Flujo de caja

1 Data for Flexural Design : 2 Design Criterion, Loadings, Design Data (Materials) & Different Factors :

i) Design Criterion : AASHTO Load Resistance Factor Design (LRFD-USD).

ii) Type of Loads : Combined Application of AASHTO HS20 Truck, Lane & Pedestrian Loadings.

iii) Design AASHTO HS20 Truck Loading :

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

9.300N/mm through the Length of Gridge for Single and acting over a 3.000m 9.300 kN/m Wide Strip in Transverse Direction.

v) Design AASHTO Pedestrian Loading :

a) Design Pedestrian Loading is an Uniformly Distributed Load having Magnitude LL_-Pedest 0.003600 N/mm^2 of 3.600*10^-3MPa through the Length of Sidewalk on both side and acting over 3.600 kN/m^2 the total Wide of Sidewalk.

vi) Unit Weight of Different Materials in kg/m³:

(Having value of Gravitional Acceleration, g = 9.807 m/sec²)

vii) Unit Weight of Materials in kN/m³ Related to Design Forces :

a) Unit weight of Normal Concrete w_c 24.000 kN/m^3

b) Unit weight of Wearing Course w_WC 23.000 kN/m^3

c) Unit weight of Normal Water wWater-Nor. 10.000 kN/m^3

d) Unit weight of Saline Water wWater-Sali. 10.250 kN/m^3

e) Unit weight of Earth (Compected Clay/Sand/Silt) w_Eatrh 18.000 kN/m^3 viii) Strength Data related to Ultimate Strength Design( USD & AASHTO-LRFD-2004) :

a) Concrete Ultimate Compressive Strength, f^/c (Normal Concrete) f^/c 21.000 MPa ix) Conventional Resistance Factors for Ultimate Stressed Design & Construction (AASHTO LRFD-5.5.4.2.1) :

(Respective Resistance Factors are mentioned as f or b value)

a) For Flexural & Tension in Reinforced Concrete f_Flx-Rin. 0.90 b) For Flexural & Tension in Prestressed Concrete fFlx-Pres. 1.00 c) For Shear & Torsion of Normal Concrete fShear/Torsion. 0.90 d) For Axil Comression with Spirals or Ties & Seismic Zones at Extreme Limit fSpir/Tie/Seim. 0.75

Page 170

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

State (Zone 3 & 4).

viii) Dead Load Multiplier Factors for Strength Limit State Design (USD) According to AASHTO-LRFD-3.4.1;

Table 3.4.1-1&2 :

a) Dead Load Multiplier Factor for Structural Components & Attachments-DC gDC 1.250 Applicable to All Components Except Wearing Course & Utilities (Max. value

of Table 3.4.1-2)

b) Dead Load Multiplier Factor for Wearing Course & Utilities- DW , g_DW 1.500 (Max. value of Table 3.4.1-2)

c) Multiplier Factor for Horizontal Active Earth Pressure on Substructure gEH 1.500 Components of Bridge-EH ; Applicable to Abutment & Wing Walls, (Max.

value of Table 3.4.1-2)

d) Multiplier Factor for Vertical Earth Pressure on Substructure Components of g_EV 1.350 Bridge-EV ; Applicable toAbutment & Wing Walls, (Max. value of Table 3.4.1-2)

e) Multiplier Factor for Surchage Pressure on Substructure Components of g_ES 1.500 Bridge-ES ; Horizontal & Vertical Loads on Abutment & Wing Walls,

(Max. value of Table 3.4.1-2)

ix) Live Load Multiplier Factors for Strength Limit State Design (USD) According to AASHTO-LRFD-3.4.1;

Table 3.4.1-1&2 :

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

g) Multiplier Factor for Vhecular Breaking Force-BR . gLL-BR. 1.750

h) Multiplier Factor for Live Load Surcharge-LS g_LL-LS. 1.750

i) Multiplier Factor for Water Load & Stream Pressure-WA g_LL-WA. 1.000

j) Multiplier Factor for Wind Load on Structure-WS STRENGTH - III g_LL-WS. 1.400 l) Multiplier Factor for Wind Load on Live Load-WL STRENGTH - V gLL-WL 1.000 k) Multiplier Factor for Water Load & Stream Pressure-FR g_LL-FR. 1.000

l) Multiplier Factor for deformation due to Uniform Temperature Change -TU g_LL-TU. 1.000 (With Elastomeric Bearing).

