shear stirrups.
The positive reinforcement was determined that the 7#11 bars would be cut off to
4#11 bars at a distance greater than 15.29m from the column and less than 4.08m
from the column, taking proper development into account.
The shear calculations per ACI 12.10.5.1 all passed and no design changes were
needed in that regard. The following is the graphs used in the design of the bar
development. For calculations See Appendix2.1 and for more detail see drawings IV
and V in section IX. Drawings.
Graph 1: Shear Design Envelope including factored resistances per the girder shear design and plots of the
shear for the maximum positive moment case and maximum negative moment case.
0
200
400
600
800
1000
1200
1400
1600
1800
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Sh
ear
Fo
rce k
N i
n G
ird
er
Distance x from Column Face (m)
Shear Design Envelope
Positive Moment
Negative Moment
Design Capacity
Case 3:
фVn = 1600kN
Case 2: фVn = 733kN
23
Graph 2: Moment Design Envelope used for designing bar development of the girder section. The graph
includes maximum positive moment demand and maximum negative moment demand, then plotted are the
corresponding cutoff rebar locations and the distances from the column face.
-4000
-3000
-2000
-1000
0
1000
2000
3000
4000
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Mo
men
t k
N-m
in
Gir
der
Distance x from Column Face (m)
Moment Degign Envelope & Bar Cutoffs
Positive Moment
Negative Moment
B-CutOff (+)
B-CutOff (-)
A-CutOff (-)
Max Positive Moment
xA
-=6.0
4m
xB
-=3.2
7m
xB
L+=
4.0
8m
xB
R+=
15.2
9m
24
VIII. COLUMN DESIGN
i. Column Analysis Results
The analysis for the column was performed through the simplification of the bars chosen
for a potential design. The following schematic illustrates the simplification:
Figure 36: Column Reinforcement
The following results were calculated using five cases that determine the
resistance-flexure axial load interaction diagram. These results are then used as the limits
and criteria for determining the amount of #10 bars that will be used in the column
reinforcement. The cover for the stirrups from the edge of the column is considered to be
50 mm while the stirrup used along the reinforcement is a 12 mm bar. The calculations
for the column design can be found in Appendix 2.2.
25
ρ = .01 ρ = .04
Case φPn(MN) φMn(MN-m) φPn(MN) φMn(MN-m)
1 -17 0 -22.3 0
2 2.7 0 10.76 0
3 -2.88 1.81 -0.2 3.36
4 -4.26 2.24 -2.66 4.27
5 -6.34 2.054 -6.08 3.48
Table 12: Design schematic of the cross section of the bridge (girder) with appropriate dimensions
ii. Factored Resistance-Flexure Axial Load Interaction Diagram
Graph 3: This table provides the chosen design for the girder; the graph displays all the maximum values
from the results of the structural analyses are within the red circle. The chosen design is marked by the red
dashed circle.
26
Graph 4: Linear Interpolation Graph
From the linear interpolation of the data from the resistance-flexure axial load interaction
diagram, the value for rho was found to be .0213. This can now determine the
reinforcement that will be used for the
column.
iii. Column Final Design
The final column reinforcement
design is the following:
20 #10 Bars with a 50 mm
cover from the edge of the
column; 12 mm stirrup at 250
o.c.
0.01, 0.875
0.0213, 1.86
0.04, 3.5
0
0.5
1
1.5
2
2.5
3
3.5
4
0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045
φM
n
ρg
Linear Interpolation of ρ
Figure 37: Final Column
Reinforcement Design
27
iv. Column Bar Development
For images and Detailed drawings of Bar development for the Column please refer to Section IX.
Drawings.
Bar Development For Column
A development length 0f 1.3m will cause teh rebar to protrude from the decking surface. Use Std hooks.
ACI 12.5.4 - At the ends of member, in this case the coloumn member, the factor shall be 1.0
(ACI 12.5.3)
db10 32.26mm
ld_col
12 fy t_bottom e 20 fc MPa
db10 1.3m
Factor 1.0
ldh_col max0.02e fy fc MPa
db10 Factor 8 db10 150mm
0.258m
12 db10 0.387m
D10 8 db10 0.258m
R10
D10
20.129m
28
IX. DRAWINGS
I. T
r
a
n
s
v
e
r
s
e
R
e
b
a
r
S
p
a
c
i
n
29
II. L
o
n
g
i
t
u
d
i
n
a
l
R
e
b
a
r
S
p
a
c
i
n
g
a
n
30
III. L
o
n
g
i
t
u
d
i
n
a
l
R
e
b
a
r
S
p
a
c
i
n
g
31
IV. G
i
r
d
e
r
R
e
i
n
f
o
r
c
e
m
e
n
32
V. S
u
p
p
o
r
t
R
e
b
a
r
33
34
35
36
X. APPENDIX
APPENDIX 1.1: CALCULATIONS FOR AG,SLAB ,IXX,SLAB AND SE,SLAB
Ixx_slab
be hf3
12
Se_slab
Ixx_slab
hf
2
m3
Girder Calculations
APPENDIX 1.2: CALCULATIONS FOR AG,COLUMN , IXX,COLUMN AND SE,COLUMN .
