SE151TermProjectReport Jimmy Nikko v2

SE 151A Sycamore Canyon Pedestrian Bridge Design of Reinforced Concrete

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RFI Response On behalf of Situ-Sera Engineering, we would like to apologize for the errors found in our previous submission. We have ensured that every noted error was fixed. Should any other errors be found, the engineers at Situ-Sera Engineering will guarantee a timely and accurate response. The following changes have been made: Section 2 Dimensions & Section Properties,

Dimensions of the slab cross section were updated Section 4 Structural Analysis

The plots were made clearer Section 5 Slab/Deck Design

The final design is highlighted


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University of California, San Diego Department of Structural Engineering

Sycamore Canyon Pedestrian Bridge

SE 151A: Structural Concrete Term Project Professor Jose Restrepo

Winter 2015 Wenjin Situ (A97034409)

Nicholas Sera (A09849716) March 18th, 2015


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TABLE OF CONTENTS:

1. References . 5 2. Dimensions & Section Properties ..... 5

a. Slab (Deck)... 5 b. Girder... 6 c. Column & Pile...... 7

3. Design Loads..... 8 a. Slab (Deck)... 8

i. Dead Load... 8 ii. Superimposed Dead Load.... 9

iii. Live Load. 9 b. Girder .. 9

i. Dead Load... 9 ii. Superimposed Dead Load... 9

iii. Live Load.... 10 4. Structural Analysis ...... 10

a. Slab (Deck).. 10 i. Model.. 10

ii. Load Combinations.... 11 iii. Bending Moment Diagrams of Load Combinations... 12 iv. Shear Force Diagrams of Load Combinations 13 v. Design Envelopes... 13

b. Girder .... 14 i. Model.. 14

ii. Load Combinations. 14 iii. Bending Moment Diagrams of Load Combinations... 17 iv. Shear Force Diagrams of Load Combinations... 19 v. Design Envelopes... 20

5. Slab/Deck Design..... 22 a. Flexure Design of Critical Sections.... 22 b. Design for shear ..... 25

6. Girder Design... 25 a. Flexure Design of Critical Section.. 25

i. Rough Design. 25 ii. Positive Moment (Bottom reinforcement).................................. 25

iii. Negative Moment (Top reinforcement)...................................... 25 iv. Bar Spacing..... 26 v. Effective Section Properties.... 27

vi. Design Strength Mn- and Mn+............................................... 28 b. Design of Shear Reinforcement ...... 28

7. Development of Longitudinal Reinforcement...................................................... 31 a. Slab Reinforcement.................................................................................. 31

i. Longitudinal Bar Development................................................... 31


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ii. Shrinkage and Temperature......................................................... 31 iii. Cross Section Sketches................................................................ 32

b. Girder Reinforcement............................................................................... 32 i. Longitudinal Bar Development................................................... 33

ii. Cross Section Sketches................................................................. 34 8. Column Design....................................................................................................... 35

a. Interaction diagrams.................................................................................. 35 b. Pu and Mu combinations............................................................................ 36 c. Design for Shear....................................................................................... 36 d. Longitudinal Bar Development................................................................. 38

9. Extra Credit: Pile Design 39 10. Drawings................................................................................................................ 43 11. Appendix........ 45 12. Work Hours Recorded Chart.......... 71


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Sec. 1. References The proposed design is a continuous two-span pedestrian bridge to be built in Sycamore Canyon located in East San Diego County. The purpose of this bridge is to allow safe passage for pedestrians across the 5 lane low-volume roadway that is set in a small valley. The bridge is composed of two continuous identical 46 ft long double T girders that are supported on two neoprene bearings at each abutment and by a moment resisting bent-cap at midspan. The bent cap is supported by an inclined column as determined by the state landscape architect for aesthetic reasons. The depth of the slab(Deck) is 8 in and the depth of the girder is 36 in in accordance to ACI 318-11 Table 9.5(a). The column has a diameter of 4 ft. The concrete used has a compressive strength of 4.0ksi. The grade of the steel reinforcement is ASCE A706 Grade 60, fy=60 ksi.

Figure 1. Elevation View of Proposed Roadway Crossing

Sec. 2. Dimensions & Section property 2.a Slab/Deck The design of the slab is shown in Figure 2 below. It has a thickness of 6 inches at the two edges and a overall depth of 8 inches at the center. The top of the slab has a length of 186 inches while its bottom is 160 inches long. The slab is assumed to consist of a series of 1 foot long one-way solid planks supported by the girders. The left and right ends of the planks are modeled as cantilevers. The cross-section of the slab is shown in Figure 3, and Figure 4 shows the simplified model. The overall thickness of the slab is demanded to be at least 8 deep by the client, while it should also satisfy ACI 318-11 codes. In this case, the ratio of the span is less than . According to Table 9.5 (a) of ACI 318-11, the depth should be greater than L/20 for one way solid slab and simply supported structure. Therefore, the depth of the slab is determined to be 8 inches by Equation 1 below.

h=max(144/20 in, 8 in)= 8 Equation 1.


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Figure 2. Slab geometry (unit in inches) Figure 3. Slab cross section(inch)

Figure 4. Simplified Model(in)

With the dimensions found, the section properties of the slab are calculated in Table 1. Detail calculations can be found in Figure 5 in Appendix.

Table 1. Section properties of Slab

Area of Slab (in2) 96

Centroid of Slab (in) 4

Moment of Inertia of Slab, Izz (in4) 512

Elastic Section Modulus of Slab (in3) 128

2. b Girder The girder is simplified into 4 sections of lengths 2ft, 46 ft, 46 ft, and 2ft with supports 2 feet from the end of each span and an inclined column at midspan.The simplified model is shown in Figure 6.

Figure 6. Simplified Model of Girder ( inches)


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Using the simplified model, the girder depth can be determined based on ACI 318-11 Table 9.5(a). The 2ft span is too short to be considered to provide continuity therefore the 552 inches span is treated as one end continuous. In general, a section is considered continuous if its length exceeds 1/4th of the main length. Based on Table 9.5(a), the minimum thickness h for one end continuous solid one-way slab is determined by Equation 2:

h=L/18.5=552/18.5=29.8 Equation 2. To simplify manufacturing, the depth of the girder is determined to be 36. The dimensions of the cross section of the double T girder are shown in Figure 7.

