Design Data, Factors & Methods for Analysis of Flexural Design of Structural Elements:

AASHTO-LRFD-3.8.1.2.3)

D. Design Data, Factors & Methods for Analysis of Flexural Design of Structural Elements:

1 General Data for Construction Materials of Different Structural Components :

Description Notation Dimensions Unit.

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

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

ii) Unit Weight of Different Materials in kN/m³:

a) Unit weight of Normal Concrete wc 24.000 kN/m³

b) Unit weight of Wearing Course w_WC 23.000 kN/m³

c) Unit weight of Normal Water w_W-Nor. 10.000 kN/m³

d) Unit weight of Saline Water w_W-Sali. 10.250 kN/m³

e) Unit weight of Earth (Compected Clay/Sand/Silt) wE 18.000 kN/m³ iii) 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 iv) Strength Data related to Working Stress Design & Service Load Condition ( WSD & AASHTO-SLS ) :

a) Modular Ratio, n = Es/Ec  6 = 8.384 Say n 8 b) Value of Ratio of Steel & Concrete Flexural Strength, r = fs/fc r 19.524

c) Value of k = n/(n + r) k 0.291

d) Value of j = 1 - k/3 j 0.903

e) Value of R = 0.5*(fckj) R 1.102

v) Design Data for Resistance Factors for Conventional Construction (AASHTO LRFD-5.5.4.2.1). :

(Respective Resistance Factors are mentioned as f )

Flexural value of f of Compression Member will Increase Linearly as the Factored Axil Load Resitance, fP_n, Decreases from 0.10f^/_cA_g to 0.

Resistance Factor f = 0.90 + 0.10*(PPR) in which,

PPR = Apsfpy/(Apsfpy + Asfy), where; PPR is Partial Prestress Retio. PPR

As = Steel Area of Nonprestressing Tinsion Reinforcement in mm² As mm²

A_ps = Steel Area of Prestressing Steel mm² A_ps mm²

f_y = Yeiled Strength of Nonprestressing Bar in MPa. f_y 410.00 N/mm²

fpy = Yeiled Strength of Prestressing Steel in MPa. fpy N/mm²

vi)b Factors for Conventional RCC & Prestressed Concrete Design (AASHTO LRFD-5.7.2.2). :

a) Flexural value of b₁, the Factor of Compression Block in Reinforced Concrete b₁ 0.85 up to 28 MPa.

i) For Further increases of Strength of Concrete after 28 MPa agaunst each 7MPa the value of b₁ will decrese by 0.05 & the Minimum Value of b₁ will be 0.65.

ii) For Composite Concrete Structure, b_1avg = Σ(f^/cA_ccb₁)/Σ(f^/cA_cc); where, Acc =Area of Concrete Element in Compression of Crresponding Strength.

b) Value of b for Flexural Tension of Reinforcement in Concrete b 0.85

vii) Ultimate Strength Data for Design of Prestressing Components ( USD & AASHTO-LRFD-2004) : a) For Uncoated & Stress-relieved 7 (Seven) Wire according to AASHTO-LRFD Bridge Construction

Specifications (AASHTO-LRFD-5.4.4) will be;

f) Yield Strength for Strand with Grade 250 having Diameter 6.35 to 15.24mm, fpy-250-Str. 1,466 Mpa

2 Different Load Multiplying Fatcors for Strength Limit State Design (USD) & Load Combination : i) Formula for Load Factors & Selection of Load Combination :

a) Formula for Load Factors Q = Σ ηig_iQ_i  f R_n = R_r; (ASSHTO LRFD-1.3.2.1-1 & 3.4.1-1) Where, η_i is Load Modifier having values

η_i = η_Dη_Rη_I  0.95 in which for Loads a Maximum value of g_iApplicable; (ASSHTO LRFD-1.3.2.1-2), &