m) Multiplier Factor for deformation due to Creep on Concrete-CR g_LL-CR. 1.000 (With Elastomeric Bearing).

n) Multiplier Factor for deformation due to Shrinkage of Concrete-SH gLL-SH. 1.000 (With Elastomeric Bearing).

o) Multiplier Factor for Temperature Gradient-TG g_LL-TG. 1.000 (With Elastomeric Bearing).

p) Multiplier Factor for Settlement of Concrete-SE g_LL-SE. 1.000 (With Elastomeric Bearing).

q) Multiplier Factor for Earthquake -EQ g_LL-EQ.

-r) Multiplier Factor for Vehicular Collision Force-CT g_LL-CT.

-t) Multiplier Factor for Vessel Collision Force-CV g_LL-CV. 1.000

x) Design Data for Site Conditions :

a) Velocity of Wind Load in Normal Condition V_WL-Nor. 90.000 km/hr b) Velocity of Wind Load in Cyclonic Storm Condition VWL-Spe. 260.000 km/hr c) Velocity of Water/Stream Current Causing Water/Stream Load VWA 4.200 m/s

3 Design Phenomena, Selection of T-Girder Flange Width, Girder Depth & Calculations for Monent & Shear : i) Design Phenomena :

a) The Flexural of Girders will be according to AASHTO LRFD or Ultimate Strength Design (USD) Procedures.

b) Since the Interior Girders of the Bridge have the Max. Moments & Shearing Forces caused by Applied Loads (DL

& LL), thus it is require to conduct the Flexural Design for Reinforcements of Bridge Girders Based on Calculated

Page 172

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

respective Moments & Shears. Since the Bridge Deck Slab is integral Part of Girders, thus the Design of Girders will be under T-Beam if the Provisions in these Respect Satisfy, otherwise Designee will be under Provisions for the Rectangular Beam.

c) The T-Girder will have to Provide Longitudinal Shrinkage & Temperature Reinforcement on Compression Face with a reasonable Steel Area, thus an Equivalent Additional Steel Area can also Provide on Tension Face against those Shrinkage & Temperature Reinforcement. These arrangement will provide a Higher Stiffness for the Structure within Flexural provisions.

ii) Cross Sectional Sketch Diagram of Bridge Girders & Dack Slab :

1.475

iii) Selection of T-Girder Effective Flange Width under Provisions of AASHTO-LRFD-4.6.2.6 (4.6.2.6.1) : a) Since the Bridge is a Simple Supported T-Girder Structure, thus Falnge Width will be the least Dimention of :

i) One-quarter of Effective Span Length = 1/4*SL = 6.100 m ii) 12.0 times average Depth of Slab + Greater Thickness of Web = 12*hSlab + bGir. = 2.750 m iii) One-half the Width of Girder Top Flange (It is not req. as there is no Addl. Top Flange)

iv) The average Spacing of Adjacent Beams/Girders = C/CD-Gir. = 2.000 m b) From Calculations, Average Spacing of Adjacent Beams/Girders is the b_Fl-Gir. 2.000 m

Least one, thus the Flange Width of Interior Girders, bFla-Gir = 2.000m

iv) Selection of Depth (Including Slab Depth) for T-Girder under Provisions of AASHTO-LRFD-2.5.2.6.3 & Table 2.5.2.6.3-1 :

a) Since the Bridge is a Simple Supported T-Girder Structure, thus According to Table-2.5.2.6.3-1; the Min. Required Girder Depth Including Salb Thickness is = 0.0708L; where

b) L is the Span Length, the Clear Distance between Bearing Centers of Supports L 24.400 m = SL

c) Thus required Minimum Depth of T-Girder Including Salb = 0.070*S_L h_T-Girder. 1.732 m CL

Page 173

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

d) Considering the Clear Covering both on Top & Bottom, Let Provide a Depth for h_Gir-pro. 2.000 m the T-Girder = 2.000m.

v) Calculations for Monent at Different Location of Girder :

a) From Load, Shear & Moment Calcutation Tables it appares that, the Interior Girders are facing the Max. Resultant Forces (DL & LL) causing Max. Shears & Moments, thus One of Interior Girders is considered as Typical one for the Flexural Design in respect of All Applied Loads (DL & LL) and Corresponding Moments & Shears.

b) Table for Max. Moments at Different Locations of Interior Girder due to Factored DL, Lane-LL & Wheel-LL :

Table-1. Sum. of Max. Moments Against All Applied Loads (DL & LL) on Interior Girder.