Figure 7. Double T Girder cross section

Based on the dimensions of the girder, its section properties are calculated in Table 2. Detail calculations is shown in Figure 8 in Appendix .

Table 2. Section properties for the girder

Area of Girder (in2) 2.358*103

Centroid of Girder (in) 25.197

Moment of Inertia of Girder, Izz (in4) 2.474*105

Elastic Section Modulus (Top) (in3) 2.29*104

Elastic Section Modulus (Bot) (in3) 9.817*103

2.c Columns & Pile The column has a circular cross section with a diameter of 4 ft as shown in Figure 9. The pile is also circular with a diameter of 6 ft as shown in Figure 10. The area and moment of inertia are calculated in Table 3. Details of the calculations can be found in Figure 11 in Appendix.


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Figure 9. Column cross section Figure 10. Pile cross section

Table 3. Section properties of column

Area of Column (in2) 2.895*104

Moment of Inertia of Column, Izz(in4) 2.606*105

Table 4. Section properties of pile

Area of pile (in2) 6.514*104

Moment of Inertia of pile, Izz(in4) 1.319*106

Sec. 3. Design loads 3 a. Slab (Deck) The design loads of the slab consisted of the self-weight of the pedestrian bridge, the superimposed dead loads of the asphalt and handrail, and the live loads. i. Dead load The pedestrian bridge is made of concrete with a unit weight of c=150pcf. The self-weight can be modeled as distributed trapezoidal loads as shown in Figure 12.

Figure 12. Distributed load of concrete self-weight


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ii. Superimposed Dead load The first superimposed dead load consisted of the uniform distributed load of the asphalt, which has a unit weight A=101 pcf. This design load is shown in Figure 13. The second superimposed dead load is composed of the point loads due to the weight of the handrail with linear weight of 68.5 lb/ft.This is shown in Figure 14.

Figure 13. superimposed dead load of asphalt Figure 14. superimposed dead load of handrails iii. Live load The applied live load is 86 lb/ft that can act anywhere on the entire deck. 3.b. Girder The design loads imposed on the Girder are composed of the self-weight of the pedestrian bridge, the superimposed dead loads of the asphalt and handrail, and the live loads. i. Dead load The pedestrian bridge is made of concrete with a unit weight of c=150 pcf. The self-weight dead load is composed of 3 components: the self-weight of the girder, which is idealized as uniform distributed loads, the self-weight of the bent cap, which is idealized as a point load located at the midspan and the self-weight of the column, which is idealized as a uniform distributed load along the length of the column acting in the direction of gravity. This can be seen in Figure 15 below.

Figure 15. Self-weight dead load of concrete Girder ii. Superimposed Dead load The first superimposed dead load consisted of the uniform distributed load of the asphalt, which has a unit weight A=101 pcf. This design load is shown in Figure 16. The second superimposed dead load is a uniform distributed load due to the weight of the handrail shown below in Figure 17


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Figure 16. Uniform distributed Asphalt dead load

Figure 17. Uniform distributed Handrail dead load iii. Live load The applied live load is 1333 lb/ft that can act anywhere on the entire deck. Section 4. Structural Analysis 4.a. Slab i. Model Figure 18 below shows the simplified model used for SAP analysis.

Figure 18. Model of Simplified Slab/Deck used for SAP analysis

ii.Load Combinations The load cases are unfactored loads. The load cases for the slab/deck are:


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Case 1: Concrete Self Weight Only Figure 19.1 Case 2: Asphalt Weight Only Figure 19.2 Case 3: Hand Rails Weight Only Figure 19.3 Case 4: Live Load Case 1 Figure 19.4 Case 5: Live Load Case 2 Figure 19.5 Case 6: Live Load Case 3 Figure 19.6 Four load combinations are created based on factored loads in ACI 318-11 Section 9.2 using the load cases. These combinations are: Combo 1: 1.4 x (Case 1+Case 2+Case 3) Combo 2: 1.2 x (Case 1+Case 2+Case 3)+1.6 x (Case 4) Combo 3: 1.2 x (Case 1+Case 2+Case 3)+1.6 x (Case 5) Combo 4: 1.2 x (Case 1+Case 2+Case 3)+1.6 x (Case 6) Figure 19 below shows the load cases. Case 1:

Case 2:

Case 3:

Case 4:

Case 5:


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Case 6:

Figure 19. Different Load Cases (Point Load in lb and Distributed in lb/ft)

iii. Bending Moment Diagrams of Load Combinations The bending moment diagrams corresponding to the defined load combinations are shown in Figure 20. Combo 1:

Combo 2:

Combo 3:

Combo 4:

Figure 20. Bending Moment Diagrams of Each Load Combination (kip-in)

iv. Shear Force Diagrams of Load Combinations

Figure 21 shows the shear force diagrams corresponding to the load combinations. Combo 1:


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Combo 2:

Combo 3:

Combo 4:

Figure 21. Shear Force Diagrams of Each Load Combination (kip)

v. Design Envelopes The design envelope incorporates the four load combinations to show the maximum and minimum shear forces and bending moments the pedestrian bridge may experience. These values will then be used to design the deck under any of the load combinations. The design envelope for bending moment is shown in Figure 22.1 while the envelope for shear is shown in Figure 22.2. 1. Moment Envelope:

2. Shear Envelope:

Figure 22. Design Envelopes for Slab/Deck (1.Kip-in for moments)(2.Kip for shear forces)

4. b. Girder Figure 23 below shows the simplified model below used for the SAP analysis.


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Figure 23. Model of Simplified Model of Girder

ii.Load Combinations The load cases are unfactored loads. The load cases for the girder are: Case 1: Concrete Self Weight Only Figure 24.1 Case 2: Asphalt Weight Only Figure 24.2 Case 3: Hand Rails Weight Only Figure 24.3 Case 4: Live Load Case 1 Figure 24.4 Case 5: Live Load Case 2 Figure 24.5 Case 6: Live Load Case 3 Figure 24.6 Four load combinations are created based on factored loads in ACI 318-11 Section 9.2 using the load cases. These combinations are: Combo 1: 1.4 x (Case 1+Case 2+Case 3) Combo 2: 1.2 x (Case 1+Case 2+Case 3)+1.6 x (Case 4) Combo 3: 1.2 x (Case 1+Case 2+Case 3)+1.6 x (Case 5) Combo 4: 1.2 x (Case 1+Case 2+Case 3)+1.6 x (Case 6) Figure 24 below shows the different load cases.