Ixx_slab
be hf3
126.667 10
4 m
4
h 1m hf .2m bw .750m be 1.00m
Ag_slab hf be 0.2m2
bc .850m hc .850m
Acolumn bc hc 0.722m2
Ixx_column
bc hc3
120.044m
4
Se_column
Ixx_column
hc
2
0.102m3
37
APPENDIX 1.3: CALCULATIONS FOR YB , YT , AG,GI RDER , IXX,GIRDER AND SE,GI RDER .
h 1m hf .2m bw .750m be 4.55m
hw h hf 0.8m
Agirder1 bw hw 0.6m2
Agirder2 be hf 0.91m2
y1
hw
20.4m
y2 hw
hf
2 0.9m
Ag_girder Agirder1 Agirder2 1.51m2
yb
Agirder1 y1 Agirder2 y2 Ag_girder
0.701m
yt h yb 0.299m
d1 yb y1 0.301m
d2 yb y2 0.199 m
Ixx1
bw hw3
12Agirder1 d1
2 0.086m
4
Ixx2
be hf3
12Agirder2 d2
2 0.039m
4
Ixx_girder Ixx1 Ixx2 0.1254m4
Sb_girder
Ixx_girder
yb
0.1788 m3
St_girder
Ixx_girder
yt
0.42 m3
38
APPENDIX 1.4: CALCULATIONS FOR SLAB DESIGN LOADS.
APPENDIX 1.5: CALCULATIONS FOR GIRDER DESIGN LOADS.
concrete 23.5kN
m3
asphalt 16kN
m3
hasphalt 0.05m
WDC1_slab concrete hf 1 m 4.7kN
m
WDW_slab asphalthasphalt 1 m 0.8kN
m
PDC2_slab 1kN
m
1 m 1kN
WPL_slab 4.1kN
m2
1 m 4.1kN
m
WDC1_girder concrete Ag_girder 35.485kN
m
WDW_girger asphaltbe hasphalt 3.64kN
m
WDC2_girder 2 1kN
m2
kN
m
WPL_girder 4.1kN
m2
be 18.655kN
m
39
APPENDIX 1.6: CALCULATIONS FOR THE SLAB DESIGN
Critical Negative Moment Slab - Flexure Check
Cracking Moment of Section
Internal Compressive and Tensile Forces
Moment Carrying Capacity of Section
Tesile Dominated Section
fc 38MPa fy 414MPa db4 12.7mm d 144mm l 1900mm
hf 200mm h 1000mm bw 1000mm c 14.61mm Mu 28kN m
be 1000mm
1 0.85 0.0538 28( )
7
0.779
a 1 c 11.375 mm
As_min0.25 38 MPa
fy
bw d 536.036 mm2
As 7
db4
2
2
886.738mm2
fr 0.625 38MPa 3.853 106
Pa yt 100mm Ig 6.667 104
m4
Mcr
fr Ig yt
25.686kN m
C 0.85 fc 1 c bw 3.674 105
N
T As fy 3.671 105
N
Error 2C T
C T
100 0.082
Mn T da
2
50.776 kN m
sd c( )
c
.003 0.027 s 0.005
0.9c
d
0.42if
0.65 0.15d
c
1
0.375c
d
0.42if
0c
d
0.42if otherwise
5.5.4.2.1 LRFD( )
0.9
Mn 45.698 kN m
40
AASHTO Code Checks
Mmin min 1.22Mcr 1.33Mu 31.337 kN m
Check1 "PASS" Mn Mminif
"FAIL" Mn Mminif
5.7.3.3.2 LRFD( )
Check2 "PASS" Mn Muif
"FAIL" Mn Muif
Check3 "PASS" 0.42c
dif
"FAIL" 0.42c
dif
5.7.3.3.1 LRFD( )
Check4 "PASS" As As_minif
"FAIL" As As_minif