Locations from Support-A On Support 0.375m L/8 L/4 3L/8 c.g. L/2

Loading Type Unit kN-m kN-m kN-m kN-m kN-m kN-m kN-m

a. Dead Load (FDL_Int) 0.000 181.672 1,327.681 2,313.495 2,892.428 3,120.031 3,129.494 b. Lane Live Load (FLL_Int) 0.000 50.096 363.190 625.448 786.774 945.861 847.168 c. Wheel Live Load (WLL_Int) 0.000 184.676 1,312.328 2,192.069 2,639.221 2,797.457 2,653.786 Total Moments on Each Point 0.000 278.135 3,003.199 5,131.011 6,318.423 6,863.350 6,630.449

c) Moment at Sopport Position of Girder Mu-Support. 0.000 kN-m

d) Moment at a Distance 0.375m from Sopport of Girder M_u-0.375m. 278.135 kN-m

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

a) With Maximum Amount of Prestressed & Nonprestressed Reinforcement for a c/d_e-Max. 0.420 Section c/d_e  0.42 in which;

b) c is the distance from extreme Compression Fiber to the Neutral Axis in mm c Variable c) d_e is the corresponding Effective Depth from extreme Compression Fiber to d_e Variable

the Centroid of Tensial Forces in Tensial Reinforcements in mm. Here;

i) de = (Apsfpsdp + Asfyds)/(Apsfps + Asfy), where ;

ii) A_s = Steel Area of Nonprestressing Tinsion Reinforcement in mm² A_s Variable mm²

iii) A_ps = Area of Prestressing Steel in mm² A_ps Variable mm²

iv) fy = Yeiled Strength of Nonprestressing Tension Bar in MPa. fy N/mm² vi) fps = Average Strength of Prestressing Steel in MPa. fps Variable N/mm² xi) d_p = Distance of Extreme Compression Fiber from Prestressing Tendon d_p Variable mm Centroid in mm.

xii) ds = Distance of Centroid of Nonprestressed Tensial Reinforcement from ds Variable mm the Extreme Compression Fiber in mm.

d) For a Structure having only Nonprestressed Tensial Reinforcement the values of A_ps, f_ps & d_p are = 0. Thus Equation for value of de stands to d_e = A_sf_yd_s/A_sf_y &

thus de = ds .

vii) Limits For Manimum Reinforcement, (AASHTO-LRFD-5.7.3.3.2) :

a) For Section of a Flexural Component having both Prestressed & Nonprestressed Tensile Reinforcements should have Minimum Resisting Moment Mr  1.2*M_cr or 1.33 Times the Calculated Factored Moment for the Section Based on AASHTO-LRFD-3.4.1-Table-3.4.1-1, which one is less.For Compnents having Nonprestressed Tensile Reinforcements only Mr = 1.2Mcr.

b) The Cracking Moment of a Section M_cr = S_c(f_r + f_cpe) - M_dnc(S_c/S_nc - 1)  S_cf_r M_cr Variable N-mm where;

i) f_cpe = Compressive Stress in Concrete due to effective Prestress Forces only f_cpe - N/mm² at Extreme Fiber where Tensile Stress is caused by Externally Applied Forces

after allowance for all Prestressing Losses in MPa. For Nonprestressing RCC Components value of f_cpe = 0.

ii) M_dnc = Total Unfactored Dead Load Moment acting on the Monolithic or M_dnc 2,449.720 N-mm Noncomposite Section in N-mm.

iii) S_c = Section Modulus for the Extreme Fiber of the Composite Section where S_c Variable mm³ Tensile Stress Caused by Externally Applied Loads in mm³.

iv) S_nc = Section Modulus of Extreme Fiber of the Monolithic or Noncomposite S_nc 233333333 mm³ Section where Tensile Stress Caused by Externally Applied Loads in mm³. 0.233333 m³ For the Rectangular RCC Girder Section value of Snc = (bWebhGir