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Case 1:

Case 2:

Case 3:


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Case 4:

Case 5:

Case 6:

Figure 24. Different Load Cases (Point Load in lb and Distributed in lb/ft) iii. Bending Moment Diagrams of Load Combinations The bending moment diagrams corresponding to the defined load combinations are shown in Figure 25.


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Combo 1:

Combo 2:


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Combo 3:

Combo 4:

Figure 25. Bending Moment Diagrams of Each Load Combination (kip-ft)


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iv. Shear Force Diagrams of Load Combinations Figure 26 shows the shear force diagrams corresponding to the load combinations. Combo 1:

Combo 2:


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Combo 3:

Combo 4:

Figure 26. Shear Diagrams of Each Load Combination (kip) v. Design Envelopes The design envelope incorporates the four load combinations to show the maximum and minimum shear forces and bending moments the pedestrian bridge may experience. These values would then be used to design the deck under any of the load combinations. The design envelope for bending moment is shown in Figure 27.1 while the envelope for shear is shown in Figure 27.2.


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1. Moment Envelope

2. Shear Envelope

Figure 27. Design Envelopes for Girder (1.Kip-ft for moments)(2.Kip for shear forces)


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5. Slab/Deck Design a. Flexural Design of Critical Sections

In the deck design, the goal is to ensure that the reinforced concrete has a ductile tension-controlled failure mode. This can be achieved by ensuring c/dt 0.375 and ensuring that a sufficient amount of tensile reinforcement is present in the section to absorb the cracking moment. The other goal of the flexural design is to provide enough concrete cover for the section. A rough design for a single layer of tensile reinforcement for the positive bending moment and a single reinforcement layer for the negative bending moment is shown in Figure 28 below.

Figure 28. Rough Design of Reinforcement (unit in inches) Equation 1 is used to determine the design tensile strength Mn for the reinforced rectangular beam under the conditions that the tensile reinforcement has yielded and when the sections extreme fiber in compression crushes at an assumed compressive strain 0.003.

When equation 1 is divided and multiplied by the effective section area b*d as shown in Figure 29, Equation 2 can be obtained. Equation 3 represents the tensile reinforcement ratio. If Equation 3 and 4 is substituted into Equation 2, the formula of the design flexural moment can be obtained in Equation 5.

Figure 29. Effective section area

Assuming a tension-controlled failure will occur when the extreme layer of tension reinforcement is t0.005 based on page 40 in ACI 318-11. Based on the derivation in Figure 30, Equation 6 can be obtained.


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Figure 30. strain profile for tension-controlled failure

By equating Equation 4 and Equation 6 and setting d=dt, Equation 7 can be derived; therefore, the maximum tensile reinforcement ratio is expressed in Equation 8.

To ensure there is enough tensile reinforcement to resist the cracking moment, the minimum reinforcement area is defined by Equation 9 based on ACI 318-11 Section 10.5.

This Equation is nearly the equivalent to: Therefore, in this design phase, the goal is to

make sure: Based on ACI 318-11. Section 7.7.1 (b), the concrete cover for #5 bars and smaller is 1 to 1.5. Table 5 below shows five analyzed reinforcement sections to check if they meet the design requirements.


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Table 5. Deck Flexural Design Section Analysis

Bar. No 5 4 4 4 4

Diameter(in) 0.625 0.5 0.5 0.5 0.5

Ab(in^2) 0.31 0.2 0.2 0.2 0.2

dt(in) 6.2 6.25 6.25 6.25 6.25

O.C. spacing (in) 6 12 6 4 3

No. bars/ft 2 1 2 3 4

As(in^2) 0.62 0.2 0.4 0.6 0.8

0.00833 0.00267 0.00533 0.008 0.0107

Mn(kip-ft) 16.0261 5.49265 10.7206 15.6838 20.3824

max 0.01808 0.01808 0.01808 0.01808 0.0181

1.2Mcr(Kip-ft) 5.69803 5.79030 5.7903 5.7903 5.7903

Check: Mn1.2Mcr yes no yes yes yes

max yes yes yes yes yes

From Section 4, the maximum negative moment of the deck is -5.09 kip-ft and the maximum positive moment is 0.484 kip-ft. While top reinforcement corresponds to negative moment, bottom reinforcement corresponds to positive moment. The optimum design should satisfy the two criteria:

For negative bending, the reinforcement should meet the cracking moment requirement, and thus has the same design as the reinforcement design for positive moment. Therefore, the finalized design is #4 @ 6 O.C. for both the upper and bottom deck reinforcements.


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b. Design for shear Since the deck is a solid one-way slab, a simplified method is used to determine the shear reinforcement required for each section and will be further explained in details in Section 6.d. There are 4 types of shear reinforcement specifications possible in total. Each is based on the relative values of Vc and Vu, where Vc is the factored concrete shear strength, and Vu is the ultimate required shear strength. Vc is calculated using Equation 10 below, which can be found in section 11.2.1.1 of ACI 318-11. is 0.75 based on 9.3.2.3 of ACI 318-11. Vu can be found from section 4 of the design envelope generated by SAP2000 model analysis. Vc of the slab is calculated to be 9.49 kips and Vu is 1.79 kips, based on the analysis. Based on these values, the section is classified as Type I because Vc/2Vu and thus no need for shear reinforcement. This case can be found in ACI 318-11 Section 11.4.6.1. The calculation of shear design can be found in Figure 31 in Appendix.

