3. rc tee beam

3. T-BEAM BRIDGE DESIGN

3.1 INTRODUCTION

The overall dimensions are illustrated in the figures below:

Figure 3.1: TypicalCross Section

Figure 3.2: Longitudinal Section

It shall be a reinforced concrete 2 lane bridge with an overall width of 12.27m and a span of 12.60m

between centreline of bearings. The bridge shall be designed to carry pedestrians on each side and the HL93

live load. Allowance should be made for a bituminous overlay of 50mm with an additional allowance of

50mm for future overlays. Strength of concrete shall be taken as 28MPa cylinder strength and reinforcement

yield strength of 500MPa.

The following example illustrates the design of a single span T-Beam Bridge Structure using the AASHTO

LRFD Bridge Design Specification 1998.

The T-Beam Bridge should be designed in accordance with the following parameters:

3.2 DESIGN ASSUMPTIONS

- Main Reinforcement is placed parallel to centerline of roadway

- The bottom of the slab is assumed parallel to the top surface

- Center to Center of support is assumed perpendicular to supports

3.3 OVERALL DIMENSIONS

No.of Girders = 5

C to C Girder Spacing = 2.4 m

Clear span Lc= 12 m

No. of spans = 1

Width of abutment= 0.6 m

Center to center of abutment perpendicular to Support S = L = 12.6 m

Total length of superstructure = 13.2 m

Clear width between barriers = 8 m

No. of Barriers = 2

Barrier width = 0.385 m

No. of Walkways = 2

Width of walkway = 1.75 m

Total width of superstructure= 12.27 m

No. of lanes = 2

Cross fall= 2 %

Skewness angle= 0 Deg.

Overhang = 1335 mm

3.4 LOAD FACTORS

3.4.1 Multiple Presence Factors1 Lane Loaded = 1.2

2 Lane Loaded = 1

4 Lane Loaded = 0.65

3.4.2 Material Resistance Factorsf_moment = 0.9

f_shear = 0.9

f_bearing = 0.7

3.4.3 Load Factors

The overall dimensions of the structure and those used in future calculation are shown listed below.

The relevant load factors for this design are as follows:

The main assumptions associated with this design can be summarised as the following:

(a) Strength I Limit State

Dead load of components = 1.25

Live load = 1.75

Wearing course = 1.5

(b) Service II Limit State

Dead load of components = 1

Live load = 1

Wearing course = 1

(c) Fatigue Limit State

Live load = 0.75

3.4.4 Impact Factor

1+IM/100 = Impact factor = 1.33 Where IM = 33%

3.4.5 Load Modifiers

FACTORS

Strength Limit State

Serviceability Limit State

3.5 LOAD COMBINATIONS

Critical load combinations are selected by inspection and are lised below:

DC-MIN

DC-

MAX DW-MIN

DW-

MAX LL

Strength 1 0.9 1.25 0.65 1.5 1.75

DC DW LL

Service 1 1 1 1

Service 2 1 1 1.3

Service 3 1 1 0.8

Fatigue 0 0 0.75

3.6 SLAB DESIGN

For the purpose of this example the deck thickness shall be taken as 220mm.

1

Ductiltiy Redundancy Importance

1

The design of the slab follows the empirical method as set out in AASHTO LRFD Section 9.7.2.2 and

illustrated in Example 1.

1 1

11

Minimum Deck Slab depth = 175 mm

Actual deck used = 220 mm

3.7 LIVE LOAD DISTRIBUTION

710 mm {Simple statics} Cg beam = 716 mm

890 mm {Simple statics} Cg slab = 890 mm

eg = 180 mm LRFD 4.6.2.2.1-1 eg = 174 mm

A = 824400 mm^2 LRFD 4.6.2.2.1-1 A = 854100 mm^2

Kg = 9.1E+10 LRFD 4.6.2.2.1-1 Kg = 9.14E+10

Kg/(Lts^3) = 0.68019 LRFD 4.6.2.2.2b Kg/(Lts^3) = 0.681079

I = 6.5E+10 mm^4 LRFD 4.6.2.2.1 I = 6.57E+10 mm^4

J = 2.3E+10 mm^3 LRFD 4.6.2.2.1 J = 2.32E+10 mm^3

I/J = 2.83871 mm LRFD 4.6.2.2.1 I/J = 2.825255 mm

Dm = 0.52335 ………. ………… Dm = 0.325

Dm = 0.325

Ds = 0.67579 ………. ………… Ds = 0.325

Ds = 0.325

Two wheel lines

Dm = 0.166667

Ds = 0.166667

Dm = 0.69148 ………. ………… Dm = 0.458352

Ds = 0.81636 ………. ………… Ds = 0.408178

Applicable Distribution Factors Applicable Distribution Factors

Dm = 0.69148 ………. ………… Dm = 0.458352

Ds = 0.81636 ………. ………… Ds = 0.408178

Internal T-Beam Dimensions

One wheel line

Multiple Lanes Loaded

Maximum Dm calculated above

Maximum Ds calculated above

AASHTO LRFD

Reference

Internal Beams

Stiffness Parameters Stiffness Parameters

External Beams

Stiffness parameters and distribution factors are calculated from the given internal and external beam

dimensions listed below. The formulas used in these calculations are located in the AASHTO LRFD

specification as indicated against each item below.

LRFD Table 4.6.2.2.2d-1 and

LRFD Table 4.6.2.2.3a-1 and

Multiple Lanes Loaded

(Both Evaluated

using lever rule)

One Lane Loaded

Cg beam =

Cg slab =

LRFD Table 4.6.2.2.2d-1 and

LRFD Table 4.6.2.2.3a-1 and

One Lane Loaded

Overall Depth D = 1000 mm

Web Depth dw = 780 mm

Web width bw = 380 mm

Flange Thickness ts = 220 mm

Flange Width fw = 2400 mm

Effective Flange Width be = 2400 mm

External T-Beam Dimensions

Overall Depth D= 1000 mm

Web Depth dw = 780 mm

Web width bw = 380 mm

Flange Thickness Internal tsi = 220 mm

Flange Thickness Overhang at beam tsob = 220 mm

Flange Thickness Overhang minimum tsoe = 180 mm

Flange Width internal fwi = 1200 mm

Flange Width overhang fwo = 1335 mm

Effective Flange Width be = 2535 mm

Dist ext web to inter barrier de = -300 mm

Actual de = -800 mm

(Note: Actual de: calculated for internal concrete barriers only)

3.8 LOADING

3.8.1 Dead Loads

Internal Girder DL = 20.907 KN /m span

Wearing surface DL ws = 6.14 KN/m /m span

Single Barrier kerb load = 3.57 KN/m span

Post & railing load = 0.392 KN/m span

External Girder DL = 20.907 KN/m span

Wearing surface DL ws = 6.14 KN/m span

Barrier kerb load = 3.57 KN/m span

Post & railing load = 0.392 KN/m span

Internal Girder SLS DL Moments and Shears / Girder

The wearing surface DL includes an allowance of 100mm AC in total.

According to AASHTO LRFD Section 4.5.1 dead load of and on the deck may be distributed equally to all

girders.

The tables which follow, contain the envelope of moments and shears of the evenly distributed permanent

loads at 20th points along the girder, for both the Serviceability Limit State and the Strength Limit State.

These have been summarised for both the internal and external girder. Each Limit State is factored in

accordance with the relevant factors outlined above.

Span

Ratio Distance Min Shear Max Shear

Min

Moment

Max

MomentkN kN kNm kNm

0.00 0.00 0.00 131.71 0.00 0.00

0.05 0.63 0.00 118.54 0.00 78.83

0.10 1.26 0.00 105.37 0.00 149.36

0.15 1.89 0.00 92.20 0.00 211.60

0.20 2.52 0.00 79.03 0.00 265.54

0.25 3.15 0.00 65.86 0.00 311.17

0.30 3.78 0.00 52.69 0.00 348.52

0.35 4.41 0.00 39.51 0.00 377.56

0.40 5.04 0.00 26.34 0.00 398.30

0.45 5.67 0.00 13.17 0.00 410.75

0.50 6.30 0.00 0.00 0.00 414.90

0.55 6.93 -13.17 0.00 0.00 410.75

0.60 7.56 -26.34 0.00 0.00 398.30

0.65 8.19 -39.51 0.00 0.00 377.56

0.70 8.82 -52.69 0.00 0.00 348.52

0.75 9.45 -65.86 0.00 0.00 311.17

0.80 10.08 -79.03 0.00 0.00 265.54

0.85 10.71 -92.20 0.00 0.00 211.60

0.90 11.34 -105.37 0.00 0.00 149.36

0.95 11.97 -118.54 0.00 0.00 78.83

1.00 12.60 -131.71 0.00 0.00 0.00

External Girder SLS DL Moments and Shears / Girder

Span


Min

Moment

Max

MomentkN kN kNm kNm

0.00 0.00 0.00 131.71 0.00 0.000.05 0.63 0.00 118.54 0.00 78.83

0.10 1.26 0.00 105.37 0.00 149.360.15 1.89 0.00 92.20 0.00 211.600.20 2.52 0.00 79.03 0.00 265.540.25 3.15 0.00 65.86 0.00 311.17