Check1 "PASS" Check2 "PASS" Check3 "PASS" Check4 "PASS"
41
APPENDIX 1.7: CALCULATIONS FOR THE POSITIVE GIRDER DESIGN
Critical Positive Moment Case:
Assuming No.4 Stirrup and No.11 Flexural Rebar to get a rough As (design)
and a strength reduction factor of 0.9
Assuming Number 4 stirrup
fc 38MPa fy 414MPa be 3950mm dclear 50mm db 35.81mm dstr 12.7mm
d 1000mm dclear dstrdb
2 919.395mm
Mu 2309kNm .9
a1
fy2
2 .85 fc be 671.693
1
mMPa b1 fy d 380630
1
mkN c1
Mu
2566kN m
b1 b12
4 a1 c1
2 a1559849mm
2
b1 b12
4 a1 c1
2 a16822mm
2
smin 50.8mm bw 750mm dNo9 28.65mm dNo10 32.26mm dNo11 35.81mm
ANo9 645mm2
ANo10 819mm2
ANo11 1006mm2
NNo9
bw 2 dstr 2 dclear smin dNo9 smin
8.501 ANo9_max 8 ANo9 5160mm2
NNo10
bw 2 dstr 2 dclear smin dNo10 smin
8.131 ANo10_max 8 ANo10 6552mm2
NNo11
bw 2 dstr 2 dclear smin dNo11 smin
7.798 ANo11_max 7 ANo11 7042mm2
42
Critical Positive Moment Girder - Flexure Check
Cracking Moment of Section
Internal Compressive and Tensile Forces
Moment Carrying Capacity of Section
Tensile Dominated Section
fc 38MPa fy 414MPa db11 35.84mm d 919mm l 17500mm
hf 200mm h 1000m bw 750mm c 29.41mm Mu 2309kNm
be min bw 2 8 hfl
4
3.95 103
mm
1 0.85 0.0538 28( )
7
0.779
a 1 c 0.023m
As_min0.25 38 MPa
fy
bw d 2.566 103
mm2
As 7
db11
2
2
7.062 103
m2
fr 0.625 38MPa 3.853 106
Pa yt 701mm Ig 0.1254m4
Mcr
fr Ig yt
689.21kN m
C 0.85fc 1 c be 2.921 106
N
T As fy 2.924 106
N
Error 2C T
C T
100 0.076
Mn T da
2
2.653 103
kN m
sd c( )
c
.003 0.091 s 0.005
0.9c
d
0.42if
0.65 0.15d
c
1
0.375c
d
0.42if
0c
d
0.42if otherwise
5.5.4.2.1 LRFD( )
0.9
Mn 2.388 103
kN m
43
AASHTO Code Checks
Mmin min1.22Mcr 1.33Mu 840.836kNm
Check1 "PASS" Mn Mminif
"FAIL" Mn Mminif
5.7.3.3.2 LRFD( )
Check2 "PASS" Mn Muif
"FAIL" Mn Muif
Check3 "PASS" 0.42c
dif
"FAIL" 0.42c
dif
5.7.3.3.1 LRFD( )
Check4 "PASS" As As_minif
"FAIL" As As_minif
Check1 "PASS" Check2 "PASS" Check3 "PASS" Check4 "PASS"
44
APPENDIX 1.8: CALCULATIONS FOR THE NEGATIVE GIRDER DESIGN
Critical Negative Moment Case:
Assuming No.4 Stirrup and No.11 Flexural Rebar to get a rough As (design)
and a strength reduction factor of 0.9
Assuming Number 4 stirrup Max number of flexural rebar and Max areas.