η_i = 1/(η_Dη_Rη_I)  1.00 in which for Loads a Minimum value of g_i Allpicable; (ASSHTO LRFD-1.3.2.1-3) Here:

g_i = Load Factor; a statistically based multiplier Applied to Force Effect,

f = Resistance Factor; a statistically based multiplier Applied to Nominal Resitance, ηi = Load Modifier; a Factor related to Ductility, Redundancy and Operational Functions, For Strength Limit State;

ii) Permanent & 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 g_DC 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 , gDW 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 gES 1.500 Bridge-ES ; Horizontal & Vertical Loads on Abutment & Wing Walls,

(Max. value of Table 3.4.1-2)

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

Table 3.4.1-1&2 :

a) Multiplier Factor for Multiple Presence of Live Load ( No of Lane = 2)-m m 1.000 (ASSHTO LRFD-3.6.1.1.1)

b) Multiplier Factor for Truck Loading (HS20 only)-LL-Truck . g_LL-Truck 1.750

c) Multiplier Factor for Vhecular Dynamic Load Allowence-IM as per Provision of IM 1.330 ASSHTO LRFD-3.6.2.1, Table 3.6.2.1-1;

(Applicable only for Truck Loading & Tandem Loading)

d) Multiplier Factor for Lane Loading-LL-Lane gLL-Lane 1.750

e) Multiplier Factor for Pedestrian Loading-PL. g_LL-PL. 1.750

f) Multiplier Factor for Vehicular Centrifugal Force-CE g_LL-CE. 1.750

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

h) Multiplier Factor for Live Load Surcharge-LS gLL-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 g_LL-WL 1.000 k) Multiplier Factor for Water Load & Stream Pressure-FR gLL-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 gLL-CR. 1.000 (With Elastomeric Bearing).

n) Multiplier Factor for deformation due to Shrinkage of Concrete-SH g_LL-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 gLL-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

3 Different Load Multiplying Fatcors for Service Limit State Design (WSD) & Load Combination :

i) Permanent & Dead Load Multiplier Factors for Service Limit State Design (WSD) According to AASHTO-LRFD-3.4.1 ; Table 3.4.1-1&2 :

a) Dead Load Multiplier Factor for Structural Components & Attachments-DC g_DC 1.000 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 1.000 (Max. value of Table 3.4.1-2)

c) Multiplier Factor for Horizontal Active Earth Pressure on Substructure g_EH 1.000 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 gEV 1.000 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 1.000 Bridge-ES ; Horizontal & Vertical Loads on Abutment & Wing Walls,

(Max. value of Table 3.4.1-2)

ii) Live Load Multiplier Factors for Service Limit State Design (WSD) According to AASHTO-LRFD-3.4.1;

Table 3.4.1-1&2 :

a) Multiplier Factor for Multiple Presence of Live Load ( No of Lane = 2)-m m 1.000 (ASSHTO LRFD-3.6.1.1.1)

b) Multiplier Factor for Truck Loading (HS20 only)-LL-Truck . g_LL-Truck 1.000

c) Multiplier Factor for Vhecular Dynamic Load Allowence-IM as per Provision of IM 1.000 ASSHTO LRFD-3.6.2.1, Table 3.6.2.1-1 (SERVICE - I);

(Applicable only for Truck Loading & Tandem Loading)

d) Multiplier Factor for Lane Loading-LL-Lane g_LL-Lane 1.000

e) Multiplier Factor for Pedestrian Loading-PL. g_LL-PL. 1.000

f) Multiplier Factor for Vehicular Centrifugal Force-CE SERVICE - II gLL-CE. 1.300 g) Multiplier Factor for Vhecular Breaking Force-BR . SERVICE - II g_LL-BR. 1.300 h) Multiplier Factor for Live Load Surcharge-LS g_LL-LS. 1.000

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

j) Multiplier Factor for Wind Load on Structure-WS SERVICE - IV gLL-WS. 0.700 l) Multiplier Factor for Wind Load on Live Load-WL SERVICE - II g_LL-WL 1.300 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 g_LL-SH. 1.000 (With Elastomeric Bearing).

o) Multiplier Factor for Temperature Gradient-TG gLL-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 gLL-CV. 1.000