0.30 3.78 0.00 52.69 0.00 348.52

0.35 4.41 0.00 39.51 0.00 377.56

0.40 5.04 0.00 26.34 0.00 398.30

0.45 5.67 0.00 13.17 0.00 410.75

0.50 6.30 0.00 0.00 0.00 414.90

0.55 6.93 -13.17 0.00 0.00 410.75

0.60 7.56 -26.34 0.00 0.00 398.30

0.65 8.19 -39.51 0.00 0.00 377.56

0.70 8.82 -52.69 0.00 0.00 348.52

0.75 9.45 -65.86 0.00 0.00 311.17

0.80 10.08 -79.03 0.00 0.00 265.54

0.85 10.71 -92.20 0.00 0.00 211.60

0.90 11.34 -105.37 0.00 0.00 149.36

0.95 11.97 -118.54 0.00 0.00 78.83

1.00 12.60 -131.71 0.00 0.00 0.00

Internal Girder ULS DL

Moments and Shears / Girder

Span


Min

Moment

Max

Moment

kN kN kNm kNm

0.00 0.00 0.00 164.64 0.00 0.00

0.05 0.63 0.00 148.18 0.00 98.54

0.10 1.26 0.00 131.71 0.00 186.70

0.15 1.89 0.00 115.25 0.00 264.50

0.20 2.52 0.00 98.79 0.00 331.92

0.25 3.15 0.00 82.32 0.00 388.97

0.30 3.78 0.00 65.86 0.00 435.64

0.35 4.41 0.00 49.39 0.00 471.95

0.40 5.04 0.00 32.93 0.00 497.88

0.45 5.67 0.00 16.46 0.00 513.44

0.50 6.30 0.00 0.00 0.00 518.62

0.55 6.93 -16.46 0.00 0.00 513.44

0.60 7.56 -32.93 0.00 0.00 497.88

0.65 8.19 -49.39 0.00 0.00 471.95

0.70 8.82 -65.86 0.00 0.00 435.64

0.75 9.45 -82.32 0.00 0.00 388.97

0.80 10.08 -98.79 0.00 0.00 331.92

0.85 10.71 -115.25 0.00 0.00 264.50

0.90 11.34 -131.71 0.00 0.00 186.70

0.95 11.97 -148.18 0.00 0.00 98.54

1.00 12.60 -164.64 0.00 0.00 0.00

External Girder ULS DL


Span


Min

Moment

Max

Moment

kN kN kNm kNm

0.00 0.00 0.00 164.64 0.00 0.00

0.05 0.63 0.00 148.18 0.00 98.54

0.10 1.26 0.00 131.71 0.00 186.70

0.15 1.89 0.00 115.25 0.00 264.50

0.20 2.52 0.00 98.79 0.00 331.92

0.25 3.15 0.00 82.32 0.00 388.97

0.30 3.78 0.00 65.86 0.00 435.64

0.35 4.41 0.00 49.39 0.00 471.95

0.40 5.04 0.00 32.93 0.00 497.88

0.45 5.67 0.00 16.46 0.00 513.44

0.50 6.30 0.00 0.00 0.00 518.62

0.55 6.93 -16.46 0.00 0.00 513.44

0.60 7.56 -32.93 0.00 0.00 497.88

0.65 8.19 -49.39 0.00 0.00 471.95

0.70 8.82 -65.86 0.00 0.00 435.64

0.75 9.45 -82.32 0.00 0.00 388.97

0.80 10.08 -98.79 0.00 0.00 331.92

0.85 10.71 -115.25 0.00 0.00 264.50

0.90 11.34 -131.71 0.00 0.00 186.70

0.95 11.97 -148.18 0.00 0.00 98.54

1.00 12.60 -164.64 0.00 0.00 0.00

Internal Girder SLS Wearing Course DL


Span


Min

Moment

Max

Moment

kN kN kNm kNm

0.00 0.00 0.00 38.65 0.00 0.00

0.05 0.63 0.00 34.79 0.00 23.13

0.10 1.26 0.00 30.92 0.00 43.83

0.15 1.89 0.00 27.06 0.00 62.09

0.20 2.52 0.00 23.19 0.00 77.92

0.25 3.15 0.00 19.33 0.00 91.31

0.30 3.78 0.00 15.46 0.00 102.27

0.35 4.41 0.00 11.60 0.00 110.79

0.40 5.04 0.00 7.73 0.00 116.88

0.45 5.67 0.00 3.87 0.00 120.53

0.50 6.30 0.00 0.00 0.00 121.75

0.55 6.93 -3.87 0.00 0.00 120.53

0.60 7.56 -7.73 0.00 0.00 116.88

0.65 8.19 -11.60 0.00 0.00 110.79

0.70 8.82 -15.46 0.00 0.00 102.27

0.75 9.45 -19.33 0.00 0.00 91.31

0.80 10.08 -23.19 0.00 0.00 77.92

0.85 10.71 -27.06 0.00 0.00 62.09

0.90 11.34 -30.92 0.00 0.00 43.83

0.95 11.97 -34.79 0.00 0.00 23.13

1.00 12.60 -38.65 0.00 0.00 0.00

External Girder SLS Wearing Course DL


Span


Min

Moment

Max

Moment

kN kN kNm kNm

0.00 0.00 0.00 38.65 0.00 0.00

0.05 0.63 0.00 34.79 0.00 23.13

0.10 1.26 0.00 30.92 0.00 43.83

0.15 1.89 0.00 27.06 0.00 62.09

0.20 2.52 0.00 23.19 0.00 77.92

0.25 3.15 0.00 19.33 0.00 91.31

0.30 3.78 0.00 15.46 0.00 102.27

0.35 4.41 0.00 11.60 0.00 110.79

0.40 5.04 0.00 7.73 0.00 116.88

0.45 5.67 0.00 3.87 0.00 120.53

0.50 6.30 0.00 0.00 0.00 121.75

0.55 6.93 -3.87 0.00 0.00 120.53

0.60 7.56 -7.73 0.00 0.00 116.88

0.65 8.19 -11.60 0.00 0.00 110.79

0.70 8.82 -15.46 0.00 0.00 102.27

0.75 9.45 -19.33 0.00 0.00 91.31

0.80 10.08 -23.19 0.00 0.00 77.92

0.85 10.71 -27.06 0.00 0.00 62.09

0.90 11.34 -30.92 0.00 0.00 43.83

0.95 11.97 -34.79 0.00 0.00 23.13

1.00 12.60 -38.65 0.00 0.00 0.00

Internal Girder ULS Wearing Course DL


Span


Min

Moment

Max

Moment

kN kN kNm kNm

0.00 0.00 0.00 57.98 0.00 0.00

0.05 0.63 0.00 52.18 0.00 34.70

0.10 1.26 0.00 46.38 0.00 65.74

0.15 1.89 0.00 40.58 0.00 93.14

0.20 2.52 0.00 34.79 0.00 116.88

0.25 3.15 0.00 28.99 0.00 136.97

0.30 3.78 0.00 23.19 0.00 153.40

0.35 4.41 0.00 17.39 0.00 166.19

0.40 5.04 0.00 11.60 0.00 175.32

0.45 5.67 0.00 5.80 0.00 180.80

0.50 6.30 0.00 0.00 0.00 182.62

0.55 6.93 -5.80 0.00 0.00 180.80

0.60 7.56 -11.60 0.00 0.00 175.32

0.65 8.19 -17.39 0.00 0.00 166.19

0.70 8.82 -23.19 0.00 0.00 153.40

0.75 9.45 -28.99 0.00 0.00 136.97

0.80 10.08 -34.79 0.00 0.00 116.88

0.85 10.71 -40.58 0.00 0.00 93.14

0.90 11.34 -46.38 0.00 0.00 65.74

0.95 11.97 -52.18 0.00 0.00 34.70

1.00 12.60 -57.98 0.00 0.00 0.00

External Girder ULS Wearing Course DL


Span


Min

Moment

Max

Moment

kN kN kNm kNm

0.00 0.00 0.00 57.98 0.00 0.00

0.05 0.63 0.00 52.18 0.00 34.70

0.10 1.26 0.00 46.38 0.00 65.74

0.15 1.89 0.00 40.58 0.00 93.14

0.20 2.52 0.00 34.79 0.00 116.88

0.25 3.15 0.00 28.99 0.00 136.97

0.30 3.78 0.00 23.19 0.00 153.40

0.35 4.41 0.00 17.39 0.00 166.19

0.40 5.04 0.00 11.60 0.00 175.32

0.45 5.67 0.00 5.80 0.00 180.80

0.50 6.30 0.00 0.00 0.00 182.62

0.55 6.93 -5.80 0.00 0.00 180.80

0.60 7.56 -11.60 0.00 0.00 175.32

0.65 8.19 -17.39 0.00 0.00 166.19

0.70 8.82 -23.19 0.00 0.00 153.40

0.75 9.45 -28.99 0.00 0.00 136.97

0.80 10.08 -34.79 0.00 0.00 116.88

0.85 10.71 -40.58 0.00 0.00 93.14

0.90 11.34 -46.38 0.00 0.00 65.74

0.95 11.97 -52.18 0.00 0.00 34.70

1.00 12.60 -57.98 0.00 0.00 0.00


Internal Barrier Kerb Load Moments and Shears / Girder

Span


Min

Moment

Max

Moment

kN kN kNm kNm

0.00 0.00 0.00 24.97 0.00 0.00

0.05 0.63 0.00 22.48 0.00 14.95

0.10 1.26 0.00 19.98 0.00 28.32

0.15 1.89 0.00 17.48 0.00 40.12

0.20 2.52 0.00 14.98 0.00 50.35

0.25 3.15 0.00 12.49 0.00 59.00

0.30 3.78 0.00 9.99 0.00 66.08

0.35 4.41 0.00 7.49 0.00 71.59

0.40 5.04 0.00 4.99 0.00 75.52

0.45 5.67 0.00 2.50 0.00 77.88

0.50 6.30 0.00 0.00 0.00 78.67

0.55 6.93 -2.50 0.00 0.00 77.88

0.60 7.56 -4.99 0.00 0.00 75.52

0.65 8.19 -7.49 0.00 0.00 71.59

0.70 8.82 -9.99 0.00 0.00 66.08

0.75 9.45 -12.49 0.00 0.00 59.00

0.80 10.08 -14.98 0.00 0.00 50.35

0.85 10.71 -17.48 0.00 0.00 40.12

0.90 11.34 -19.98 0.00 0.00 28.32

0.95 11.97 -22.48 0.00 0.00 14.95

1.00 12.60 -24.97 0.00 0.00 0.00


Span


Min

Moment

Max

Moment

kN kN kNm kNm

0.00 0.00 0.00 24.97 0.00 0.00

0.05 0.63 0.00 22.48 0.00 14.95

0.10 1.26 0.00 19.98 0.00 28.32

0.15 1.89 0.00 17.48 0.00 40.12

0.20 2.52 0.00 14.98 0.00 50.35

0.25 3.15 0.00 12.49 0.00 59.00

0.30 3.78 0.00 9.99 0.00 66.08

0.35 4.41 0.00 7.49 0.00 71.59

0.40 5.04 0.00 4.99 0.00 75.52

0.45 5.67 0.00 2.50 0.00 77.88

0.50 6.30 0.00 0.00 0.00 78.67

0.55 6.93 -2.50 0.00 0.00 77.88

0.60 7.56 -4.99 0.00 0.00 75.52

0.65 8.19 -7.49 0.00 0.00 71.59

0.70 8.82 -9.99 0.00 0.00 66.08

0.75 9.45 -12.49 0.00 0.00 59.00

0.80 10.08 -14.98 0.00 0.00 50.35

0.85 10.71 -17.48 0.00 0.00 40.12

0.90 11.34 -19.98 0.00 0.00 28.32

0.95 11.97 -22.48 0.00 0.00 14.95

1.00 12.60 -24.97 0.00 0.00 0.00


Internal Barrier Kerb Load Moments and Shears / Girder

External Barrier Kerb Load Moments and Shears / Girder

Span


Min

Moment

Max

Moment

kN kN kNm kNm

0.00 0.00 0.00 31.22 0.00 0.00

0.05 0.63 0.00 28.09 0.00 18.68

0.10 1.26 0.00 24.97 0.00 35.40

0.15 1.89 0.00 21.85 0.00 50.15

0.20 2.52 0.00 18.73 0.00 62.93

0.25 3.15 0.00 15.61 0.00 73.75

0.30 3.78 0.00 12.49 0.00 82.60

0.35 4.41 0.00 9.36 0.00 89.48

0.40 5.04 0.00 6.24 0.00 94.40

0.45 5.67 0.00 3.12 0.00 97.35

0.50 6.30 0.00 0.00 0.00 98.33

0.55 6.93 -3.12 0.00 0.00 97.35

0.60 7.56 -6.24 0.00 0.00 94.40

0.65 8.19 -9.36 0.00 0.00 89.48

0.70 8.82 -12.49 0.00 0.00 82.60

0.75 9.45 -15.61 0.00 0.00 73.75

0.80 10.08 -18.73 0.00 0.00 62.93

0.85 10.71 -21.85 0.00 0.00 50.15

0.90 11.34 -24.97 0.00 0.00 35.40

0.95 11.97 -28.09 0.00 0.00 18.68

1.00 12.60 -31.22 0.00 0.00 0.00


Span


Min

Moment

Max

Moment

kN kN kNm kNm

0.00 0.00 0.00 31.22 0.00 0.00

0.05 0.63 0.00 28.09 0.00 18.68

0.10 1.26 0.00 24.97 0.00 35.40

0.15 1.89 0.00 21.85 0.00 50.15

0.20 2.52 0.00 18.73 0.00 62.93

0.25 3.15 0.00 15.61 0.00 73.75

0.30 3.78 0.00 12.49 0.00 82.60

0.35 4.41 0.00 9.36 0.00 89.48

0.40 5.04 0.00 6.24 0.00 94.40

0.45 5.67 0.00 3.12 0.00 97.35

0.50 6.30 0.00 0.00 0.00 98.33

0.55 6.93 -3.12 0.00 0.00 97.35

0.60 7.56 -6.24 0.00 0.00 94.40

0.65 8.19 -9.36 0.00 0.00 89.48

0.70 8.82 -12.49 0.00 0.00 82.60

0.75 9.45 -15.61 0.00 0.00 73.75

0.80 10.08 -18.73 0.00 0.00 62.93

0.85 10.71 -21.85 0.00 0.00 50.15

0.90 11.34 -24.97 0.00 0.00 35.40

0.95 11.97 -28.09 0.00 0.00 18.68

1.00 12.60 -31.22 0.00 20.00 0.00

3.8.2 Pedestrian Live Load

External Barrier Kerb Load Moments and Shears / Girder

The negative reaction in any internal girders is conservatively neglected.

Distributed pedestrian load = 0 kPa

Span


Min

Moment

Max

Moment

kN kN kNm kNm

0 0.00 0.00 0.00 0.00 0.00

0.05 0.63 0.00 0.00 0.00 0.00

0.1 1.26 0.00 0.00 0.00 0.00

0.15 1.89 0.00 0.00 0.00 0.00

0.2 2.52 0.00 0.00 0.00 0.00

0.25 3.15 0.00 0.00 0.00 0.00

0.3 3.78 0.00 0.00 0.00 0.00

0.35 4.41 0.00 0.00 0.00 0.00

0.4 5.04 0.00 0.00 0.00 0.00

0.45 5.67 0.00 0.00 0.00 0.00

0.5 6.30 0.00 0.00 0.00 0.00

0.55 6.93 0.00 0.00 0.00 0.00

0.6 7.56 0.00 0.00 0.00 0.00

0.65 8.19 0.00 0.00 0.00 0.00

0.7 8.82 0.00 0.00 0.00 0.00

0.75 9.45 0.00 0.00 0.00 0.00

0.8 10.08 0.00 0.00 0.00 0.00

0.85 10.71 0.00 0.00 0.00 0.00

0.9 11.34 0.00 0.00 0.00 0.00

0.95 11.97 0.00 0.00 0.00 0.00

1 12.60 0.00 0.00 0.00 0.00

Distributed pedestrian load = 3.60 kPa

The Tables which follow, contain the envelope of moments and shears of the distributed pedestrian loads at

20th points along the girder, for both the Serviceability limit State and the Strength Limit State. These have

been summarized for both the internal and external girder. Each Limit State is factored in accordance with

the relevant factors outlined above. The pedestrian load has been distributed in accordance with the Lever

Rule of AASHTO LFRD Section 4.6.2.2.1. Accordingly all pedestrian load is taken by the external girder.

Internal Girder SLS Pedestrian load actions per Girder

External Girder SLS Pedestrian load actions per Girder

Span


Min

Moment

Max

Moment

kN kN kNm kNm

0 0.00 0.00 34.02 0.00 0.00

0.05 0.63 0.00 30.62 0.00 20.36

0.1 1.26 0.00 27.22 0.00 38.58

0.15 1.89 0.00 23.81 0.00 54.65

0.2 2.52 0.00 20.41 0.00 68.58

0.25 3.15 0.00 17.01 0.00 80.37

0.3 3.78 0.00 13.61 0.00 90.02

0.35 4.41 0.00 10.21 0.00 97.52

0.4 5.04 0.00 6.80 0.00 102.88

0.45 5.67 0.00 3.40 0.00 106.09

0.5 6.30 0.00 0.00 0.00 107.16

0.55 6.93 -3.40 0.00 0.00 106.09

0.6 7.56 -6.80 0.00 0.00 102.88

0.65 8.19 -10.21 0.00 0.00 97.52

0.7 8.82 -13.61 0.00 0.00 90.02

0.75 9.45 -17.01 0.00 0.00 80.37

0.8 10.08 -20.41 0.00 0.00 68.58

0.85 10.71 -23.81 0.00 0.00 54.65

0.9 11.34 -27.22 0.00 0.00 38.58

0.95 11.97 -30.62 0.00 0.00 20.36

1 12.60 -34.02 0.00 0.00 0.00

Span


Min

Moment

Max

Moment

kN kN kNm kNm

0 0.00 0.00 0.00 0.00 0.00

0.05 0.63 0.00 0.00 0.00 0.00

0.1 1.26 0.00 0.00 0.00 0.00

0.15 1.89 0.00 0.00 0.00 0.00

0.2 2.52 0.00 0.00 0.00 0.00

0.25 3.15 0.00 0.00 0.00 0.00

0.3 3.78 0.00 0.00 0.00 0.00

0.35 4.41 0.00 0.00 0.00 0.00

0.4 5.04 0.00 0.00 0.00 0.00

0.45 5.67 0.00 0.00 0.00 0.00

0.5 6.30 0.00 0.00 0.00 0.00

0.55 6.93 0.00 0.00 0.00 0.00

0.6 7.56 0.00 0.00 0.00 0.00

0.65 8.19 0.00 0.00 0.00 0.00

0.7 8.82 0.00 0.00 0.00 0.00

0.75 9.45 0.00 0.00 0.00 0.00

0.8 10.08 0.00 0.00 0.00 0.00

0.85 10.71 0.00 0.00 0.00 0.00

0.9 11.34 0.00 0.00 0.00 0.00

0.95 11.97 0.00 0.00 0.00 0.00

1 12.60 0.00 0.00 0.00 0.00

Span


Min

Moment

Max

Moment

Internal Girder ULS Pedestrian load per Girder

External Girder ULS Pedestrian load per Girder

kN kN kNm kNm

0 0.00 0.00 59.54 0.00 0.00

0.05 0.63 0.00 53.58 0.00 35.63

0.1 1.26 0.00 47.63 0.00 67.51

0.15 1.89 0.00 41.67 0.00 95.64

0.2 2.52 0.00 35.72 0.00 120.02

0.25 3.15 0.00 29.77 0.00 140.65

0.3 3.78 0.00 23.81 0.00 157.53

0.35 4.41 0.00 17.86 0.00 170.66

0.4 5.04 0.00 11.91 0.00 180.03

0.45 5.67 0.00 5.95 0.00 185.66

0.5 6.30 0.00 0.00 0.00 187.54

0.55 6.93 -5.95 0.00 0.00 185.66

0.6 7.56 -11.91 0.00 0.00 180.03

0.65 8.19 -17.86 0.00 0.00 170.66

0.7 8.82 -23.81 0.00 0.00 157.53

0.75 9.45 -29.77 0.00 0.00 140.65

0.8 10.08 -35.72 0.00 0.00 120.02

0.85 10.71 -41.67 0.00 0.00 95.64

0.9 11.34 -47.63 0.00 0.00 67.51

0.95 11.97 -53.58 0.00 0.00 35.63

1 12.60 -59.54 0.00 0.00 0.00

3.8.3 Vehicle Live Loads

The Tables contain 3 critical load combination cases:

1) Strength 1

2) Serviceability 2

3) Fatigue

The Tables which follow, contain the envelope of moments and shears of the distributed vehicular live loads

at 20th points along the girder, for both the Serviceability Limit State and the Strength Limit State. These

have been summarised for both the internal and external girder. Each Limit State is factored in accordance

with the load factors outlined above. The Tandem + Lane and HS20 Truck + Lane which equates to the

HL93 load has been distributed in accordance with the distribution factors calculated above.

For ease of calculation these tables DO NOT contain the permanent load elements which will change with

each iteration.

Accordingly these appropriately factored permanent load elements of the combinations will be added as the

calculations proceed.

Span


Min

Moment

Max

Moment

kN kN kNm kNm

0 0.00 0.00 511.23 0.00 0.00

0.05 0.63 -12.73 475.71 0.00 301.98

0.1 1.26 -25.83 440.57 0.00 563.75

0.15 1.89 -40.66 405.81 0.00 785.33

0.2 2.52 -61.01 371.42 0.00 966.70

0.25 3.15 -81.74 337.43 0.00 1107.00

0.3 3.78 -102.86 303.81 0.00 1208.00

0.35 4.41 -124.35 272.54 0.00 1282.00

0.4 5.04 -146.23 242.71 0.00 1342.00

0.45 5.67 -168.48 214.14 0.00 1361.00

0.5 6.30 -191.12 191.12 0.00 1340.00

0.55 6.93 -214.14 168.48 0.00 1361.00

0.6 7.56 -242.71 146.23 0.00 1342.00

0.65 8.19 -272.54 124.35 0.00 1282.00

0.7 8.82 -303.81 102.86 0.00 1208.00

0.75 9.45 -337.43 81.74 0.00 1107.00

0.8 10.08 -371.42 61.01 0.00 966.70

0.85 10.71 -405.81 40.66 0.00 785.33

0.9 11.34 -440.57 25.83 0.00 563.75

0.95 11.97 -475.71 12.73 0.00 301.98

1 12.60 -511.23 0.00 0.00 0.00

Designers are advised that the design lane values tabulated below were obtained by use of the QConBridge

program developed and freely distributed by the Washington State Department of Transport, Bridge and

Structures Office. Advice on freely obtaining this software is included in the ACCRA Bridge Design

Manual.

The QConBridge program builds into the output the appropriate range of load factors and permits the

designer to edit these to a particular design case.