6. Girder Design The design of the girder can be split into two parts. The first part is from the left rubber bearing support to the face of the bent cap (A-B). The second part is from the face of the bent cap to the face of the right rubber bearing (B-C). For simplicity and conservatism, the design of both sections can be taken as the larger value of the two negative and positive ultimate moments. From the previous section, the larger value of positive moment is located in the right span: +Mu=1040 kip-ft and the larger value of negative moment is -Mu= -1310 kip-ft. Our design goal is to achieve a tension controlled failure mode and the design moment capacity must be greater than 1.2 times of the cracking moment. a. Flexure Design of Critical Section i. Rough Design The rough flexural design for the girder needs to verify MnMu. The area of steel needed is

, where j is 0.9, Mu is the ultimate moment, d is the distance from the extreme fiber in compression to the centroid of the tensile reinforcement, and fy is the yield stress of the steel. ii. Positive Moment (Bottom reinforcement) The calculated demand value for As is 8.025 in2 for the positive moment. We will be using 6 #11 rebars total in the double T section, which have a total steel cross-sectional area of 9.36 in2. Details of the calculation can be found in Figure 32 in the Appendix. iii. Negative Moment (Top reinforcement) The calculated demand value for As is 10.108 in2 for the negative moment. We will be using 6 #11 and 4 #9 rebars total in the double T section, which have a total steel cross-sectional area of 13.36 in2. Details of the calculation can be found in Figure 32 in the Appendix.


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iv Bar Spacing The bar spacings must meet the requirement of ACI 318-11 in section 7.6. Based on this section, the minimum clear spacing between parallel bars in a layer shall be the diameter of the rebars used, but not less than 1 in. Thus for the design clear spacing, we use 1.5 for the #11 rebars and #9 rebars, and 0.5 for #4 rebars. Figure 33 below shows the spacing layout for the positive moment reinforcement, while Figure 34 shows the spacing layout for the negative moment reinforcement. The calculations are shown in Figure 35 in the Appendix.

Figure 33. Rebar spacing layout for Positive Reinforcement (unit in inches)


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Figure 34. Rebar spacing layout for Negative Reinforcement (unit in inches) v. Effective Section Properties Based on section 8.12 in ACI 318-11 the width of slab effective as a T-beam flange should not exceed of the span length of the beam, and the effective overhanging flange width on each side of the web should be min(8* slab thickness, clear distance to the next web). The effective section properties of the double-T girder are listed in Table 6 below; the meaning of the variables are shown in Figure 36. Details of the calculation are shown in Figure 37 in the Appendix.

Table 6. Effective section properties of girder

a1(in) 64

a2(in) 13

bf(in) 93

I(in4) 2.477*105

Stop(in3) 2.301*104

Sbottom(in3) 9.815*103


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Figure 36. Variable meaning for effective section properties

vi. Design Strength Mn- and Mn+ The flexural design strength of the girder is calculated using the fiber discretization method. It was done by creating a matlab file and the script of the file is shown in the Appendix. Specifying the number of compressive fibers to be 360, we found the design strength Mn+ to be 1709.3 kip-ft and Mn- to be -1506.4 kip-ft. On the other hand, the cracking moment for positive bending was calculated to be 387.956 kip-ft and the cracking moment for negative bending is 909.434 kip-ft. Details of the calculation can be found in Figure 38 in the Appendix. The optimum design should satisfy the following two criteria:

for positive moment: MnMu_positive; Mn1.2*Mcr, for negative moment: MnMu_negative; Mn1.2*Mcr,

Check: for positive moment: 1709.3 kip-ft > 1040 kip-ft ; 1383.4 >1.2*387.956 for negative moment: 1506.4 kip-ft > 1310 kip-ft; 1506.4 kip-ft > 1.2*909.434 kip-ft. These values capacities were chosen slightly higher in order to account for any uncertainties Therefore, we will be using 6 #11 rebars for positive bending, and 6 #11 and 2 #9 rebars for negative bending with a total area of 18.13 in2.

6.b. Design of Shear Reinforcement The design for shear can be divided into different types based on the relative values Vu,Vc,n*Vc. The different types are listed below. Type I. When Vu Vc/2, no shear reinforcement is needed. Type II. When VcVu>Vc/2, minimum shear reinforcement is used to meet 11.4.6.1 of ACI 318-11:

; the stirrup set O.C. spacing is restricted by min (d/2,24 in) based on section 11.4.5.1 of ACI 318-11.


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Type III. When 3*VcVu>Vc, it is recognized as moderate shear zone. According to 11.1 and 11.2 of ACI 318-

11: Vs=(Vu -Vc)/. The stirrup spacing can be found .Similar to Type II, the spacing should be less than d/2 and 24 in (11.4.5.1 of ACI 318-11). Type IV. When 3Vc5Vc, it is identified as likely shear failure zone caused by crushing the concrete carrying shear, and this is not permitted by ACI. Therefore, the maximum permitted value for Vs is 4*Vc by ACI 318-11. The two spans are designed identically to have the capacity to support the most critical shear values. The shear design plot is shown in Figure 42 below from the face of the rubber bearing support to the face of bent cap at mid-span. Figure 39 to 41 in the Appendix show the required spacing for different types of shear design.

Figure 42. Shear Design Plot for Left Hand Span (critical section)


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Zone 1 (0 to 2 ft) The required shear reinforcement for Zone 1 is of Type I. There is no shear requirement required for this zone, but the minimum shear reinforcement to be used is 4 #4 @ 16 O.C. to match Zone 3 and 5. Zone 2 (2 to 4 ft) The required shear reinforcement for Zone 2 is of Type III.The reinforcement that will be used in this zone is 4 #4 @ 5 O.C.. Zone 3 (4 to 13 ft) The required shear reinforcement for Zone 3 is of Type II. The reinforcement is used as 4 #4 @ 16 C.C.. Zone 4 (13 to 27 ft) The required shear reinforcement for Zone 4 is of Type I. There is no shear requirement required for this zone, but the minimum shear reinforcement to be used is 4 #4 @ 16 O.C. to match Zone 3 and 5. Zone 5 (27 to 35 ft) The required shear reinforcement for Zone 5 is of Type II. The reinforcement that will be used in this zone is 4#4 @ 16 O.C.. Zone 6 (35 to 45.3 ft) The required shear reinforcement for Zone 6 is of Type III.The reinforcement that will be used in this zone is 4 #4 @ 5 O.C.. We use the shear design from the left span and mirror it to the right hand span. The final shear reinforcement design for the girder is shown as follows: 0 to 2 ft 4 #4 bars spaced at 16 inches center to center 2 to 4 ft 4 #4 bars spaced at 5 inches center to center 4 to 35 ft 4 #4 bars spaced at 16 inches center to center 35 to 45.3 ft 4 #4 bars spaced at 5 inches center to center 45.3 to 50.7 ft No Shear Reinforcement Needed Due to Bend Cap 50.7 to 61 ft 4 #4 bars spaced at 5 inches center to center 61 to 92 ft 4 #4 bars spaced at 16 inches center to center 92 to 94 ft 4 #4 bars spaced at 5 inches center to center 94 to 96 ft 4 #4 bars spaced at 16 inches center to center Below is a figure showing all of the flexural and shear reinforcement in the Girder