3 Intensity of Different Imposed Loads (DL & LL) & Load Coefficients : i) Coefficient for Lateral Earth Pressure (EH) :

a) Coefficient of Active Horizontal Earth Pressure, ko = (1-sinf_f ) ,Where; ko 0.441 f is Effective Friction Angle of Soil

b) For Back Filling with Clean fine sand, Silty or clayey fine to medium sand f 34.000 ^O

Effective Friction Angle of Soil, f = 34⁰ .(Table 12.9, Page-138, RAINA,s Book)

c) Angle of Friction with Concrete surface & Soli d 19 to 24 ^O

AASHTO-LRFD-3.11.5.3 ;Table 3.11.5.3-1.

d) Value of Tan d (dim) for Coefficient of Friction. Tan d 0.34 to 0.45 dim = 0.34 to 0.45 (AASHTO-LRFD-3.11.5.3 ;Table 3.11.5.3-1.)

ii) Dead Load Surcharge Lateral/Horizontal Pressure Intensity (ES); AASHTO-LRFD-3.11.6.1. :

a) Constant Horizontal Earth Pressur due to Uniform Surcharge, D_p-ES 0.007935 N/mm²

D_p-ES= k_sq_sin Mpa. Where; 7.935 kN/m²

b) k_s is Coefficien of Earth Pressure due to Surcharge = k_o for Active k_s 0.441 Earth Pressure,

c) qs is Uniform Surcharge applied to upper surface of Active Earth Wedge(Mpa) qS 0.018 N/mm² = w_E*10^-3N/mm²

iii) Live Load Surcharge Vertical & Horizontal Pressure Intensity (LS); AASHTO-LRFD-3.11.6.4. :

a) Constant Earth Pressur both Vertical & Horizontal for Live Load Dp-LL-Ab<6.00m 0.007141 N/mm² Surcharge on Abutment Wall (Perpendicular to Traffic), Where; 7.141 kN/m²

D_p-LS= kg_sgh_eq*10^-9 Dp-LL-Ab6.00m 0.004761 N/mm²

4.761

kN/m²

b) Constant Horizontal Earth Pressur due to Live Load Surcharge for Dp-LL-WW<6.00m 0.008331 N/mm²

Wing Walls (Parallel to Traffic), Where; 8.331 kN/m² g) h_eq is Equivalent of Height of Abutment Wall Soil for Vehicular Load (mm). heq-Ab<6.00m. 900.000 mm

Having, H < 6000mm & for having H  6000mm ; heq-Ab6.00m. 600.000 mm AASHTO-LRFD-3.11.6.4; Table-3.11.6.4-1.

h) Width of Live Load Surcharge Pressure for Abutment having Weq-Ab<6.00m. 900.000 mm

H < 6000mm.& H  6000mm. 0.900 m

AASHTO-LRFD-3.11.6.4; Table-3.11.6.4-1. Weq-Ab6.00m. 600.000 mm

0.600 m

i) h_eq is Equivalent of Height of Abutment Wall Soil for Vehicular heq-WW<6.00m. 1050.000 mm Load (mm). Having, H < 6000mm & for having H  6000mm ; heq-WW6.00m. 600.000 mm AASHTO-LRFD-3.11.6.4; Table-3.11.6.4-2.

j) Width of Live Load Surcharge Pressure for Wing Walls, Weq-WW<6.00m. 600.000 mm

Having H < 6000mm.& H  6000mm. 0.600 m

Weq-WW6.00m. 600.000 mm

0.600 m

iv) Wind Load Intensity on Superstructure Elements (WS) :

a) Horizontal Wind Load Intensity on Vertical Fcaes of Superstructure pWind-Sup-Let. 0.000800 Mpa Elements in Lateral Direction of Wind Flow (Parallel to Traffic). 0.800 kN/m² AASHTO-LRFD-3.8.1.2.2; Table-3.8.1.2.2-1.