Servicability_2 Envelope for the LL aspects/Lane

Internal Girder Load

Span


Min

Moment

Max

Moment

kN kN kNm kNm

0 0.00 0.00 511.23 0.00 0.00

0.05 0.63 -12.73 475.71 0.00 301.98

0.1 1.26 -25.83 440.57 0.00 563.75

0.15 1.89 -40.66 405.81 0.00 785.33

0.2 2.52 -61.01 371.42 0.00 966.70

0.25 3.15 -81.74 337.43 0.00 1107.00

0.3 3.78 -102.86 303.81 0.00 1208.00

0.35 4.41 -124.35 272.54 0.00 1282.00

0.4 5.04 -146.23 242.71 0.00 1342.00

0.45 5.67 -168.48 214.14 0.00 1361.00

0.5 6.30 -191.12 191.12 0.00 1340.00

0.55 6.93 -214.14 168.48 0.00 1361.00

0.6 7.56 -242.71 146.23 0.00 1342.00

0.65 8.19 -272.54 124.35 0.00 1282.00

0.7 8.82 -303.81 102.86 0.00 1208.00

0.75 9.45 -337.43 81.74 0.00 1107.00

0.8 10.08 -371.42 61.01 0.00 966.70

0.85 10.71 -405.81 40.66 0.00 785.33

0.9 11.34 -440.57 25.83 0.00 563.75

0.95 11.97 -475.71 12.73 0.00 301.98

1 12.60 -511.23 0.00 0.00 0.00

Span


Min

Moment

Max

Moment

kN kN kNm kNm

0 0.00 0.00 417.35 0.00 0.00

0.05 0.63 -10.39 388.35 0.00 208.81

0.1 1.26 -21.09 359.66 0.00 389.82

0.15 1.89 -33.19 331.28 0.00 543.04

0.2 2.52 -49.81 303.21 0.00 668.45

0.25 3.15 -66.73 275.46 0.00 765.47

0.3 3.78 -83.97 248.01 0.00 835.31

0.35 4.41 -101.51 222.49 0.00 886.48

0.4 5.04 -119.37 198.14 0.00 927.97

0.45 5.67 -137.54 174.81 0.00 941.10

0.5 6.30 -156.02 156.02 0.00 926.58

0.55 6.93 -174.81 137.54 0.00 941.10

0.6 7.56 -198.14 119.37 0.00 927.97

0.65 8.19 -222.49 101.51 0.00 886.48

0.7 8.82 -248.01 83.97 0.00 835.31

0.75 9.45 -275.46 66.73 0.00 765.47

0.8 10.08 -303.21 49.81 0.00 668.45

0.85 10.71 -331.28 33.19 0.00 543.04

0.9 11.34 -359.66 21.09 0.00 389.82

0.95 11.97 -388.35 10.39 0.00 208.81

1 12.60 -417.35 0.00 0.00 0.00

Servicability_2 LL only / Internal Girder

Servicability_2 LL only / External Girder

Servicability_2 Envelope for the LL aspects/ Lane

External Girder Load

Span


Min

Moment

Max

Moment

kN kN kNm kNm

0 0.00 0.00 208.67 0.00 0.00

0.05 0.63 -5.19 194.17 0.00 138.41

0.1 1.26 -10.54 179.83 0.00 258.40

0.15 1.89 -16.60 165.64 0.00 359.96

0.2 2.52 -24.90 151.61 0.00 443.09

0.25 3.15 -33.37 137.73 0.00 507.40

0.3 3.78 -41.98 124.01 0.00 553.69

0.35 4.41 -50.76 111.24 0.00 587.61

0.4 5.04 -59.69 99.07 0.00 615.11

0.45 5.67 -68.77 87.41 0.00 623.82

0.5 6.30 -78.01 78.01 0.00 614.19

0.55 6.93 -87.41 68.77 0.00 623.82

0.6 7.56 -99.07 59.69 0.00 615.11

0.65 8.19 -111.24 50.76 0.00 587.61

0.7 8.82 -124.01 41.98 0.00 553.69

0.75 9.45 -137.73 33.37 0.00 507.40

0.8 10.08 -151.61 24.90 0.00 443.09

0.85 10.71 -165.64 16.60 0.00 359.96

0.9 11.34 -179.83 10.54 0.00 258.40

0.95 11.97 -194.17 5.19 0.00 138.41

1 12.60 -208.67 0.00 0.00 0.00

Span


Min

Moment

Max

Moment

kN kN kNm kNm

0 0.00 0.00 688.19 0.00 0.00

0.05 0.63 -17.13 640.38 0.00 406.50

0.1 1.26 -34.77 593.07 0.00 758.89

0.15 1.89 -54.73 546.28 0.00 1057.00

0.2 2.52 -82.13 500.00 0.00 1301.00

0.25 3.15 -110.04 454.23 0.00 1491.00

0.3 3.78 -138.46 408.97 0.00 1627.00

0.35 4.41 -167.39 366.88 0.00 1726.00

0.4 5.04 -196.84 326.72 0.00 1806.00

0.45 5.67 -226.80 288.26 0.00 1833.00

0.5 6.30 -257.27 257.27 0.00 1805.00

0.55 6.93 -288.26 226.80 0.00 1833.00

0.6 7.56 -326.72 196.84 0.00 1806.00

0.65 8.19 -366.88 167.39 0.00 1726.00

0.7 8.82 -408.97 138.46 0.00 1627.00

0.75 9.45 -454.23 110.04 0.00 1491.00

0.8 10.08 -500.00 82.13 0.00 1301.00

0.85 10.71 -546.28 54.73 0.00 1057.00

0.9 11.34 -593.07 34.77 0.00 758.89

0.95 11.97 -640.38 17.13 0.00 406.50

1 12.60 -688.19 0.00 0.00 0.00

Internal Girder Lane Load

External Girder Lane Load

Strength_1 Envelope for the LL aspects only

Strength_1 Envelope for the LL aspects only

Span


Min

Moment

Max

Moment

kN kN kNm kNm

0 0.00 0.00 688.19 0.00 0.00

0.05 0.63 -17.13 640.38 0.00 406.50

0.1 1.26 -34.77 593.07 0.00 758.89

0.15 1.89 -54.73 546.28 0.00 1057.00

0.2 2.52 -82.13 500.00 0.00 1301.00

0.25 3.15 -110.04 454.23 0.00 1491.00

0.3 3.78 -138.46 408.97 0.00 1627.00

0.35 4.41 -167.39 366.88 0.00 1726.00

0.4 5.04 -196.84 326.72 0.00 1806.00

0.45 5.67 -226.80 288.26 0.00 1833.00

0.5 6.30 -257.27 257.27 0.00 1805.00

0.55 6.93 -288.26 226.80 0.00 1833.00

0.6 7.56 -326.72 196.84 0.00 1806.00

0.65 8.19 -366.88 167.39 0.00 1726.00

0.7 8.82 -408.97 138.46 0.00 1627.00

0.75 9.45 -454.23 110.04 0.00 1491.00

0.8 10.08 -500.00 82.13 0.00 1301.00

0.85 10.71 -546.28 54.73 0.00 1057.00

0.9 11.34 -593.07 34.77 0.00 758.89

0.95 11.97 -640.38 17.13 0.00 406.50

1 12.60 -688.19 0.00 0.00 0.00

Span


Min

Moment

Max

Moment

kN kN kNm kNm

0 0.00 0.00 561.81 0.00 0.00

0.05 0.63 -13.98 522.77 0.00 281.09

0.1 1.26 -28.39 484.16 0.00 524.76

0.15 1.89 -44.68 445.96 0.00 730.89

0.2 2.52 -67.04 408.17 0.00 899.62

0.25 3.15 -89.83 370.81 0.00 1031.00

0.3 3.78 -113.03 333.87 0.00 1125.04

0.35 4.41 -136.65 299.50 0.00 1193.49

0.4 5.04 -160.69 266.72 0.00 1248.81

0.45 5.67 -185.15 235.32 0.00 1267.48

0.5 6.30 -210.03 210.03 0.00 1248.12

0.55 6.93 -235.32 185.15 0.00 1267.48

0.6 7.56 -266.72 160.69 0.00 1248.81

0.65 8.19 -299.50 136.65 0.00 1193.49

0.7 8.82 -333.87 113.03 0.00 1125.04

0.75 9.45 -370.81 89.83 0.00 1031.00

0.8 10.08 -408.17 67.04 0.00 899.62

0.85 10.71 -445.96 44.68 0.00 730.89

0.9 11.34 -484.16 28.39 0.00 524.76

0.95 11.97 -522.77 13.98 0.00 281.09

1 12.60 -561.81 0.00 0.00 0.00

Span


Min

Moment

Max

Moment

Strength_1 LL only / Internal Girder

Strength_1 LL only / External Girder

kN kN kNm kNm

0 0.00 0.00 280.91 0.00 0.000.05 0.63 -6.99 261.39 0.00 186.32

0.1 1.26 -14.19 242.08 0.00 347.840.15 1.89 -22.34 222.98 0.00 484.48

0.2 2.52 -33.52 204.09 0.00 596.320.25 3.15 -44.91 185.41 0.00 683.40

0.3 3.78 -56.52 166.93 0.00 745.740.35 4.41 -68.33 149.75 0.00 791.12

0.4 5.04 -80.35 133.36 0.00 827.780.45 5.67 -92.58 117.66 0.00 840.16

0.5 6.30 -105.01 105.01 0.00 827.33

0.55 6.93 -117.66 92.58 0.00 840.160.6 7.56 -133.36 80.35 0.00 827.78

0.65 8.19 -149.75 68.33 0.00 791.120.7 8.82 -166.93 56.52 0.00 745.74

0.75 9.45 -185.41 44.91 0.00 683.400.8 10.08 -204.09 33.52 0.00 596.32

0.85 10.71 -222.98 22.34 0.00 484.480.9 11.34 -242.08 14.19 0.00 347.84

0.95 11.97 -261.39 6.99 0.00 186.321 12.60 -280.91 0.00 0.00 0.00

3.8.4 Load Combinations

1) Strength 1 - 1.25 Girder DL + 1.25 Barrier L + 1.5 Wearing Course + 1.75 HL93 + 1.75 Ped L

2) Serviceability 2 - 1.0 Girder DL + 1.0 Barrier DL + 1.0 Wearing Course + 1.3 HL93 + 1.3 Ped L

Span


Min

Moment

Max

MomentkN kN kNm kNm

0.00 0.00 0.00 612.68 0.00 0.00

0.05 0.63 -10.39 564.15 0.00 325.720.10 1.26 -21.09 515.93 0.00 611.330.15 1.89 -33.19 468.02 0.00 856.850.20 2.52 -49.81 420.42 0.00 1062.260.25 3.15 -66.73 373.13 0.00 1226.95

0.30 3.78 -83.97 326.15 0.00 1352.17

0.35 4.41 -101.51 281.09 0.00 1446.41

0.40 5.04 -119.37 237.20 0.00 1518.67

0.45 5.67 -137.54 194.35 0.00 1550.27

0.50 6.30 -156.02 156.02 0.00 1541.90

0.55 6.93 -194.35 137.54 0.00 1550.27

0.60 7.56 -237.20 119.37 0.00 1518.67

0.65 8.19 -281.09 101.51 0.00 1446.41

0.70 8.82 -326.15 83.97 0.00 1352.170.75 9.45 -373.13 66.73 0.00 1226.950.80 10.08 -420.42 49.81 0.00 1062.260.85 10.71 -468.02 33.19 0.00 856.850.90 11.34 -515.93 21.09 0.00 611.33

0.95 11.97 -564.15 10.39 0.00 325.721.00 12.60 -612.68 0.00 0.00 0.00

External Girder

Serviceability Limit State Combination Serviceability 2

Serviceability Limit State Combination Serviceability 2

Internal Girder

The T- Beam is designed for the critical limit state combinations as outlined above. For this example the

critical case occurs for the combinations tabulated below.

Span


Min

Moment

Max

Moment

kN kN kNm kNm

0.00 0.00 0.00 448.24 0.00 0.00

0.05 0.63 -5.19 409.78 0.00 281.79

0.10 1.26 -10.54 371.48 0.00 530.06

0.15 1.89 -16.60 333.34 0.00 744.81

0.20 2.52 -24.90 295.35 0.00 926.05

0.25 3.15 -33.37 257.51 0.00 1073.37

0.30 3.78 -41.98 219.83 0.00 1187.58

0.35 4.41 -50.76 183.11 0.00 1274.32

0.40 5.04 -59.69 146.98 0.00 1339.55

0.45 5.67 -68.77 111.36 0.00 1370.90

0.50 6.30 -78.01 78.01 0.00 1368.82

0.55 6.93 -111.36 68.77 0.00 1370.90

0.60 7.56 -146.98 59.69 0.00 1339.55

0.65 8.19 -183.11 50.76 0.00 1274.32

0.70 8.82 -219.83 41.98 0.00 1187.58

0.75 9.45 -257.51 33.37 0.00 1073.37

0.80 10.08 -295.35 24.90 0.00 926.05

0.85 10.71 -333.34 16.60 0.00 744.81

0.90 11.34 -371.48 10.54 0.00 530.06

0.95 11.97 -409.78 5.19 0.00 281.79

1.00 12.60 -448.24 0.00 0.00 0.00

Span


Min

Moment

Max

Moment

kN kN kNm kNm

0.00 0.00 0.00 815.65 0.00 0.00

0.05 0.63 -13.98 751.23 0.00 433.01

0.10 1.26 -28.39 687.22 0.00 812.61

0.15 1.89 -44.68 623.64 0.00 1138.68

0.20 2.52 -67.04 560.48 0.00 1411.35

0.25 3.15 -89.83 497.73 0.00 1630.68

0.30 3.78 -113.03 435.40 0.00 1796.68

0.35 4.41 -136.65 375.65 0.00 1921.11

0.40 5.04 -160.69 317.49 0.00 2016.41

0.45 5.67 -185.15 260.71 0.00 2059.07

0.50 6.30 -210.03 210.03 0.00 2047.70

0.55 6.93 -260.71 185.15 0.00 2059.07

0.60 7.56 -317.49 160.69 0.00 2016.41

0.65 8.19 -375.65 136.65 0.00 1921.11

0.70 8.82 -435.40 113.03 0.00 1796.68

0.75 9.45 -497.73 89.83 0.00 1630.68

0.80 10.08 -560.48 67.04 0.00 1411.35

0.85 10.71 -623.64 44.68 0.00 1138.68

0.90 11.34 -687.22 28.39 0.00 812.61

0.95 11.97 -751.23 13.98 0.00 433.01

1.00 12.60 -815.65 0.00 0.00 0.00

Internal Girder

External Girder

Strength Limit State Combination Strength 1


Span


Min

Moment

Max

Moment

kN kN kNm kNm

0.00 0.00 0.00 594.28 0.00 0.00

0.05 0.63 -6.99 543.42 0.00 373.87

0.10 1.26 -14.19 492.77 0.00 703.20

0.15 1.89 -22.34 442.34 0.00 987.91

0.20 2.52 -33.52 392.11 0.00 1228.07

0.25 3.15 -44.91 342.09 0.00 1423.74

0.30 3.78 -56.52 292.28 0.00 1574.92

0.35 4.41 -68.33 243.76 0.00 1689.39

0.40 5.04 -80.35 196.03 0.00 1775.41

0.45 5.67 -92.58 149.00 0.00 1817.40

0.50 6.30 -105.01 105.01 0.00 1814.44

0.55 6.93 -149.00 92.58 0.00 1817.40

0.60 7.56 -196.03 80.35 0.00 1775.41

0.65 8.19 -243.76 68.33 0.00 1689.39

0.70 8.82 -292.28 56.52 0.00 1574.92

0.75 9.45 -342.09 44.91 0.00 1423.74

0.80 10.08 -392.11 33.52 0.00 1228.07

0.85 10.71 -442.34 22.34 0.00 987.91

0.90 11.34 -492.77 14.19 0.00 703.20

0.95 11.97 -543.42 6.99 0.00 373.87

1.00 12.60 -594.28 0.00 20.00 0.00

3.9 Design

The design of the T-Beam works through a series of steps. These steps are summarised as follows:

1. Calculate the section properties for each girder.

2. Calculate the serviceability limit state required flexural reinforcement.

3. Check the strength limit state flexural reinforcement required.

4. Calculate the serviceability limit state deflections including live load deflection and camber.

6. Determine the minimum longitudinal reinforcement for combined flexure and shear.

7. Check that the allowable fatigue range is not exceeded.

8. Develop reinforcement envelope

3.9.1 Girder Section Properties

Internal Girder:

T-Beam width be = 2400 mm

Girder Overall Depth D = 1000 mm

Reo. Cover = 25 mm

Reo Dia. = 32 mm

Ast = 6434 mm2

Ligs = 12 mm

no of reo layers = 3

c/c layer spacing = 80 mm

dr3 = 787 mm

5. Check the strength limit state shear capacity and calculate the additional shear reinforcement required.

dr2 = 867 mm

dr1 = 947 mm

d = 867 mm

f'c = 32 mPa

Fsy = 500 mPa

Ec = 28600 mPa

Es = 200000 mPa

n(ST) = 6.99

n(LT) = 13.99

b1 = 0.821

Gross section:

Ig=bh3/12= 6.46E+10 mm4

External Girder:

Slab width B = 2535 mm

Slab Depth D = 1000 mm

Reo. Cover = 25 mm

Reo Dia. = 32 mm

Ast = 5630 mm2

Ligs = 12 mm

no of reo layers = 3

c/c layer spacing = 80 mm

dr3 = 787 mm

dr2 = 867 mm

dr1 = 947 mm

d = 867 mm

f'c = 32 mPa

Fsy = 500 mPa

Ec = 28600 mPa

Es = 200000 mPa

n(ST) = 6.99

n(LT) = 13.99

b1 = 0.821

Gross section:

Ig=bh3/12= 6.57E+10 mm4

1. Cracked T-Beam section moment of inertia. This is required for both live load and permanent loads.

2. Cracking moment. This is used in estimating the effective inertia used in deflection calculations.

3. The effective moment of inertia for both short and long term loads.

(a) Cracked Section Properties for Permanent and Live Load

(i) Instantaneous cracked section properties for Live Load( Note: short term cracked section properties are based on n = Es/Ec )

The following calculations determine the required section properties of the T-Beam in accordance with the

AASHTO LRFD. These section properties include:

Internal Girder

The depth x to the neutral axis of a cracked section is:

x = [ -nAs + { ( nAs)^2 + 2bnAsd }^0.5 ] / b

This is the Quadratic solution in the form of:

[ -b + { b^2 - 4ac }^0.5 ] / 2a

where :

a = 1200

b = 44993.6

c = -4E+07

And x = 163 mm

Neutral axis is in the Flange

Icr (ST) = 2.58E+10 mm^4

External Girder

x = -nAs/b + { ( nAs/b)^2 + 2nAsd/b}^0.5


[ -b + { b^2 - 4ac }^0.5 ] / 2a

where :

a = 1200

b = 44993.6

c = -4E+07

And x = 163 mm


Icr (ST) = 2.32E+10 mm^4

(ii) Long term cracked section properties for Permanent Loads( Note: long term cracked section properties are based on n = 2*Es/Ec )

Internal Girder


x = [ -nAs + { ( nAs)^2 + 2bnAsd }^0.5 ] / b


[ -b + { b^2 - 4ac }^0.5 ] / 2a

where :

The depth x to the neutral axis of a

a = 1200

b = 89987.2

c = -8E+07

And x = 220 mm

The neutral axis is in the web - x taken as flange ts

This yeilds a Icr (Long Term) = 4.62E+10 mm^4

External Girder


x = [ -nAs + { ( nAs)^2 + 2bnAsd }^0.5 ] / b


[ -b + { b^2 - 4ac }^0.5 ] / 2a

where :

a = 1200

b = 89987.2

c = -8E+07

And x = 220 mm

The neutral axis is in the web - x taken as flange ts

This yeilds a Icr (Long Term) = 4.62E+10 mm^4

(b) Section Cracking Moment

Internal Girder:

yt= 710.23 mm

LRFD Art 5.4.2.6 fr= 3.56 Mpa

LRFD Eq.5.7.3.6.2-2; Mcr = frIg/yt= 324.23 KNm/m

External Girder:

yt= 716.48 mm

LRFD Art 5.4.2.6 fr= 3.56 Mpa

LRFD Eq.5.7.3.6.2-2; Mcr = frIg/yt= 326.60 KNm/m

(c) Section Effective Moment of Inertia for both Long and Short term Loads

Internal Girder:

SLS Max Moment Ma = 1550.27 kNm

(Mcr/Ma)^3 = 0.01

Ief (Short Term) = 2.61E+10 mm4

Ief (Long Term) = 4.64E+10 mm4

External Girder:

SLS Max Moment Ma = 1370.90 kNm

(Mcr/Ma)^3 = 0.01

Ief (Short Term) = 2.37E+10 mm4

Ief (Long Term) = 4.65E+10 mm4

(a) Crack Control

fs= Z/(dcA)1/3 <=0.6fy LRFD Eq 5.7.3.4-1

Z= crack width parameter in N/mm

Z= 30000 N/mm For moderate climates.

dc=

A=

Internal girder dc = 50 mm

ys = 133 mm

A = 12635 mm

Therefore the limiting stress = fs = 300 Mpa

To limit cracking this SLS stress limit must be greater than the actual stress

SLS actual steel stress: (using cracked section)

Actual reo stress = fs = n*M*(d-x)/Icr = 296.43 Mpa

OK, Cracking is controlled.

From Modular theory, np = 0.02

k = ((np)^2+2*np)^.5-np = 0.19

j = 0.94

Required SLS reo = As = M/(fjd) = 6358 mm^2/m

External girder dc = 50 mm

ys = 133 mm

A = 12635 mm

Therefore the limiting stress = fs = 300 Mpa

depth of concrete measured from extreme tension fiber to center of bar; for

calculation purpose, the thickness of clear cover used to compute dc shall

not be taken greater than 50mm.

area of concrete having the same centroid as the principal tension

reinforcement and bounded by the surfaces of the cross section and a

straight line parallel to the neutral axis, divided by the number of bar.

3.9.2 Calculate the serviceability limit state required flexural

reinforcement

To control flexural cracking of the concrete, tension reinforcement shall be well distributed within the

maximum flexural zones. To prevent this kind of cracking the calculated stress in the reinforcement at

service load, fs, in Mpa shall not exceed the value computed by.

To limit cracking this SLS stress limit must be greater than the actual stress

SLS actual steel stress: (using cracked section)


OK, Cracking is controlled.

From Modular theory, np = 0.05

k = ((np)^2+2*np)^.5-np = 0.26

j = 0.91

Required SLS reo = As = M/(fjd) = 5781 mm^2/m

(b) Selection of Reinforcement.

Reinforcement Bar Number

(Required Reinforcement Area known)

INPUT - Diameter of Reinforcement Bars 32

X-Area of Reinforcement Bars 804

INPUT - Known Reinforcement Area 6358

Required Number of Bars 7.91

Reinforcement Area

(Required Reinforcement Bar No. known)



INPUT - Known Number of Bars 8

Required Reinforcement Area 6434

Summary of proposed Reinforcement in Internal girder

Area = 6434

mm^2/m

i.e. = 32 @ 90

Reinforcement Bar Number

(Required Reinforcement Area known)



INPUT - Known Reinforcement Area 5592

Required Number of Bars 6.95

Because the serviceability limit state cracking criteria usually governs the quantity of flexural reinforcement

required, this is an appropriate stage in the design process to select the actual amount of reinforcement.

Reinforcement Area

(Required Reinforcement Bar No. known)



INPUT - Known Number of Bars 7

Required Reinforcement Area 5630

Summary of Proposed Reinforcement in External girder

Area = 5630

mm^2/m

i.e. = 32 @ 90

As = -f fy d +/- [( f fy d) ^ 2 - ( 4 f Mu fy ^ 2 ) / (2*0.85 fc b) ] ^0.5 / ( 2 f fy ^ 2 / (2 * 0.85 fc b )

This is the Quadratic solution in the form of:[ -b + { b^2 - 4ac }^0.5 ] / 2a

Where:

Critical design Internal Girder Mu = 2059.07 KNm/m

And internal girder coefficients a,b,and c are:

a =

b =

c =

Therefore:

Required ULS As = 5407 mm^2/m

( Note: SLS case governs )

Check on reinforcement used:

Check maximum reinforcement is not exceeded:

c = As*fy/(0.85*f"c*b1*b)= 59.99 mm

a = b1*c = 49.28 mm

d = 867 mm

2.06E+09

The reinforcement for the strength limit state maximum moment is calculated by considering only the

tension steel (compression steel is conservatively ignored). This is done by solving the second degree

polynomial in terms of As, developed from LRFD art 5.7.3.2.2-1 as follows:

1.72

-3.90E+05

3.9.3 Check the strength limit state flexural reinforcement required

c/d = 0.07 < 0.42

OK, Under-reinforced

Check greater than minimum is used (ie greater than 1.2 Mcr or approx 0.03*f"c/fy):

Ag = 824400 mm^2

r = As/Ag = 0.00309

r min = 0.03*f"c/fy = 0.00192

Asmin = 1582.85 mm^2

OK, Sufficient Reinforcement

Where:

Critical design External Girder Mu = 1817.40 KNm/m

And external girder coefficients a,b,and c are:

a =

b =

c =

Therefore:

Required ULS As = 4753 mm^2/m

( Note: SLS case governs )

Check on reinforcement used:

Check maximum reinforcement is not exceeded:

c = As*fy/(0.85*f"c*b1*b)= 49.70 mm


a = b1*c = 40.83 mm

d = 867 mm

c/d = 0.06 < 0.42

OK, Under-reinforced

Check greater than minimum is used (ie greater than 1.2 Mcr or approx 0.03*f"c/fy):

Ag = 824400 mm^2

r = As/Ag = 0.00683

r min = 0.03*f"c/fy = 0.00192

Asmin = 1582.85 mm^2

OK, Sufficient Reinforcement

Permanent Load camber in Internal Girder:

wdl = wgirder + wwc = 27.04 kN/m/m

1.82E+09

3.9.4 Calculate the serviceability limit state deflections including live

load deflection and camber.

1.63

-3.90E+05

Using Ie from LRFD article 5.7.3.6.2

Def DL = 5*wdl*L^4/(384*Ec*I elt) = 6.69 mm

Long term def = 12.05 mm

Using Ig from LRFD article 5.7.3.6.2

Def DL = 5*wdl*L^4/(384*Ec*Ig) = 4.80 mm


Adopt a minimum camber = 19.21 mm

Round to say = 20.00 mm

Live Load Deflection:

Max Moment (ll + Dl) = 941.10 kNm/m

Instantaneous Def = 5*M*L^2/(48*Ec*Ie) = 20.83 mm

Max Instantaneous deflection = Span/800 = 15.75 mm

Actual Instantaneous Span/deflection = 605

Exceeds Suggested Maximum of 800

Permanent Load camber in External girder:

wdl = wgirder + wwc = 27.04 kN/m/m

Using Ie from LRFD article 5.7.3.6.2

Def DL = 5*wdl*L^4/(384*Ec*Ielt) = 6.68 mm


Using Ig from LRFD article 5.7.3.6.2

Def DL = 5*wdl*L^4/(384*Ec*Ig) = 4.73 mm


Adopt a minimum camber = 18.90 mm

Round to say = 20.00 mm

Live Load Deflection:

Max Moment (ll + Dl) = 623.82 kNm/m

Instantaneous Def = 5*M*L^2/(48*Ec*Ie) = 15.19 mm

Max Instantaneous deflection = Span/800 = 15.75 mm

Actual Instantaneous Span/deflection = 829

Instantaneous Deflection is OK!

External quarter of Girder:

Maximum (ULS) shear = Vu = 815.65 kN/m

Vn max = 0.25*fc*bv*dv = 2372.11 kN/m

OK,Shear required < PermissibleMaximum!

Vc = 0.083*2*fc^.5*bv*dv = 321.15 kN/m

NOT GOOD, Require shear REO

Shear reo spacing = 150 mm

No. of legs at each spacing = 2

Area of transverse reo per leg = 106 mm^2 / leg

Vs = 275 kN/m

Note: 12 mm dia bar; As = 113mm^2 & 16 mm dia bar; As = 201mm^2

Minimum shear Reinforcement = 26.7626 mm^2 / leg @ S

OK, Shear steel provided greater than minimum!

Internal half of Girder:


Vn max = 0.25*fc*bv*dv = 2372.11 kN/m


Vc = 0.083*2*fc^.5*bv*dv = 321.15 kN/m





Vs = 98 kN/m


Minimum shear Reinforcement = 53.5252 mm^2 / leg @ Spacing


External quarter of Girder:


Vn max = 0.25*fc*bv*dv = 2372.11 kN/m


Vc = 0.083*2*fc^.5*bv*dv = 321.15 kN/m





Vs = 152 kN/m


Minimum shear Reinforcement = 27 mm^2 / leg @ S


3.9.5 Check the strength limit state shear capacity and calculate the

additional shear reinforcement required.

Internal half of Girder:


Vn max = 0.25*fc*bv*dv = 15824.5 kN/m


Vc = 0.083*2*fc^.5*bv*dv = 321.15 kN/m





Vs = 12 kN/m


Minimum shear Reinforcement = 54 mm^2 / leg @ Spacing

NOT GOOD, Require more shear REO


Internal Girder

LRFD 5.8.3.5-1 Minimum Area of Longitudinal steel = [ Mu/dv/f + Vu/f - 0.5*Vs] / fy

Span

Ratio Distance Max Shear 0.5 Vs

Max

Moment Min As

kN kN kNm mm^2

0.00 0.00 815.65 137.3599 0.00 1538

0.05 0.63 751.23 137.3599 433.01 26280.10 1.26 687.22 137.3599 812.61 35670.15 1.89 623.64 137.3599 1138.68 43540.20 2.52 560.48 137.3599 1411.35 49900.25 3.15 497.73 137.3599 1630.68 5475

0.30 3.78 435.40 49.049365 1796.68 59860.35 4.41 375.65 49.049365 1921.11 62080.40 5.04 317.49 49.049365 2016.41 63500.45 5.67 260.71 49.049365 2059.07 63450.50 6.30 210.03 49.049365 2047.70 62000.55 6.93 260.71 49.049365 2059.07 63450.60 7.56 317.49 49.049365 2016.41 63500.65 8.19 375.65 49.049365 1921.11 6208

0.70 8.82 435.40 49.049365 1796.68 5986

0.75 9.45 497.73 137.3599 1630.68 5475

0.80 10.08 560.48 137.3599 1411.35 4990

0.85 10.71 623.64 137.3599 1138.68 4354

0.90 11.34 687.22 137.3599 812.61 3567

0.95 11.97 751.23 137.3599 433.01 2628

1.00 12.60 815.65 137.3599 0.00 1538


External Girder

Span

Ratio Distance Max Shear 0.5 Vs

Max

Moment Min As

kN kN kNm mm^2

0.00 0.00 594.28 75.868 0.00 11690.05 0.63 543.42 75.868 373.87 21210.10 1.26 492.77 75.868 703.20 2946

3.9.6 Determine the minimum longitudinal reinforcement for

combined flexure and shear.

0.15 1.89 442.34 75.868 987.91 36450.20 2.52 392.11 75.868 1228.07 42170.25 3.15 342.09 75.868 1423.74 46630.30 3.78 292.28 5.8165588 1574.92 51230.35 4.41 243.76 5.8165588 1689.39 53410.40 5.04 196.03 5.8165588 1775.41 54800.45 5.67 149.00 5.8165588 1817.40 54950.50 6.30 105.01 5.8165588 1814.44 53890.55 6.93 149.00 5.8165588 1817.40 5495

0.60 7.56 196.03 5.8165588 1775.41 54800.65 8.19 243.76 5.8165588 1689.39 53410.70 8.82 292.28 5.8165588 1574.92 51230.75 9.45 342.09 75.868 1423.74 46630.80 10.08 392.11 75.868 1228.07 4217

0.85 10.71 442.34 75.868 987.91 3645

0.90 11.34 492.77 75.868 703.20 29460.95 11.97 543.42 75.868 373.87 21211.00 12.60 594.28 75.868 0.00 1169

3.9.7 Check that the allowable fatigue range is not exceeded.

ff = 145 -0.33fmin +0.55(r/h) in MPa

Since fmin = 0 for a simply supported span

ff = 161.5 MPa

Span

Ratio Distance Max Shear Min Shear

Min

Moment

Max

MomentkN kN kNm kNm

0.00 0.00 0.00 214.39 0.00 0.000.05 0.63 -8.34 197.72 0.00 124.560.10 1.26 -16.68 181.04 0.00 228.110.15 1.89 -25.01 164.37 0.00 310.660.20 2.52 -33.35 151.86 0.00 382.700.25 3.15 -41.69 141.51 0.00 445.770.30 3.78 -50.03 131.16 0.00 495.800.35 4.41 -58.71 120.81 0.00 532.790.40 5.04 -69.06 110.46 0.00 556.740.45 5.67 -79.41 100.11 0.00 567.650.50 6.30 -89.76 89.76 0.00 565.510.55 6.93 -100.11 79.41 0.00 567.650.60 7.56 -110.46 69.06 0.00 556.740.65 8.19 -120.81 58.71 0.00 532.790.70 8.82 -131.16 50.03 0.00 495.80

0.75 9.45 -141.51 41.69 0.00 445.770.80 10.08 -151.86 33.35 0.00 382.700.85 10.71 -164.37 25.01 0.00 310.660.90 11.34 -181.04 16.68 0.00 228.11

0.95 11.97 -197.72 8.34 0.00 124.56

1.00 12.60 -214.39 0.00 0.00 0.00

Maximum Moment = 567.65 kNm

For the External Girder the actual reo stress = fs = n*M*(d-x)/Icr = 108.54 Mpa

Since this is less than the allowable range, fatigue is

deemed OK.

Span

Ratio Distance Max Shear Min Shear

Min

Moment

Max

Moment

LRFD Section 5.5.3.2 specifies an allowable stress range to prevent fatigue problems. This range is

determined for Internal Girder as:

kN kN kNm kNm

0.00 0.00 0.00 214.39 0.00 0.00

0.05 0.63 -8.34 197.72 0.00 124.56

0.10 1.26 -16.68 181.04 0.00 228.11

0.15 1.89 -25.01 164.37 0.00 310.66

0.20 2.52 -33.35 151.86 0.00 382.70

0.25 3.15 -41.69 141.51 0.00 445.77

0.30 3.78 -50.03 131.16 0.00 495.80

0.35 4.41 -58.71 120.81 0.00 532.79

0.40 5.04 -69.06 110.46 0.00 556.74

0.45 5.67 -79.41 100.11 0.00 567.65

0.50 6.30 -89.76 89.76 0.00 565.51

0.55 6.93 -100.11 79.41 0.00 567.65

0.60 7.56 -110.46 69.06 0.00 556.74

0.65 8.19 -120.81 58.71 0.00 532.79

0.70 8.82 -131.16 50.03 0.00 495.80

0.75 9.45 -141.51 41.69 0.00 445.77

0.80 10.08 -151.86 33.35 0.00 382.70

0.85 10.71 -164.37 25.01 0.00 310.66

0.90 11.34 -181.04 16.68 0.00 228.11

0.95 11.97 -197.72 8.34 0.00 124.56

1.00 12.60 -214.39 0.00 0.00 0.00

Maximum Moment = 567.65 kNm


Since this is less than the allowable range, fatigue is

deemed OK.

3.9.8 Develop reinforcement envelope

Internal Girder Required Reo. at 20th points

Strength 1

Span

Ratio Distance Max Mom Reo Min.

kNm Reqd. Reo.

0.00 0.00 0.00 0 1582.85

0.05 0.63 433.01 1115 1582.85

0.10 1.26 812.61 2102 1582.85

0.15 1.89 1138.68 2957 1582.85

To assist in determining cut off points for steel reinforcing it is necessary to determine governing steel

requirements for the Strength I Limit State, Serviceability II Limit State and Combined Flexure and Shear

requirements.

This is achieved by plotting envelopes of steel requirements for each criteria at 20th points along the girder

and finding those which govern. The governing requirements are shown in the table "Minimum Reo

Envelope" table.

0.20 2.52 1411.35 3677 1582.85

0.25 3.15 1630.68 4260 1582.85

0.30 3.78 1796.68 4703 1582.85

0.35 4.41 1921.11 5036 1582.85

0.40 5.04 2016.41 5292 1582.85

0.45 5.67 2059.07 5407 1582.85

0.50 6.30 2047.70 5376 1582.85

0.55 6.93 2059.07 5407 1582.85

0.60 7.56 2016.41 5292 1582.85

0.65 8.19 1921.11 5036 1582.85

0.70 8.82 1796.68 4703 1582.85

0.75 9.45 1630.68 4260 1582.85

0.80 10.08 1411.35 3677 1582.85

0.85 10.71 1138.68 2957 1582.85

0.90 11.34 812.61 2102 1582.85

0.95 11.97 433.01 1115 1582.85

1.00 12.60 0.00 0 1582.85

External Girder Required Reo. at 20th points

Strength 1

Span

Ratio Distance Max Mom Reo Min.

kNm Reqd. Reo.

0.00 0.00 0.00 0 1582.85

0.05 0.63 373.87 962 1582.85

0.10 1.26 703.20 1816 1582.85

0.15 1.89 987.91 2560 1582.85

0.20 2.52 1228.07 3190 1582.85

0.25 3.15 1423.74 3707 1582.85

0.30 3.78 1574.92 4107 1582.85

0.35 4.41 1689.39 4411 1582.85

0.40 5.04 1775.41 4641 1582.85

0.45 5.67 1817.40 4753 1582.85

0.50 6.30 1814.44 4745 1582.85

0.55 6.93 1817.40 4753 1582.85

0.60 7.56 1775.41 4641 1582.85

0.65 8.19 1689.39 4411 1582.85

0.70 8.82 1574.92 4107 1582.85

0.75 9.45 1423.74 3707 1582.85

0.80 10.08 1228.07 3190 1582.85

0.85 10.71 987.91 2560 1582.85

0.90 11.34 703.20 1816 1582.85

0.95 11.97 373.87 962 1582.85

1.00 12.60 0.00 0 1582.85

Internal Girder Required Reo. at 20th points

Serviceability 2

Span

Ratio Distance Max Mom Reo Reqd.kNm

0.00 0.00 0.00 0

0.05 0.63 325.72 1336

0.10 1.26 611.33 2507

0.15 1.89 856.85 3514

0.20 2.52 1062.26 4356

0.25 3.15 1226.95 5032

0.30 3.78 1352.17 5545

0.35 4.41 1446.41 5932

0.40 5.04 1518.67 6228

0.45 5.67 1550.27 6358

0.50 6.30 1541.90 6323

0.55 6.93 1550.27 6358

0.60 7.56 1518.67 6228

0.65 8.19 1446.41 5932

0.70 8.82 1352.17 5545

0.75 9.45 1226.95 5032

0.80 10.08 1062.26 4356

0.85 10.71 856.85 3514

0.90 11.34 611.33 2507

0.95 11.97 325.72 1336

1.00 12.60 0.00 0

External Girder Required Reo. at 20th points

Serviceability 2

Span

Ratio Distance Max Mom Reo Reqd.kNm

0.00 0.00 0.00 0

0.05 0.63 281.79 1188

0.10 1.26 530.06 2235

0.15 1.89 744.81 3141

0.20 2.52 926.05 3905

0.25 3.15 1073.37 4527

0.30 3.78 1187.58 5008

0.35 4.41 1274.32 5374

0.40 5.04 1339.55 5649

0.45 5.67 1370.90 5781

0.50 6.30 1368.82 5772

0.55 6.93 1370.90 5781

0.60 7.56 1339.55 5649

0.65 8.19 1274.32 5374

0.70 8.82 1187.58 5008

0.75 9.45 1073.37 4527

0.80 10.08 926.05 3905

0.85 10.71 744.81 3141

0.90 11.34 530.06 2235

0.95 11.97 281.79 1188

1.00 12.60 0.00 0

Minimum Reo Envelope at 20th Points

Internal Girder

Span

Ratio Distance Reo Reqd.

0.00 0.00 1583

0.05 0.63 2628

0.10 1.26 3567

0.15 1.89 4354

0.20 2.52 4990

0.25 3.15 5475

0.30 3.78 5986

0.35 4.41 6208

0.40 5.04 6350

0.45 5.67 6358

0.50 6.30 6323

0.55 6.93 6358

0.60 7.56 6350

0.65 8.19 6208

0.70 8.82 5986

0.75 9.45 5475

0.80 10.08 4990

0.85 10.71 4354

0.90 11.34 3567

0.95 11.97 2628

1.00 12.60 1583


External Girder

Span


0.00 0.00 1583

0.05 0.63 2121

0.10 1.26 2946

0.15 1.89 3645

0.20 2.52 4217

0.25 3.15 4663

0.30 3.78 5123

0.35 4.41 5374

0.40 5.04 5649

0.45 5.67 5781

0.50 6.30 5772

0.55 6.93 5781

0.60 7.56 5649

0.65 8.19 5374

0.70 8.82 5123

0.75 9.45 4663

0.80 10.08 4217

0.85 10.71 3645

0.90 11.34 2946

0.95 11.97 2121

1.00 12.60 1583


External Girder

Span


0.00 0.00 1583

0.05 0.63 2628

0.10 1.26 3567

0.15 1.89 4354

0.20 2.52 4990

0.25 3.15 5475

0.30 3.78 5986

0.35 4.41 6208

0.40 5.04 6350

0.45 5.67 6358

0.50 6.30 6323

0.55 6.93 6358

0.60 7.56 6350

0.65 8.19 6208

0.70 8.82 5986

0.75 9.45 5475

0.80 10.08 4990

0.85 10.71 4354

0.90 11.34 3567

0.95 11.97 2628

1.00 12.60 1583

0

1000

2000

3000

4000

5000

6000

7000

0 2 4 6 8 10 12

RE

INF

OR

CE

ME

NT

AR

EA

(sq

mm

)

DISTANCE ALONG BEAM (m)

MINIMUM AREA OF FLEXURAL REINFORCEMENT FOR INTERNAL GIRDER

Combined Flexural and Shear minimum Reinforcement Mu/dv/f + Vu/f - 0.5*Vs] / fy

Reinforcement Area Envelope For Internal Girder

Reinforcement Area Envelope for External Girder shown for comparison

Strength Limit State minimum

Servicability Limit State

Strength Limit State Flexural reinforcement

Main reinforcement area provided = 6434 sq mm ie. 9 / 32 dia bars

Theoretical cut-off point

Note: Because theoretical cut-off of 3 bars is close to the beam end, each bar will extend the full length of the T-Beam.

Area of 6 / 32 dia bars

Dist M/V Strenght Min-Str Serv Envel-Int Envel-Ext Reo

0 1538 0 1583 0 1583 1583 6434

0.63 2628 1115 1583 1336 2628 2121 6434

1.26 3567 2102 1583 2507 3567 2946 6434

1.89 4354 2957 1583 3514 4354 3645 6434

2.52 4990 3677 1583 4356 4990 4217 6434

3.15 5475 4260 1583 5032 5475 4663 6434

3.78 5986 4703 1583 5545 5986 5123 6434

4.41 6208 5036 1583 5932 6208 5374 6434

5.04 6350 5292 1583 6228 6350 5649 6434

5.67 6345 5407 1583 6358 6358 5781 6434

6.3 6200 5376 1583 6323 6323 5772 6434

6.93 6345 5407 1583 6358 6358 5781 6434

7.56 6350 5292 1583 6228 6350 5649 6434

8.19 6208 5036 1583 5932 6208 5374 6434

8.82 5986 4703 1583 5545 5986 5123 6434

9.45 5475 4260 1583 5032 5475 4663 6434

10.08 4990 3677 1583 4356 4990 4217 6434

10.71 4354 2957 1583 3514 4354 3645 6434

11.34 3567 2102 1583 2507 3567 2946 6434

11.97 2628 1115 1583 1336 2628 2121 6434

12.6 1538 0 1583 0 1583 1583 6434

6/9 reo

4289.333

4289.333

4289.333

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4289.333

3. rc tee beam

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