Use 17 No.9 bars for critical negative moment
fc 38MPa fy 414MPa be 750mm dclear 50mm db 35.81mm dstr 12.7mm
d 1000mm dclear dstrdb
2 919.395mm
Mu 3295kNm .9
a1
fy2
2 .85 fc be 3.538 10
3
1
mMPa b1 fy d 380630
1
mkN c1
Mu
3661kN m
As_design1
b1 b12
4 a1 c1
2 a196918mm
2 As_design2
b1 b12
4 a1 c1
2 a110678mm
2
smin 50.8mm bw 3950mm dNo9 28.65mm dNo10 32.26mm dNo11 35.81mm
ANo9 645mm2
ANo10 819mm2
ANo11 1006mm2
NNo9
bw 2 dstr 2 dclear smin dNo9 smin
48.778 ANo9_max 48 ANo9 30960mm2
NNo10
bw 2 dstr 2 dclear smin dNo10 smin
46.658 ANo10_max 46 ANo10 37674mm2
NNo11
bw 2 dstr 2 dclear smin dNo11 smin
44.745 ANo11_max 44 ANo11 44264mm2
NNo.9design
As_design2
ANo9
16.556
45
Critical Negative Moment Girder - Flexure Check
Cracking Moment of Section
Internal Compressive and Tensile Forces
Moment Carrying Capacity of Section
Tensile Dominated Section
fc 38MPa fy 414MPa db9 28.7mm d 923mm
hf 200mm h 1000mm bw 750mm c 240mm Mu 3295kNm
be 3950mm
1 0.85 0.0538 28( )
7
0.779
a 1 c 186.857mm
As_min0.25 38 MPa
fy
bw d 2.577 103
mm2
As 17
db9
2
2
1.1 104
mm2
fr 0.625 38MPa 3.853 106
Pa yt 299mm Ig 0.1254m4
Mcr
fr Ig yt
1.616 103
kN m
C 0.85fc 1 c bw 4.527 106
N
T As fy 4.553 106
N
Error 2C T
C T
100 0.582
Mn T da
2
3.777 103
kN m
sd c( )
c
.003 0.009 s 0.005
0.9c
d
0.42if
0.65 0.15d
c
1
0.375c
d
0.42if
0c
d
0.42if otherwise
5.5.4.2.1 LRFD( )
0.9
Mn 3.399 103
kN m
46
AASHTO Code Checks
Mmin min 1.22Mcr 1.33Mu 1.971 103
kN m
Check1 "PASS" Mn Mminif
"FAIL" Mn Mminif
5.7.3.3.2 LRFD( )
Check2 "PASS" Mn Muif
"FAIL" Mn Muif
Check3 "PASS" 0.42c
dif
"FAIL" 0.42c
dif
5.7.3.3.1 LRFD( )
Check4 "PASS" As As_minif
"FAIL" As As_minif
Check1 "PASS" Check2 "PASS" Check3 "PASS" Check4 "PASS"
47
APPENDIX 1.9: CALCULATIONS FOR THE SHEAR DESIGN – SLAB SECTION
bw 1000mm d 144mm Vu 28kN fc 38MPa 0.75
Vc1
6
38 MPa bw d 147.946kN
Case "Case 1 - No Required Reinforcement" Vu Vc
2if
"Needs Reinforcement" Vu Vc
2if
Case "Case 1 - No Required Reinforcement"
48
APPENDIX 2.0: CALCULATIONS FOR THE SHEAR DESIGN – GIRDER SECTION
Shear Design per ACI-318
Due To seismic loads native to California Case 1 will be ignored and considered Case2
Case 2: Minimum Shear Reinforcement
Design using 4#3 @ 400mm o.c.
Case 3: Shear Reinforcement
Design using 4#4 @ 400mm o.c.
bw 750mm d 919mm fc 38MPa fy 414MPa 0.75
Vc1
6
38 MPa bw d 708.137kN
Case1max Vc
2 265.551kN
Case2max Vc 531.103kN
Case3max 3 Vc 1.593 103
kN
Case4max 5 Vc 2.656 103
kN
Vul567kN
6.677m
6.677m d( ) 4.89 105
N
Vur 918kN
10.810m
10.810m d( ) 8.4 105
N
s2max mind
2
600mm
0.46m
s2 400mm
Av_min maxbw s2 3 414( )
38MPa bw s2 16 fy
279.185mm2
db3 9.525mm
Av2 4db3
2
2
285.023mm2
s3max mind
2
600mm
0.46m
s3 135mm
Av3min
3 Vc
Vc
1
fy
s3
d
502.534mm2
db4 12.7mm
Av3 4db4
2
2
506.707mm2
49
Case 4&5: Shear Reinforcement
Does not occur in Design
Locations and # Sets for Cases in Girder
Per the Shear Envelope - Designing for Critical Case 3 and Using Case 2 everywhere else.
Case 3 must be designed for at 4557m from the column or more.