b) Horizontal Wind Load Intensity on Vertical Fcaes of Superstructure pWind-Sup-Long. 0.0009000 Mpa Elements in Longitudinal Direction of Wind Flow (Perpendicular to Traffic). 0.900 kN/m²

v) Wind Load Intensity on Substructure Elements (WS) :

a) Horizontal Wind Load Intensity on Vertical Fcaes of Substructure pWind-Sub-Let. 0.000950 Mpa Elements in Lateral Direction (Parallel to Traffic). = 0.0019*cos60⁰ Mpa, 0.950 kN/m² Considering 60⁰ Skew Angle of Main Force; (AASHTO-LRFD-3.8.1.2.3).

b) Horizontal Wind Load Intensity on Vertical Fcaes of Substructure pWind-Sub-Long. 0.001645 Mpa Elements in Longitudinal Direction (Perpendicular to Traffic). 1.645 kN/m² = 0.0019*sin60⁰ Mpa; Considering 60⁰ Skew Angle of Main Force;

(AASHTO-LRFD-3.8.1.2.3).

vi) Wind Load Intensity on Live Load (WL) :

a) Horizontal Wind Load Intensity on Live Load upon Superstructure pWind-LL-Sup-Let. 0.550 N/mm in Longitudinal Direction (Parallel to Traffic). = 0.550 N/mm, having 0.550 kN/m action at 1800mm above Deck & Considering 60⁰ Skew Angle of Force;

for Two Lane Bridge. (AASHTO-LRFD-3.8.1.3; Table- 3.8.1.3-1).

b) Horizontal Wind Load Intensity on Live Load upon Superstructure pWind-LL-Sup-Long. 0.500 N/mm in Lateral Direction (Perpendicular to Traffic) = 0.500N/mm having 0.500 kN/m action at 1800mm above Deck & Considering 60⁰ Skew Angle of Main

Force; for Two Lane Bridge.(AASHTO-LRFD-3.8.1.3; Table- 3.8.1.3-1).

vii) Intensity on Breaking Force (BR) :

a) Intensity of Horizontal Breaking on Superstructure is the Greater value of pLL-Sup-Break. 162.500 kN i) 25% of the Axle Weight of Design Truck/Design Tendem, or pLL-25%-Truck. 162.500 kN ii) 5% of Design (Truck + Lane Load) or (Design Tendem + Lane Load) pLL-5%-(Tru+Lane.) 55.750 kN Breaking Force is for Two Lane Bridge & its Action at 1800mm above Deck.

(AASHTO-LRFD-3.6.4).

4 Calculations of Effects due to Imposed Deformations under Strut-and-Tie Model, (AASHTO-LRFD-5.6.3) :

i) Structural Modeling (AASHTO-LRFD-5.6.3.2) : a) Factored Resistance of Strut-and-Tie, Pr = fP_{n .}

i) For Unreinforced Compressive Struts P_r-Unrin. 179928.000 N

ii) For Reinforced Compressive Struts Pr-Rin. 2488118.954 N

b) P_n = Nominal Resistance of Strut or Tie in N.

i) For Unreinforced Compressive Struts Pn-Unrin. 257040.000 N

ii) For Reinforced Compressive Struts Pn-Rin. 3554455.649 N

c)f = Tension/Compression Resistance Factor as required for the Component. f 0.70

ii) Proportioning of Strength for Unreinforced Compressive Struts, (AASHTO-LRFD-5.6.3.3.1) :

a) Nominal Resistance of Unreinforced Strut in N, P_n-Unrin.= f_cuA_cs; where, P_n-Unrin. 257040.000 N 257.040 kN

b) fcu = Limiting Compressive Stress in MPa as per AASHTO-LRFD-5.6.3.3.3. fcu. 17.850 N/mm² = f^/c/(0.8+172e _l)  0.85f^/_c, here, e _l= 0.002 mm/mm, the Pricapal

Tensile Strain of Crack Concrete due to Factored Load. Thus f^/_c/(0.8+172e _l) = 18.357 & 0.85f^/_c= 17.850

c) A_cs = Effective X-Sectional Area of Strut in mm² under the provision of A_cs. 14,400.000 mm² AASHTO-LRFD-5.6.3.3.2. For Strut Anchored by Reinforcement the Length

of Strut is 6-times the Main bar Diameter & Width is Width of Component.