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Figure 43. Steel Reinforcement in the girder

7. Development of Longitudinal Reinforcement and Miscellaneous Requirements 7.a Slab Reinforcement The longitudinal bar development is designed off of the positive moment 5.81kip-in and a negative moment of 61.09kip-in i. Longitudinal Bar Development The bars used were #4 bars spaced 6 inches on center for the top and bottom longitudinal reinforcement. The longitudinal bar development for #4 bars is 19 in (rounded up from 18.97 in) The calculation may be found in Figure 44 in the Appendix. This reinforcement size and spacing is kept constant throughout the entire length of the bridge. ii. Shrinkage and Temperature The temperature and shrinkage reinforcement will be perpendicular to the flexural reinforcements. Based on ACI 318-11 Section 7.12.2, Ast0.0018*hdeck*s, where Ast is the total cross-sectional area of steel, hdeck is the height of the slab, and s is the spacing between the temperature and shrinkage reinforcements. #4 bars @ 12 O.C. were tried first and were then checked to ensure that the spacing was not more than five times of the slab thickness nor greater than 18 inches.

Check: Ab=0.2in2>12*8*0.0018 (O.K) 12


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Figure 46. Shrinkage and Temperature Reinforcement.

iii. Cross Section Sketches

Figure 47. Cross section view of deck reinforcement

7.b Girder Reinforcement The longitudinal bar development is designed off of the positive moment 1040 kip-ft and a negative moment of 1310 kip-ft i. Longitudinal Bar Development The bars used were #9 and #11 for the top longitudinal reinforcement and #11 for the bottom longitudinal reinforcement. The development length for #9 bars is 8ft (rounded up from 5.796ft) and the development length for #11 bars is 8 ft (rounded up from 7.246ft). The development length of the #9 bars was rounded up to match the development length of the #11 bars for easier constructability. The calculation may be found in Figure 44 in the Appendix. This reinforcement varies throughout the length of the girder as shown in the figures below. The length of the required flexural reinforcement was determined using ACI-318 12.10.3 and 12.2.2. Details on the calculation can be found in the Appendix Figure 49. For both the positive and negative flexural reinforcement, the cut off length was chosen from the maximum from the left and right span of the bridge. For the negative reinforcement, Bars B were chosen to be cut off. Bars B consist of 4#9 bars totaling to an area of 4 in2. The B bars were determined to be 9 ft measured from the center of the bent cap. ACI


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section 12.12.3 and 12.10.5 were used to determine these lengths. Details on the calculation can be found in the Appendix Figure 50 and 52 For the negative reinforcement, the A bars were chosen to continue through the length of the bridge. The A bars consist of 6#11 bars totaling to an area of 9.36 in2 The minimum length of Bars A are 19 ft measured from the center of the bent cap. Although the bars A are not required for flexural stability of the bar, the reinforcement continues throughout the length for the bridge in order for the installment of shear reinforcement. ACI section 12.12.3 and 12.10.5 were used to determine these lengths. Details on the calculation can be found in the Appendix Figure 51 and 53. For the positive reinforcement, Bars B were chosen to be cut off. Bars B consist of 2#11 bars totaling to an area of 3.12 in2. The B bars were determined to be 10 ft measured from the center of maximum moment which is located 18 ft measured from the simple support. ACI section 12.11.1 and 12.10.5 were used to determine these lengths. Details on the calculation can be found in the Appendix Figure 56 and 57. For the positive reinforcement, the A bars were chosen to continue through the length of the bridge. The A bars consist of 4#11 bars totaling to an area of 6.24 in2. The reinforcement continues throughout the length for the bridge in order for the installment of shear reinforcement. The ACI section 12.12.3 and 12.10.5 were used to determine these lengths. Details on the calculation can be found in the Appendix Figure 55. The positive reinforcement hook near the rubber bearing has a clear distance of 12.25 in which is larger than .5db=7.05 in. Details on the location of the hook can be found in Figure 57 in Section 9: Drawings ii Cross Section Sketches The location of the cut off reinforcement can be seen in Figure 58 below.

Figure 58. Zones within the longitudinal girder flexural reinforcement (Not to scale)

Zone 1 has 6#11 bars and 4#9 bars at the top and 4#11 bars on the bottom


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Figure 59. Girder flexural reinforcement in zone 1

Zone 1 has 6#11 bars at the top and 4#11 bars on the bottom







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8. Column Design

a. Interaction Diagram The interaction diagram shown in Figure 63 was formed using a Matlab code applying the concept of fiber discretization to reinforced concrete columns. This code can be found in the Appendix. The diameter of the column was previously defined to be 4 while the reinforcement was assumed to be composed of 12 bars. With the interaction diagram, the reinforcement ratio of the column was determined as well as the required diameter of each bars, The value of Pn is capped at:

to prevent brittle failure due to concrete crushing.

Figure 63. Interaction Diagram of Column

Each red cross represents a different Mu, Pu pair found using the load combination detailed in section 4 of the structural analysis section,


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b. Pu, Mu Combinations The load combinations can be found in Section 4 of the structural analysis section, Table 7 below shows the Pu,Mu combinations from SAP analysis.