3/12)/(hGit/2) 233.333/10^3 m³ v) fr = Modulus of Rupture of Concrete in RCC in Mpa,(AASHTO LRFD-5.4.2.6). fr 2.887 N/mm² c) For Nonprestressing & Monolithic or Noncomposite Beam or Elements, Mcr 673638627.159 N-mm

Page 175

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

S_c = S_nc & f_cpe = 0, thus Equation for Cracking Moment Stands to M_cr = S_ncf_r 673.639 kN-m d) Thus Calculated value of Mcr according to respective values of Equation Mcr-1 Variable N-mm

e) The value of Mcr = Scfr Mcr-2 Variable N-mm

f) Cpoputed value of M_cr = 1.33*M_Ext Factored Moment due to External Forces M_cr-3 Variable N-mm g) Table-3 Showing Allowable Resistance Moment M_r for requirment of Minimum Reinforcement at Different Sections

Location of Value of Value of Actuat Acceptable 1.2 Times M 1.33 Times M_r Maximum Section Unfactored M_cr-1 Cracking M_cr of M_cr Factored ^{of M,} Allowable Flexural

from Dead Load As per Moment Cracking Cracking Moment Factored Min. Moment Moment Support Moment Equation Value Moment Moment of Section Moment for RCC M_u

M_DL-UF 5.7.3.3.2-1 S_ncf_r (M_cr-1S_ncf_r) (1.2*M_cr) M (1.33*M) 1.2Mcr (M  M_r)

kN-m kN-m kN-m kN-m kN-m kN-m kN-m kN-m kN-m

At Support 0.000 673.639 673.639 673.639 808.366 0.000 0.000 808.366 808.366

At L0.375m 142.152 673.639 673.639 673.639 808.366 278.135 369.920 808.366 808.366

At L/8 1039.048 673.639 673.639 673.639 808.366 3003.199 3994.255 808.366 3003.199 At L/4 1811.021 673.639 673.639 673.639 808.366 5131.011 6824.245 808.366 5131.011 At 3L/8 2263.908 673.639 673.639 673.639 808.366 6318.423 8403.503 808.366 6318.423 At c.g/L/2 2449.720 673.639 673.639 673.639 808.366 6863.350 9128.255 808.366 6863.350

viii) Flexural Design of Main Girder with Max, Moment value (At c.g. Position) :

a) The Absolute Max. Moments on Interior Girder is at c.g. Point. Since it is very M_U 6,863.350 kN-M close to Middle Position of Span having value M_U.= 6863.350*10^6 N-mm, thus 6863.350*10^6 N-mm this value is Considerd as the Moment at Middle Position of Span.

b) Let the Clear Cover at Bottom Surface of Girder, C-Cov.Bot. = 50mm, C-Cov-Bot. 50 mm Let the Clear Cover at Top of Girder, C-Cov.Top = 50mm, C-Cov-Top. 50 mm Let the Clear Cover at Vertical Faces of Girder, C_-Cov.Vert. =38mm, C-Cov-Side. 38 mm

c) Let the Main Reinforcements are 32f Bars in 4 Layers, DBar 32 mm

d) X-Sectional Area of Main Reinforcements Af = p*D_Bar²/4mm² A_f-32 804.248 mm² e) The Vertical Spacing between Reinforcement Bars, s_Ver. = 32 mm s_Ver. 32 mm

f) Let the Transverse/Shear Reinforcements (Stirrups) are of 12f Bars, DStir. 12 mm g) Let Assume Main Tensile Reinforcements are being placed in 4 Layers each dasu-L/2 1,826.000 mm

having Equal nos. of Bars, thus the Effective Depth of Reinforcements from Top of Girder up to the Centroid of Assumed Group of Reinforcements

= (hGir - C-Cov-Bot -DStri -2*DBar - 1.5*sVer.)

h) Balanced Steel Ratio for Grider Section according to AASHTO-1996-8.16.2.2 r_b. 0.022

Page 176

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

r_b. = (0.85*0.85*(f^/_c/f_y)*(599.843/(599.843+f_y))

i) Max. Steel Ratio, r_Max = 0.75*r_b. (AASHTO-1996-8.16.2.1) r_Max 0.0165

ix) Checking's Whether the Bridge Girder would Designed as T-Beam or Rectangular Beam Provisions : a) According to Ultimate Stressed Design Provisions a Rectangular having Flange with Reasonable Thickness on its

Top should be Designed as T-Beam if Depth of Equivalent Compression Block 'a' is Less than Flange Thickness

b) Let Consider the T-Girder will behave as Rectangular Beam for which the Total Flange Width-'b' will be the Width of Rectangular Beam.

c) For a Rectangular Section having Assumed Effective Depth d_acu; Beam Width a 108.509 mm b and the Calculated Max. Factored Ultimate Moment (Absolute Moment) MU; a<hFln

the value Equivalent Compression Block a = de(1 - (1 - 2MU/0.85f^/cbde 2)^1/2)

d) Since the Calculated value of Equivalent Compression Block a < hFln; the thickness of Girder Flange, thus Flexural Design of T-Girder will as a Rectangular Beam Provisions.

4 Flexural Design for Provisions of Tensile Reinforcements at Different Section of Bridge Girder :

i) Provision of Tensile Reinforcements at Central Section at L/2 from Support (Mid Span) against Calculated Moments :

a) The Calculated Factored Max. Moment at Central Section is being Considered M_Cent. 6863.350 kN-m the Factored Moment at Absolute Moment Position which is also Greater than 6863.650*10^6 N-m the Required Minimum Moment M_r, thus M_Cent. is the Governing Moment in Mr. 808.366 kN-m Flexural Designe for the Central (Mid) Section of Girder. 808.366*10^6 N-m

b) Since the Calculated Factored Moment MCent. is the Governing Moment for the MU 6,863.35 kN-m Flexural Design, thus it is also the Uiltimate Design Moment MU. 6863.650*10^6 N-m

c) With MU, Design Moment; b, Width of Rectangular Beam; dasu-L/2, Assumed As-req.-L/2 10,498.045 mm² Effective Depth for the Section & 'a' Calculated Equivalent Compression Block

against Factored Moment for the Section, the Required Tensile Steel Area for the Section; As = MU/[ff_y(dasu-L/2 - a/2)]

d) Number of 32f bers required = As-req-Total/A_f-32 N_Bar-req 13.053 nos.

e) Let Provide 18nos 32f bars in 5 (Five) Layers having 4 nos. of Bars on each of N_Bar-pro. 18 nos the Bottom 4-Layers & 2 nos on Top Layer.

f) Provided Steel Area for the Section with 20 nos. 32f bars = N_bar-pro*A_f A_s-pro 14,476.459 mm²

g) With provided arrangement of Reinforcement Bars & Steel Area for the Section de-pro 1,808.222 mm the Actual Effective Depth of Tensile Reinforcement's Centroid from the Extreme

Fiber of Compression Face = {4*Asf-32*(hGir - CCov-Bot -DStir.-DBar/2)

Page 177

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

+ 4*Asf-32(hGir-CCov-Botr-DStir.-DBar-sVer.-DBar/2) +4*Asf-32(hGir-CCov-Bot-DStir.-2*DBar-2*sVer.-DBar/2)

+ 4*A_sf-32(h_Gir-C_Cov-Bot-D_Stir.-3*D_Bar-3*s_Ver.-D_Bar/2)+2*A_sf-32(h_Gir-C_Cov-Bot-D_Stir.-4*D_Bar-4*s_Ver.-D_Bar/2)}/A_s-pro

h) Value of Equivalent Compression Block 'a' against Provided Steel Area for apro 166.256 mm Rectangular Section of Girder = A_s-pro*f_y/(0.85*f^/_c*b) a<hFln Satisfied

i) The Developed Resisting Moment against provided Steel Area for the Section, MResis 10239.034 kN-m

= A_s-pro*f_y(d_e-pro - a_pro/2)/10⁶ Mr>Mu Satisfied

j) Steel Ratio against Provided Steel Area for the GirderSection = As-pro./b*de-pro r_pro 0.004

p-pro<p-max Satisfied

k)Since against Provided Steel Area; i) the Equivalent Compression Block 'a'< hFln, Thickness of Girder Flange; ii) the Developed Resisting Moment M_Resis > M_U, the Design Moment & iii) the Provided Steel Ratio p_pro < p_Max. Allowable Max. Steel Ratio; thus the Provision & Flexural Design for Tensile Reinforcement for Central Section is OK.

ii) Checking according to Provisions of AASHTO-LRFD-5.7.3.3.1 :

f) Relation between c/de-Max. & c/de-pro (Whether c/de-pro< c/de-Max. or Not) c/de-pro<c/de-max. OK iii) Provision of Tensile Reinforcements at Section 3L/4 from Support against Calculated Moments:

a) The Calculated Factored Moment a Section 3L/8 from Support is being Greater M_3L/8. 6318.423 kN-m than the Required Minimum Moment M_r, thus the Calculated Factored Moment. 6318.423*10^6 N-m

M3L/8. is the Governing Moment in Flexural Designe for the Section 3L/8. 808.366 kN-m

808.366*10^6 N-m

b) Since the Calculated Factored Moment M3L/8. is the Governing Moment for the MU 6318.423 kN-m Flexural Design, thus it is also the Uiltimate Design Moment MU. 6318.423*10^6 N-m

c) With MU, Design Moment; b, Width of Rectangular Beam; dasu-L/2, Assumed As-req.-3L/8 9,664.537 mm² Effective Depth for the Section & 'a' Calculated Equivalent Compression Block

against Factored Moment for the Section L/2, the Required Tensile Steel Area for the Section at 3L/8; As = MU/[ff_y(dasu-L/2 - a/2)]

d) Number of 32f bers required = As-req-Total/A_f-32 N_Bar-req 12.017 nos.

e) Let Provide 18nos 32f bars in 5 (Five) Layers having 4 nos. of Bars on each of N_Bar-pro. 20 nos

Page 178

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

the Bottom 4-Layers & 2 nos on Top Layer.

f) Provided Steel Area for the Section with 16nos. 32f bars = N_bar-pro*A_f A_s-pro 16,084.954 mm²

g) With provided arrangement of Reinforcement Bars & Steel Area for the Section de-pro 1,794.000 mm the Actual Effective Depth of Tensile Reinforcement's Centroid from the Extreme

Fiber of Compression Face = {4*A_sf-32*(h_Gir - C_Cov-Bot -D_Stir.-D_Bar/2)

+ 4*A_sf-32(h_Gir-C_Cov-Botr-D_Stir.-D_Bar-s_Ver.-D_Bar/2) +4*A_sf-32(h_Gir-C_Cov-Bot-D_Stir.-2*D_Bar-2*s_Ver.-D_Bar/2)

+ 4*A_sf-32(hGir-CCov-Bot-DStir.-3*DBar-3*sVer.-DBar/2)+2*A_sf-32(hGir-CCov-Bot-DStir.-4*DBar-4*sVer.-DBar/2)}/As-pro

h) Value of Equivalent Compression Block 'a' against Provided Steel Area for a_pro 184.729 mm Rectangular Section of Girder = As-pro*fy/(0.85*f^/c*b) a<hFln Satisfied

i) The Developed Resisting Moment against provided Steel Area for the Section, M_Resis 11221.998 kN-m

= A_s-pro*f_y(d_e-pro - a_pro/2)/10⁶ Mr>Mu Satisfied

j) Steel Ratio against Provided Steel Area for the GirderSection = A_s-pro./b*d_e-pro r_pro 0.004

p-pro<p-max Satisfied

k)Since against Provided Steel Area; i) the Equivalent Compression Block 'a'< h_Fln, Thickness of Girder Flange; ii) the Developed Resisting Moment MResis > MU, the Design Moment & iii) the Provided Steel Ratio ppro < pMax. Allowable Max. Steel Ratio; thus the Provision & Flexural Design for Tensile Reinforcement for Section at 3L/8 is OK.

iv) Provision of Tensile Reinforcements at Central Section at L/4 from Support against Calculated Moments : a) The Calculated Factored Moment a Section L/4 from Support is being Greater ML/4. 5131.011 kN-m

than the Required Minimum Moment M_r, thus the Calculated Factored Moment. 5131.011*10^6 N-m M_L/4. is the Governing Moment in Flexural Designe for the Section L/4. 808.366 kN-m

808.366*10^6 N-m

b) Since the Calculated Factored Moment M3L/8. is the Governing Moment for the MU 5,131.011 kN-m Flexural Design, thus it is also the Uiltimate Design Moment MU. 5131.011*10^6 N-m

c) With M_U, Design Moment; b, Width of Rectangular Beam; d_asu-L/2, Assumed As-req.-L/4 7,848.29 mm² Effective Depth for the Section & 'a' Calculated Equivalent Compression Block

against Factored Moment for the Section L/2, the Required Tensile Steel Area for the Section at L/4; As = MU/[ffy(dasu-L/2 - a/2)]

d) Number of 32f bers required = As-req-Total/A_f-32 N_Bar-req 9.759 nos.

e) Let Provide 14nos 32f bars in 4(Four) Layers having 4 nos. of Bars on each of NBar-pro. 14 nos Bottom 3-Layers & 2 nos on Top Layer.

f) Provided Steel Area for the Section with 14nos. 32f bars = N_bar-pro*A_f A_s-pro 11,259.468 mm²

g) With provided arrangement of Reinforcement Bars & Steel Area for the Section de-pro 1,851.714 mm the Actual Effective Depth of Tensile Reinforcement's Centroid from the Extreme

Page 179

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Fiber of Compression Face = {4*Asf-32*(hGir - CCov-Bot -DStir.-DBar/2)

+ 4*A_sf-32(h_Gir-C_Cov-Botr-D_Stir.-D_Bar-s_Ver.-D_Bar/2) +4*A_sf-32(h_Gir-C_Cov-Bot-D_Stir.-2*D_Bar-2*s_Ver.-D_Bar/2) + 2*A_sf-32(h_Gir-C_Cov-Bot-D_Stir.-3*D_Bar-3*s_Ver.-D_Bar/2))}/A_s-pro

h) Value of Equivalent Compression Block 'a' against Provided Steel Area for a_pro 21.266 mm Rectangular Section of Girder = A_s-pro*f_y/(0.85*f^/_c*b) a<hFln Satisfied

i) The Developed Resisting Moment against provided Steel Area for the Section, MResis 8499.134 kN-m

= A_s-pro*f_y(d_e-pro - a_pro/2)/10⁶ Mr>Mu Satisfied

j) Steel Ratio against Provided Steel Area for the GirderSection = As-pro./b*de-pro r_pro 0.003

p-pro<p-max Satisfied

k)Since against Provided Steel Area; i) the Equivalent Compression Block 'a'< h_Fln, Thickness of Girder Flange; ii) the Developed Resisting Moment M_Resis > M_U, the Design Moment & iii) the Provided Steel Ratio p_pro < p_Max. Allowable Max. Steel Ratio; thus the Provision & Flexural Design for Tensile Reinforcement for Section at L/4 is OK.

v) Provision of Tensile Reinforcements at Section L/8 from Support against Calculated Moments :

a) The Calculated Factored Moment a Section L/8 from Support is being Less ML/8 3003.199 kN-m than the Required Minimum Moment Mr, thus the Required Minimum Momen 3003.199*10^6 N-m Mr. is the Governing Moment in Flexural Designe for the Section L/8. 808.366 kN-m

808.366*10^6 N-m

b) Since the Calculated Factored Moment M3L/8. is the Governing Moment for the M_U 3,003.199 kN-m Flexural Design, thus it is also the Uiltimate Design Moment M_U. 3003.199*10^6 N-m

c) With M_U, Design Moment; b, Width of Rectangular Beam; d_asu-L/2, Assumed As-req.-L/8 4,593.635 mm² Effective Depth for the Section & 'a' Calculated Equivalent Compression Block

against Factored Moment for the Section L/2, the Required Tensile Steel Area for the Section at L/8 ; A_s = M_U/[ff_y(d_asu-L/2 - a/2)]

d) Number of 32f bers required = As-req-Total/Af-32 NBar-req 5.712 nos.

e) Let Provide 10 nos 32f bars in 3 (Three) Layers having 4 nos. of Bars on each NBar-pro. 10 nos

e) Let Provide 10 nos 32f bars in 3 (Three) Layers having 4 nos. of Bars on each NBar-pro. 10 nos

In document UNIVERSIDAD NACIONAL DE PIURA (página 101-110)