For RCC Girder Diameter of Bar f_Bar= 32 mm & Width of Girder b = 450 mm. Acs = fBar*b

iii) Proportioning of Strength for Reinforced Compressive Struts, (AASHTO-LRFD-5.6.3.3.2) :

a) Nominal Resistance of Reinforced Strut in N, P_n-Rin.= f_cuA_cs+ f_yA_ss ; where, P_n-Rin. 3,554,455.649 N

v) Proportioning of Node Regions at Bearing Positions on Support, (AASHTO-LRFD-5.6.3.5.) :

a) The Compressive Stress of Node Regions Bounded by Compressive Struts fc-Node-Bearing N/mm² and Brearing Area will be, fc-Node-Bearing  0.85ff^/_c

b) The Compressive Stress of Node Regions Anchoring by a One-direction fc-Node--1-Dir-Ten-Tie N/mm² Tension Ties will be, fc-Node-1-Dir-Ten-Tie  0.75ff^/_c

c) The Compressive Stress of Node Regions Anchoring by a Two-direction fc-Node-2-Dir-Ten-Tie N/mm² Tension Ties will be, fc-Node-2-Dir-Ten-Tie  0.65ff^/_c

vi) Design AASHTO HS20 Truck Loading : over a 3.000m Wide Dcak Strip in Transverse Direction. Thus Lane Load

per meter Length of Bridge for 1 (One) Lane = (9.300*1000/1000)kN/m

b) Design Lane Loading is an Uniformly Distributed Load having Magnitude of LLLane-Int. 3.100 kN/m/m-Wd.

9.300N/mm through the Length of Gridge for Single and acting over a 3.000m 0.003100 N/mm/mm-Wd.

Wide Strip in Transverse Direction. Thus Intensity of Lane Load per meter Length & for per meter Width = 9.300/3.000kN/m/m-Wd.

viii) Design AASHTO Pedestrian Loading :

a) Design Pedestrian Loading is an Uniformly Distributed Load having Magnitude LL-Pedest 0.003600 N/mm² of 3.600*10^-3MPa through the Length of Sidewalk on both side and acting over 3.600 kN/m² the total Wide of Sidewalk.

ix) Design Live Line Loading of Sidewalk :

a) According to AASHTO-LRFD-3.6.1.3.4 Bridges having Overhanging Deck PLL-Line. 14.600 kN/m Slab Span not Exceeding 1800 mm from Center of Exterior Girder & where

Exists a Structurally Continuous Concrete Railing, there will be a Longitudinal

& Uniformly Distributed Line Live Load (LL) of Magnitude of 14.600N/mm.

Action of Line Load will be at Distance 300mm from the Face of Railing & it would Replace the Outside Row of Wheel Load. Since the Design Strip is in

Transverse Direction with 1.000m Width, thus Action on Line Load will like a Concentrated Load having Magnitude = 14.600*1000/1000kN.

4 Calculations of Respective Events for Design of Flexural And Axial Force Effects, (AASHTO-LRFD-5.6.3) : i) Stress in Prestressing Steel at Nominal Flexural Resistance for Flexural Members, (AASHTO-LRFD-5.7.3.1):

a) In Components having Bonded Prestressing Tendon in f_ps N/mm²

One Axis, the Average Stress in Prestressing Steel fps = fpu(1-k*c/dp)  0.5* fpu

In which,

i) k = 2.00*(1.04-f_ps/f_pu) k

ii) For T-Section behavior of Components, c_T-Secton mm

the value of c = (A_psf_ps+A_sf_y -A^/f^/y -0.85b₁f^/_c(b-b_w)h_f)/(0.85f^/_cb₁b_w+kA_psf_pu/d_p)