Table 7: Pu Mu Combinations

Load Combination Location Mu(kip-ft) Pu(kip)

Combo 1 Top 525 584

Bot 1201 584

Combo 2 Top 620 621

Bot 1347 621

Combo 3 Top 671 561

Bot 1054 561

Combo 4 Top 400 560

Bot 1323 560

c. Design for Shear Based on ACI 318-11 Section 21.6.4, the plastic hinge region should be greater than the maximum of :

a. The depth of the member at the joint face or at the section where flexural yielding is likely to occur (48 in)

b. One-sixth of the clear span of the member (44 in) c. 18 in.

According to ACI 318-11 Section 21.6.4.3, the spacing of transverse reinforcement along the length l0 of the member shall not exceed the the least of:

a. of the minimum member dimension (12 in) b. 6 times the diameter of the smallest longitudinal bar (10.14 in) c. Equation 21-2 with the provision that the spacing will not exceed 6 nor be less than 4

Therefore, the spacing is determined to be 4 inches for sections within plastic hinge region. Based on 7.10.5.1, the transverse size for longitudinal size #14 should be at least #4 rebar. The spacing of the hoops within the remainder of the column will be taken as the minimum of the following criteria:

a. 16 times of the longitudinal rebar diameter (27.04 in) b. 48 times of the hoop wire diameter (24 in) c. Least Dimension of Column (48 in)


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Thus, a transverse bar spacing 27 inches will be specified for the remainder of the column. However, for the ease of construction and be conservative, the company uses a spacing of 14 inches. Table 8 summarizes the spacing of shear reinforcement of the column design. Figure 65 shows the detailing of the transverse reinforcement.

Table 8. transverse spacing of column design

Plastic Hinge Length 48

Spacing and bar size in the plastic hinge region #4 @ 4 O.C.

Remaining Bar Size and Spacing #4 @ 14 O. C.

Figure 65. Transverse spacing of column (inches)

Applying the interaction diagram shown in Figure 63, the required reinforcement ratio is found to be less than 1%, and the results using 8 #14 rebars will be sufficient. However, given the inexperience of the designers and the importance of the column for structural integrity, 10 #14 will be used for the longitudinal reinforcement of the column. This provides a new reinforcement ratio of 1.24% which more than exceed the require. Figure 64 details the column flexural reinforcement layout.


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Figure 64. Column Reinforcement Cross Section Cut (inches)

d. Longitudinal Bar Development The longitudinal bar development is based on ACI 318-11 Section 12.3.2. Based on ACI, deformed bars and deformed wire ldc should be the larger of

is defined as 1.0 based on 12.2.4 (d), db is 1.69 inches for #14. ldc is therefore determined as 33 inches. The company decides to have the longitudinal development length of the column to be 33 inches for the portions of both bent cap and pile for the ease of construction. Even though the development length is longer than the depth of the bent cap, we can leave the longitudinal bars to extend outside of the bent cap for connection purpose. Figure 66 shows the detailing for the bent cap, while Figure 67 shows the detailing for the reinforcements in the pile.

Figure 66. Bar Development into the Bent Cap(inches)


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Figure 67. Bar Development into the Pile (inches)

9. Extra Credit: Pile Design The pile of the bridge has a circular cross session with a diameter of 6, and the height of the pile is 90 ft. The company idealizes the pile as P-y spring system with the bottom joint constrained by a pin. The tributary areas are given as:

The empirical relationship for the springs is given by:

Figure 68 shows the spreadsheet used to generate the SAP model, while Figure 69 shows the generated model of the pile using SAP 2000.


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Figure 68. Excel sheet for SAP Model Figure 69. Generated SAP Model Applying the axial forces and moments in the top joint with the demand values from section 4, we can obtain the demand loads and moments with SAP 2000. We have also included the self-weight of the concrete pile in the applied axial loads. Table 9 shows the Pu, Mu combinations for the pile design. The calculation of the self weight of the pile is shown in Figure 70 in the Appendix.


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Table 9. Load Combos

Load combo Pu+concrete self weight (kip) Mu (kip-ft)

1 966 1201

2 1003 1347

3 943 1054

4 942 1323

Moment diagrams of applied P,M combinations:

Combo 1: Combo 2: Combo 3: Combo 4: The company then calculate the required ratio using the normalized P-M diagram of the column section, and normalize the demand load and moment of the pile with the section of pile:

Pu/(Agfc) Mu/(AgfcD)

Figure 71 shows the generated P-M interaction diagram, the matlab codes used to generate this plot can be found in the Appendix.


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Figure 71. P-M interaction Diagram for pile

Since the required ratio is less than 1%, the company decides to have 18 #14 rebars for the longitudinal rebars design to have 1% steel ratio. Figure 72 shows the designed cross section of the pile.

Figure 72. Pile Cross section

For the ease of construction, the spacing of transverse reinforcement of the pile is determined to be the same as the transverse reinforcement of the column in the plastic region, which is 4 inches. #5 rebars will be used for the transverse reinforcement. Figure 73 shows the detailing of the reinforcement.


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Figure 73. transverse spacing of pile

10. Drawing

Figure 55 Dimensions of Girder Flexural reinforcement


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Figure 56 Dimensions of Girder Flexural reinforcement bar cutoff

Figure 57 Details of the positive standard hook


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11. Appendix:

Figure 5. Slab section properties hand calculation


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Figure 8. Girder section properties hand calculation

Figure 11. Column&pile section properties hand calculation


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Figure 31. Shear Design of Deck

Figure 32. Rough Design Calculations to meet minimum steel area requirement


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Figure 35. Hand calculation of Bar spacing

Figure 37. Effective section properties of Girder section

Figure 38. Cracking moment calculations for positive and negative bending


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Figure 39. Girder Shear Design part I

Figure 40. Girder Shear Design part II


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Figure 41. Girder Shear Design part III


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Figure 48. Negative Girder Bar development part I


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Figure 49. Negative Girder Bar development part II


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Figure 50. Negative Girder Bar development part III

Figure 51. Negative Girder Bar development part IV


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Figure 52 Negative Girder Bar development part V


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Figure 53 Negative Girder Bar development part VI


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Figure 54 Positive Girder Bar development part I


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Figure 55 Positive Girder Bar development part II

Figure 56 Positive Girder Bar development part III


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Figure 57 Positive Girder Bar development part IV


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Figure 58 Hook Lengths

Figure 70. Pile weight Code to determine positive moment capacity using fiber discretization %Fiber Discretization Positive Moment clear, clc f_y=60; %ksi %variable f_c=4; %ksi %variable h=36; %in %variable %variable


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%step 1 %width b=zeros(1,360); i=1:1:360; %number of horizontal fibers b(1,1:round(8/h*360))=93; b(1,round(8/h*360)+1:360)=16; %variable t=h/length(i); %thickness %step 2 y_c(i)=(i-1/2)*t; a_c(i)=b(i).*t; %step 3 B=.85 - (f_c - 4) * .05; if B>=.65 B=B; else B=.65; end %step 4 n=0; error(n+1)=1; error(n+2)=1; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% while (sign(error(n+1))==sign(error(n+2))) n=n+1; a=n*t; %step 5 c=a/B; %step 6 stress and force in reinforcement n_r=1; % # of layers of reinforcement %variable E=29000; %ksi E_y=f_y/E; E_cu=-.003; phi=-E_cu / c; y_s=zeros(1,n_r); y_s(1,1:n_r)=[33.3]; %variable d_t=y_s(1); A_s=zeros(1,n_r); A_s(1,1:n_r)=[1.56*3]; %variable for i=1:n_r E_s(i) = phi * (y_s(i) - c); f_s(i) = sign(E_s(i))*min(abs(E_s(i)*E), f_y); %stress in layer i F_s(i) = A_s(i) * f_s(i); %force in layer i end %step 7 for i=1:1:360 if i


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end end %step 8 error(n+2) = sum(F_s) + sum(F_c); if sign(error(n+1))==-sign(error(n+2)) & (abs(error(n+1)) < abs(error(n+2))) n=n-1; a=n*t; %step 5 c=a/B; %step 6 stress and force in reinforcement phi=-E_cu / c; for i=1:n_r E_s(i) = phi * (y_s(i) - c); f_s(i) = sign(E_s(i))*min(abs(E_s(i)*E), f_y); %stress in layer i F_s(i) = A_s(i) * f_s(i); %force in layer i end %step 7 for i=1:1:360 if i


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Code to determine negative moment capacity using fiber discretization %Fiber Discretization Negative Moment clear, clc f_y=60; %ksi %variable f_c=4; %ksi %variable h=36; %in %variable %variable %step 1 %width b=zeros(1,360); i=1:1:360; %number of horizontal fibers b(1,1:round(28/h*360))=16; b(1,round(28/h*360)+1:360)=93; %variable t=h/length(i); %thickness %step 2 y_c(i)=(i-1/2)*t; a_c(i)=b(i).*t; %step 3 B=.85 - (f_c - 4) * .05; if B>=.65 B=B; else B=.65; end %step 4 n=0; error(n+1)=1; error(n+2)=1; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% while (sign(error(n+1))==sign(error(n+2))) n=n+1; a=n*t; %step 5 c=a/B; %step 6 stress and force in reinforcement n_r=2; % # of layers of reinforcement %variable E=29000; %ksi E_y=f_y/E; E_cu=-.003; phi=-E_cu / c; y_s=zeros(1,n_r); y_s(1,1:n_r)=[33.3,29.53]; %variable d_t=y_s(1); A_s=zeros(1,n_r); A_s(1,1:n_r)=[1.56*3,1]; %variable for i=1:n_r E_s(i) = phi * (y_s(i) - c); f_s(i) = sign(E_s(i))*min(abs(E_s(i)*E), f_y); %stress in layer i


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F_s(i) = A_s(i) * f_s(i); %force in layer i end %step 7 for i=1:1:360 if i


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end disp('Beta_1 ='), disp(B) disp('Nominal Moment Strnegth, M_n (kip-ft) ='), disp(M_n) disp('curvature * h (radians) ='), disp(phi * h) disp('c/d_t ='), disp(k) disp('E_s1/E_y^2 ='), disp(E_s(1)/E_y) disp('Phi Factor ='), disp(phi_2) disp('Phi*M_n (kip-ft)= '), disp(phi_2 * M_n) Column Fiber Discretization: fc=4;%ksi fy=60;%ksi %find beta x=0.85-(fc-4)*0.05; if x


65

phi_Mn=zeros(2,1); phi_Pn=zeros(2,1); Pn=zeros(2,1); radius=diameter/2; for i=1:n1 yc(i)=(i-0.5)*t; if i


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for i=1:2 Pn(i,1)=(sum(Fs(:,i))+sum(Fc)); ultimate=0.8*phi*(0.85*fc*(Ag-Ast)+fy*Ast); if Pn(i)>=ultimate Pn(i)=ultimate; end end for i=1:2 Mn(i)= (Fc(1:n)'*yc(1:n)'+Fs(:,i)'*ys)-Pn(i)*h/2; end Mn=Mn/12;%kip-ft; phi_Mn=phi*Mn; phi_Pn=phi*Pn; for j=1:2 phi_Mn_matrix(j,n+1)=phi_Mn(j); phi_Pn_matrix(j,n+1)=phi_Pn(j); Mn_matrix(j,n+1)=Mn(j); Pn_matrix(j,n+1)=Pn(j); end end Pn_T=Ast*fy; phi_Pn_T=0.9*Pn_T; Mn_T=[0,0]; Pn_C= -(Ast*fy+0.85*(Ag-Ast)*fc); phi_Pn_C=0.65*Pn_C; Mn_C=[0 0]; for s=1:2 phi_Pn_matrix(s,1)=phi_Pn_T(s); phi_Pn_matrix(s,0.8*n1+1)=phi_Pn_C(s); Pn_matrix(s,1)=Pn_T(s); Pn_matrix(s,0.8*n1+1)=Pn_C(s); phi_Mn_matrix(s,1)=Mn_T(s); phi_Mn_matrix(s,0.8*n1+1)=Mn_C(s); Mn_matrix(s,1)=Mn_C(s); Mn_matrix(s,0.8*n1+1)=Mn_C(s); end figure(1) plot(Mn_matrix(1,:),Pn_matrix(1,:),'b','linewidth',0.3);hold on plot(Mn_matrix(2,:),Pn_matrix(2,:),'g','linewidth',0.3) xlabel('Mn [kip-ft]') ylabel('Pn [kip]') title('Pn-Mn Interraction Diagram') legend('0.01 \rho','0.04 \rho') grid on set(gca,'Ydir','reverse') figure(2) plot(phi_Mn_matrix(1,:),phi_Pn_matrix(1,:),'b','linewidth',0.3);hold on


67

plot(phi_Mn_matrix(2,:),phi_Pn_matrix(2,:),'g','linewidth',0.3) xlabel('\phiMn [kip-ft]') ylabel('\phiPn [kip]') title('\phiPn-\phiMn Interraction Diagram') legend('0.01 \rho','0.04 \rho') Mu=[525,1201,620,1347,671,1054,400,1323]; Pu=[-584,-584,-621,-621,-561,-561,-560,-560]; scatter(Mu,Pu,'rx'); grid on set(gca,'Ydir','reverse') Pile Design Code: fc=4;%ksi fy=60;%ksi %find beta x=0.85-(fc-4)*0.05; if x


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Ag=pi*diameter^2/4; %area of the concrete rho=[0.01,0.04]'; %steel ratio Ast=Ag.*rho; %steel area Ab_guess=(Ast./nb_guess); %approx. area for each rebar db_guess=sqrt(4*Ab_guess/pi); %approximate the area as square ey=fy/29000; %steel yield strain %radial location of rebar bars=[1 2 2 2 1]; %number of bars in each layer As=zeros(5,2); t=h/n1; %thickness of each layer b=[]; yc=[]; Pn_matrix=zeros(2,0.8*n1+1); Mn_matrix=zeros(2,0.8*n1+1); phi_Pn_matrix=zeros(2,0.8*n1+1); phi_Mn_matrix=zeros(2,0.8*n1+1); Mn=zeros(2,1); phi_Mn=zeros(2,1); phi_Pn=zeros(2,1); Pn=zeros(2,1); radius=diameter/2; norm_Pu=Ag*fc; norm_Mu=Ag*fc*diameter; for i=1:n1 yc(i)=(i-0.5)*t; if i


69

Fc=zeros(n,1); for i=1:5 es(i)=0.003/c*(ys(i)-c); fs(i)=sign(es(i))*min(abs(es(i))*29000,fy); Fs(i,:)=As(i,:)*fs(i)'; end for i=1:n Fc(i)=Ac(i)*(-0.85*fc); end %determine reduction factor if c/dt>=0.6 phi=0.65; elseif c/dt0.375 phi=0.9-0.25/0.225*(c/dt-0.375); %stirrup-tie elseif c/dt=ultimate Pn(i)=ultimate; end end for i=1:2 Mn(i)= (Fc(1:n)'*yc(1:n)'+Fs(:,i)'*ys)-Pn(i)*h/2; end Pn=Pn/norm_Pu; Mn=Mn/norm_Mu; Mn=Mn/12;%kip-ft; phi_Mn=phi*Mn; phi_Pn=phi*Pn; for j=1:2 phi_Mn_matrix(j,n+1)=phi_Mn(j); phi_Pn_matrix(j,n+1)=phi_Pn(j); Mn_matrix(j,n+1)=Mn(j); Pn_matrix(j,n+1)=Pn(j); end end Pn_T=Ast*fy/norm_Pu; phi_Pn_T=0.9*Pn_T; Mn_T=[0,0]; Pn_C= -(Ast*fy+0.85*(Ag-Ast)*fc)/norm_Pu; phi_Pn_C=0.65*Pn_C; Mn_C=[0 0]; for s=1:2 phi_Pn_matrix(s,1)=phi_Pn_T(s); phi_Pn_matrix(s,0.8*n1+1)=phi_Pn_C(s);


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Pn_matrix(s,1)=Pn_T(s); Pn_matrix(s,0.8*n1+1)=Pn_C(s); phi_Mn_matrix(s,1)=Mn_T(s); phi_Mn_matrix(s,0.8*n1+1)=Mn_C(s); Mn_matrix(s,1)=Mn_C(s); Mn_matrix(s,0.8*n1+1)=Mn_C(s); end figure(1) plot(Mn_matrix(1,:),Pn_matrix(1,:),'b','linewidth',0.3);hold on plot(Mn_matrix(2,:),Pn_matrix(2,:),'g','linewidth',0.3) xlabel('normalized Mn [kip-ft]') ylabel('normalized Pn [kip]') title('normalized Pn-Mn Interraction Diagram') legend('0.01 \rho','0.04 \rho') grid on set(gca,'Ydir','reverse') figure(2) plot(phi_Mn_matrix(1,:),phi_Pn_matrix(1,:),'b','linewidth',0.3);hold on plot(phi_Mn_matrix(2,:),phi_Pn_matrix(2,:),'g','linewidth',0.3) xlabel('normalized \phiMn [kip-ft]') ylabel('\normalized phiPn [kip]') title('normalized \phiPn-\phiMn Interraction Diagram') Ag_pile=pi*72^2/4;%in^2 Norm_pile_P=Ag_pile*fc; Norm_pile_M=Ag_pile*fc*72; Mu=[1201,1347,1054,1323]; Pu=[-966,-1003,-943,-942]; Mu=Mu/Norm_pile_M; Pu=Pu/Norm_pile_P; scatter(Mu,Pu,'rx'); legend('0.01 \rho','0.04 \rho','Combos') grid on set(gca,'Ydir','reverse')


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12. Work Hours Recorded Chart

Date Wenjin Siu (hrs) Nicholas (Nikko) Sera

(hrs)

1/11/2015 1.5 1.5

1/14/2015 4

1/15/2015 2.5 2

1/16/2015 2

1/17/2015 3 3

1/18/2015 3 3

1/19/2015 3

2/16/2015 3 3

2/17/2015 2 2

2/18/2015 2 2

2/21/2015 6 6

2/22/2015 6 6

3/01/2015 4 4

3/07/2015 6 6

3/08/2015 8 8

3/11/2015 5 5

3/13/2014 6 6

3/14/2015 6 6

3/15/2015 5 6

3/16/2015 8 6

3/18/2015 6 6

Total 89 84.5

Date post:	16-Nov-2015
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