Use 35 sets of Case 3 - Stirrups
Case 2 - starting at 50mm of clear cover from the end of the girder at the support
Use 32 sets of Case 2 - Stirrups
x3min531kN 10.810 m 918kN 10.810 m( )
918 kN4557.157mm
n3min4557mm 50mm( )
135mm
1 34.385
n3 35
x3 50mm n3 1 135 mm 4640mm
n2max17375mm 2 50 mm 4640mm( )
400mm
1 32.587
n2 32
x2 50mm n2 1 400 mm 12450mm
dx 17375mm 2 50 mm x2 x3 185mm
50
APPENDIX 2.1: BAR DEVELOPMENT GIRDER CALCULATIONS
Bar Development per ACI-318
Bar Cutoff per ACI-318
Development Length
(1) Negative Bar Cutoff
Bars Cutting off 11#9 bars- 10 in the flanges and one in the web
Determined Via MATLAB
Extrapolated From Graph
Vu_neg x( ) 9181450
17.075
x kN Mu_neg x( )1450
34.15
x2
918x 3295
kN m
Vu_pos x( )1453
17.075
x 824 kN Mu_pos x( )1453
34.15
x2
824x 1684
kN m
fc 38 MPa fy 414MPa bw 750mm d max 919mm923mm( ) lr 17.075m
As_min max 0.25 fc MPa 1.4MPa bw d
fy
2.577 103
mm2
10.5.1 ACI( )
t_top 1.3 t_bottom 1.0 e 1.0 s 1
1 db11 35.81mm db9 28.65mm
ld_neg
12 fy t_top e 20 fc MPa
db9 1.501m Top Bars: Negative Moment
ld_pos
12 fy t_bottom e 20 fc MPa
db11 1.443m Bottom Bars: Positive Moment
AsA1 6db9
2
2
3.868 103
m2
AsB1 11db9
2
2
7.091 103
m2
Mn A1 1283kNm
xtrB1 2.475m
xrB1 maxxtrB1 maxd 12db9 ld_neg 3.398m
Vu_neg 3.398( ) 6.294 105
N
51
Negative moment ends @ xp1r
Vc1
6
fc MPa bw d 7.112 105
N
Av2 279.185mm2
Av3 502.534mm2
s2 400mm s3 135mm
Vs2 Av2 fyd
s2
2.667 105
N Vs3 Av3 fyd
s3
1.422 106
N
V n x( ) 0.75 Vc Vs3 x 4.690if
0.75 Vc Vs2 x 4.690if
V n 3.398( ) 1.6 106
N
Check1neg "PASS" AsA1 As_minif
"FAIL" AsA1 As_minif
10.5.1 ACI( )
Check1neg "PASS"
Check2neg "PASS" AsA1
AsA1 AsB1 3
if
"FAIL" AsA1
AsA1 AsB1 3
if
12.12.3 ACI( )
Check2neg "PASS"
Check3neg "PASS"Vu_neg 3.398( )
V n 3.398( )
2
3if
"FAIL"Vu_neg 3.398( )
V n 3.398( )
2
3if
12.10.51 ACI( )
Check3neg "PASS"
xpir 4.54m
xrAmin max xpir max d 12 db9lr
16
xpir ld_neg
6.041m
52
(2) Positive Bar Cutoff
Bars Cutting off 3#11 bars, every very other in the in the web
Determined Via MATLAB
Extrapolated From Graph
By Symmetry: x.l2 will pass the same checks so no calculations shown.
Bars A per (10.5.1-ACI) & (12.11.1-ACI) need to be embedded 150mm into column.
AsA2 4db11
2
2
4.029 103
m2
AsB2 3db11
2
2
3.021 103
m2
Mn A2 1371kNm
xtl2 4.9967m
xlB2 maxxtl2 maxd 12db11 ld_pos 5.92m
Vu_pos 5.623( ) 3.455 105
N
V n 9.7 5.623( ) 1.6 106
N
Check1pos "PASS" AsA2 As_minif
"FAIL" AsA2 As_minif
10.5.1 ACI( )
Check1pos "PASS"
Check2pos "PASS" AsA2
AsA2 AsB2 3
if
"FAIL" AsA2
AsA2 AsB2 3
if
12.12.3 ACI( )
Check2pos "PASS"
Check3pos "PASS"Vu_neg 5.623( )
V n 5.623( )
2
3if
"FAIL"Vu_neg 5.623( )
V n 5.623( )
2
3if
12.10.51 ACI( )
Check3pos "PASS"
53
APPENDIX 2.2 : COLUMN DESIGN SAMPLE CALCULATION
Using AASHTO code for Design:
Column Schematic (Idealized version):
(Calculation of the distance from L1 fiber to L3 fiber)
Column Analysis (Case 1):
Strength Reduction Factor ϕ
Column Analysis (Case 2):
Strength Reduction Factor ϕ
Column Analysis (Case 3):
Assumed the value of c at .23*h of the column
since the yield ε s1 is less greater than .005
h 850mm
b 850mm
gh h 2 5 1232.3
2
gh 693.7mm
g .01 g .04
Ast g Ag 7225mm2
28900mm2
Pn Ast fy Ag Ast .85 fprime_c 26.09 MN 34.37 MN
Mn 0MN 0MN 0MN
.65 .65
Pn Ast fy 2.99MN 11.96MN
Mn 0MN 0MN 0MN
.90 .90
ccolumn .23h
a 1 c .779 195.5.5mm( ) .90
a 195.5mm
c
c1.535 10
5 dh
21 g( ) 772mm
54
Layer (1)
Layer (2):
Layer (3):
Summing the Forces:
Summing the Moments:
s1 d c( ) .0085
s1 0 fs1 minEs s1 fy fs1 414MPa
s2 h
2c
.0035
s2 0 fs2 minEs s2 fy fs2 414MPa
s3 h
21 g( ) c
.0018
s3 0 ah
21 g( ) c
fs3 maxs3 fy 0.85fprime_c fs3 327.7 MPa
g .01 g .04
Fs13
8Ast fs1 1122kN 4487kN
748kN 2991kNFs2
2
8Ast fs2
889 kN 3551 kN
Fs33
8Ast fs3
4181 kN 4181 kNCc .85 fprime_c a b
Pn 3200 kN 253 kN
Mn Fs1 x1 Fs3 x3 Cc xc 2.01MN m 3.73MN m
x1gh
23.468 x3
gh
23.468
xch
2
a
2
348.9
55
APPENDIX 2.3: MATLAB PROGRAM USED FOR LINEAR INTERPOLATION
The linear interpolation of the actual graph was determined through the use of MATLAB code.
clc;
clear;
y1 = input ('y1 value=');
y0 = input ('y0 value=');
x1 = input ('x1 value=');
x0 = input ('x0 value=');
y = input ('y value=');
% x = input ('x value=');
x = x0+(y-y0)*((x1-x0)/(y1-y0))
% y = y0+(x-x0)*((y1-y0)/(x1-x0))
Results with Reduction Factors
Column Analysis (Case 4):
Column Analysis (Case 5):
P n M n 2.88 MN 1.81MN m( ) .2 MN 3.36MN m( )
ccolumn3
8d 289.43mm
a 1 c 194.3mm
.003
289.431.037 10
5
ccolumn
cu
cu y d 463.2mm
a 1 c 360.83mm
b.003
463.2
The Calculations for these cases
is similar to Case 3.
56
XI. HOURS SPENT PER STUDENT
Hours Spent
Luke Robinson
Alvin Aguelo
1. References
0 0.5
2. Dimensions & Section Properties
a. Slab 1 1
b. Girder 1 1
c. Column 1 1
3. Design Loads
a. slab 0 0
i. Dead Load 1 1
ii. Superimposed Dead Load 1 1
iii. Live Load 1 1
b. Girder
i. Dead Load 2 2
ii. Superimposed Dead Load 2 2
iii. Live Load 2 2
4. Structural Analysis
a. Slab 0 0
i. Model 1 1
ii. Load Combinations 1 1
iii. Bending Moment Diagrams of Load Combinations 1 1
iv. Shear Force Diagrams of Load Combinations 1 1
v. Design Envelopes 1 1
b. Girder
i. Model
ii. Load Combinations and Factors 2 2
iii. Bending Moment Diagrams of Load Combinations 2 2
iv. Shear Force Diagrams of Load Combinations 2 2
v. Design Envelopes 2 2
5. Slab Design
a. Flexure Design of Critical Section 0 4
b. Design for Shear 0.25 0
6. Girder Design
a. Flexure Design of Critical Section 1 0
i. Negative Moment 1 0
ii. Positive Moment 1 0
b. Design for Shear 1 0
57
7. Development of Longitudinal Reinforcement and Miscellaneous Requirements
a. Slab reinforcement 2 0
i. Longitudinal Bar Development 2 0
ii. Shrinkage and Temperature 2 0
iii. Cross Section Sketches 2 0
b. Girder Reinforcement 2 0
i. Longitudinal Bar Development 2 0
ii. Cross Section Sketches 2 0
8. Column Design
a. Interaction diagrams 0 2
b. Pn, Mu combinations 0 2
c. Design for Shear 0 2
d. Longitudinal Bar Development 0 2
9. Handrail Base Design
0 0
10. Drawings
1 1
10. Editing/Formatting Report
15 25
Total Hours Spent
Luke Robinson 59.25
Alvin Aguelo 58.5
Recommended