iii) For Rectangular Section behavior of Components, cRec-Secton mm

the value of c = (A_psf_ps+A_sf_y -A^/f^/y)/(0.85f^/_cb₁b+kA_psf_pu/d_p) Where,

iv) As = Steel Area of Nonprestressing Tinsion Reinforcement in mm² As mm²

v) A_ps = Steel Area of Prestressing Steel mm² A_ps mm²

vi) A^/_s = Steel Area of Nonprestressing Compression Reinforcement in mm² A^/_s mm² vii) f_y = Yeiled Strength of Nonprestressing Tension Bar in MPa. f_y N/mm² viii) fy = Yeiled Strength of Nonprestressing Tension Bar in MPa. f^/y N/mm²

ix) fpy = Yeiled Strength of Prestressing Steel in MPa. fpy N/mm²

x) b = Width of Compression Flange in mm. b mm

xi) bw = Width of Web in mm. bw mm

xii) hf = Height of Compression Flange in mm. hf mm

xiii) d_p = Distance of Extreme Compression Fiber from Prestressing Tendon Centroid d_p mm in mm.

xix) c = Distance of Neutral Axis from Compression Face of Component in mm. c mm

xx) b₁ = Compression Stress Block Factor in mm. b₁ 0.85

ii) Factored Flexural Resistance for Prestressed or RCC Elements (AASHTO-LRFD-5.7.3.2.1):

a) Factored Flexural Resistance for any Section of Component, Mr = fM_n, where; Mr N-mm

i) Mn is Nominal Resistance Moment for the Section in N-mm Mn N-mm

ii) f is Resistance Factor for Flexural in Tension of Reinforcement/Prestressing. f 0.90

b) The Nominal Resistance for a Flanged Section subject to One Axis Stress as per AASHTO-LRFD-5.7.3.2.2 is Mn = Apsfps(dp-a/2) + Asfy(ds-a/2) - A^/sf^/y(d^/s-a/2) + 0.85f^/c(b-bw)b1hf(a/2-hf/2).

Where;

i) A_s = Steel Area of Nonprestressing Tinsion Reinforcement in mm² A_s mm²

ii) Aps = Area of Prestressing Steel in mm² Aps mm²

iii) A^/s = Steel Area of Nonprestressing Compression Reinforcement in mm² A^/s mm²

iv) f_y = Yeiled Strength of Nonprestressing Tension Bar in MPa. f_y N/mm² vi) f^/_y = Yeiled Strength of Nonprestressing Tension Bar in MPa. f^/_y N/mm²

vii) fps = Average Strength of Prestressing Steel in MPa. fps N/mm²

viii) b = Width of Compression Flange in mm. b mm

ix) b_w = Width of Web in mm. b_w mm

x) hf = Depth of Compression Flange for I or T Member in mm. hf mm xi) dp = Distance of Extreme Compression Fiber from Prestressing Tendon dp mm Centroid in mm.

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

xiii) d^/_s = Distance of Centroid of Nonprestressed Compression Reinforcement d^/_s mm from the Extreme Compression Fiber in mm.

xix) b₁ = Compression Stress Block Factor in mm. b₁ 0.85

xx) a = cb_1;Depth of Equivalent Stress Block in mm. a mm

c) For Nonprestressing Element of Structure the corresponding values against Aps,fps,dp all are = 0,. Whereas for Singly Reinforced Structural Elements the Respective values of f^/_y & d^/_s = 0. Thus Equation for Nominal Resistance of I or T Member with having Flenge & Web Components Stand at M_n = A_sf_y(d_s-a/2) + 0.85f^/_c(b-b_w)b₁h_f(a/2-h_f/2)

d) For Nonprestressing Element of Structure having only Rectangular Component b = bw & hf = 0. Thus Equation for Nominal Resistance of Singly Reinforced Structural Member Stand at M_n = A_sf_y(d_s-a/2)

5 Limits For Maximum & Minimum Reinforcement, (AASHTO-LRFD-5.7.3.3) : i) Limits For Maximum Reinforcement, (AASHTO-LRFD-5.7.3.3.1) :

a) With Maximum Amount of Prestressed & Nonprestressed Reinforcement for a c/de

Section c/d_e  0.42 in which;

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

ii) As = Steel Area of Nonprestressing Tinsion Reinforcement in mm² As mm²

iii) Aps = Area of Prestressing Steel in mm² Aps mm²

iv) fy = Yeiled Strength of Nonprestressing Tension Bar in MPa. fy N/mm²

vi) f_ps = Average Strength of Prestressing Steel in MPa. f_ps N/mm²

xi) d_p = Distance of Extreme Compression Fiber from Prestressing Tendon d_p mm Centroid in mm.

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

b) For a Structure having only Nonprestressed Tensial Reinforcement the values of Aps, fps & dp are = 0. Thus Equation for value of de stands to de = Asfyds/Asfy &

thus d_e= d_s .

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

a) For Section of a Flexural Component having Prestressed & Nonprestressed Tensile Reinforcements or only with Nonprestressed Tensile Reinforcements should have Minimum Resisting Moment Mr  1.2*Mcr 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.

b) The Cracking Moment of a Section Mcr = Sc(fr + fcpe) - Mdnc(Sc/Snc - 1)  S_cfr Mcr N-mm where;

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

after allowance for all Prestressing Losses in MPa.

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

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

v) f_r = Modulus of Rupture of Concrete in RCC in Mpa,(AASHTO LRFD-5.4.2.6). f_r 2.887 N/mm² c) For Nonprestressing & Monolithic or Noncomposite Beam or Elements, M_cr N-mm

S_c = S_nc & f_cpe = 0, thus Equation for Cracking Moment Stands to M_cr = S_ncf_r

d) Thus Calculated value of M_cr according to respective values of Equation M_cr-1 N-mm

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

f) Computed value of Mcr = 1.33*MExt Factored Moment due to External Forces Mcr-3 N-mm 6 Control of Cracking By Distribution of Reinforcement, (AASHTO-LRFD-5.7.3.4) :

a) The Tensial Reinforcement of all Concrete Elements under Service Limit State f_sa N/mm² Load according to AASHTO-LRFD-3.4.1-Table-3.4.1-1 (Except Deck Slab Design

under AASHTO-LRFD-9.7.2), fsa =Z/(dcA)^1/3  0.6f_y, Where;

i) dc = Depth of Concrete Extrime Tension Face from the Center of the Closest dc mm Tension Bar considering the Max. Clear Cover = 50mm.

For a Particular Section of the Component d_c = f_Bar/2 + C_Cover-Bot. (Max. 50mm)

ii) A = Area of Concrete Surrounding a Single Tension Bar, which is Calculted by A mm² Dividing the Total Concrete Area bounded in between Extreme Tension Face &

a Straight Line parallel to Neutral Axis of Component having equal distance from the Centrioed of Main Tension Reinforcement Bars on both sideded by the total Number of Main Bars as Tensial Reinforcement (The Max. Clear Cover = 50mm.) Thus, A = 2*(C_Cover-Bot.(Max.= 50mm) + (N_B-Layers+ s_Bar-Vert)/2)/N_Bar

iii) Z = Crack Width Parameter for Cast In Place Components in N/mm. Other then Cast in Place Box Culvert;

Max. value of Crack Width Parameter for Moderate Exposure Components Z_Mode-Expo. 30,000 N/mm Max. value of Crack Width Parameter for Severe Exposure Components ZSever-Expo. 23,000 N/mm Max. value of Crack Width Parameter for Buried Components ZBuried. 17,000 N/mm iv) In Transverse Design of Segmental Concrete Box-Girder the Max. value of ZBox-Gir-Trans. 23,000 N/mm

In document ARMYBR~1 (Page 45-69)

Design Data, Factors & Methods for Analysis of Flexural Design of Structural Elements:

AASHTO-LRFD-3.8.1.2.3)

D. Design Data, Factors &amp; Methods for Analysis of Flexural Design of Structural Elements:

D. Design Data, Factors & Methods for Analysis of Flexural Design of Structural Elements: