Kiểm toán cống hộp 4x4m bằng phần mềm midas civil

Project: Trung Luong My Thuan Expressway Item Box Culvert 4x4M Section: Bottom Slab (Checking to Y axis longitudinal section of box culvert ) CHECKING SHEAR RESISTANCE Materials Yield strength of reinforcement fy 400 MPa Elastic modulus of Prestressing Steel Ep 197,000 MPa Elastic modulus of Reinforcement Es 200,000 MPa Elastic modulus of Concrete Ec 26,630 MPa Compress strength of concrete fc 30 MPa Checking load Maximum moment Mu 14,715 N.mm Maximum shear Vu 27,468 N Section properties Depth h 350 mm Effective web width b w 1 ,000 mm d s 110 mm Tension reinforcement Diameter mm 12 bar 5 Area of cross section of tensile reinforcement A st 565 mm2 dst 240 mm Effective shear depth dv 252 mm Sức kháng cắt Vr = j Vn V n = min {j(Vc + Vs + Vp); 0.25fcbvdv + Vp} + V c : nominal shear resistance of concrete 0.083b(fc)0.5bwdv + V s : nominal shear resistance of reinforcement Ayfydv(cosq+cosa)sina)s Distance from extreme tension fiber to the centroid tensile reinforcement Quantity Distance from extreme compression fiber to the centroid tensile reinforcement a : angle of inclination of transverse reinforcement to longitudinal axis b : factor indicating ability of diagonally cracked concrete to transmit tension q : inclination angle of diagonal compressive stress Resistance factor for shear j 0.9 Xác định b q Factor indicating ability of diagonally cracked concrete to transmit tension b 3.7 Strain in the tensile reinforcement ex 0.000 Inclination angle of diagonal compressive stress q 27.79 độ V c Nominal shear resistance of concrete Vc 426,796 N V p Component of effective prestresed force in the direction of the applied shear Vp 0 N Checking region requiring transverse reinforcement: Vu và 0.5j(Vc+Vp) Unncessary Minimum tranverse reinforcement within distance s s: A v 170.479 mm2 Data of transverse reinforcement Group 1 a1 90 degrees Spacing of stirrups s1 150 mm Area of shear reinforcement within a distance s: Av1 Diameter 12 mm Area of cross section of shear reinforcement Av1 mm2 Nominal shear resistance of reinforcement Vs1 N Group 2 a2 45 degrees Spacing of stirrups s2 500 mm Area of shear reinforcement within a distance s: Av2 Diameter 12 mm Quantity Angle of inclination of transverse reinforcement to longitudinal axis + V p : component of effective prestresed force in the direction of the applied shear Angle of inclination of transverse reinforcement to longitudinal axis Quantity Project: Trung Luong My Thuan Expressway

Project :

CALCULATION SHEET OF BOX CULVERT ACCORDING TO 22TCN272-05

I LOADS

Self weigth of box culvert Pb (T) Pb = γc x (h x 2 x dw + Bc x (dn + dñ)) = 15.23

2 Dead loads

Max horizontal pressure P A (T/m2) PA = K0 x [γañ x dañ + γs x (H + dbn/2 + htt)] = 5.78

Min horizontal pressure p A (T/m2) PA = K0 x [γañ x dañ + γs x (H + dbn/2)] = 1.86

3 Water loads

4 Live loads ( Design vehicular and Design Lane )

Distributing tire pressure on the top slab of box culvert

5 Additional backfill load of vehicular

Load of additional live load: ∆p (T/m2) ∆p=ko.γ.heq = 0.68

6 Defining coefficient of subgrade reaction

Project : Trung Luong - My Thuan Expressway

II Load combinations

Dead load

Water load

Live load

CALCULATION SHEET OF BOX CULVERT ACCORDING TO 22TCN272-05

KẾT QUẢ PHÂN TÍCH (RESULT OF ANALYSIS)

1 SƠ ĐỒ TÍNH TOÁN (DESIGN SHEME)

(Biểu đồ moment Mxx– Moment diagram Mxx)

b Strength Ib

(Biểu đồ moment Mxx– Moment diagram Mxx)

(Biểu đồ moment Myy– Moment diagram Myy)

b Strength Ib

(Biểu đồ moment Myy– Moment diagram Myy)

(Biểu đồ lực cắt Qxx– Shear diagram Qxx)

3.2 Qyy (Strength Ia)

(Mặt cắt duyệt nội lực – Checking position of shear)

(Biểu đồ lực cắt Qyy– Shear diagram Qyy)

4 AXIAL FORCE DIAGRAMS

4.1 Fxx (strength Ib)

(Mặt cắt duyệt nội lực – Checking position of axial force)

(Biểu đồ lực dọc Fxx– Axial force diagram Fxx)

4.2 Fyy (strength Ia)

(Mặt cắt duyệt nội lực – Checking position of axial force)

(Biểu đồ lực dọc Fyy– Axial force diagram Fyy)

Project: Trung Luong - My Thuan Expressway

CHECKING FLEXURAL & AXIAL RESISTANCE

The factored flexural resistance Mr shall be taken as: M r =ϕM n

Where :

- Mn : Nominal resistance

- ϕ : Resistance factor as specified in Article 5.5.4.2

- As : Area of nonprestressed tension reinforcement

- A's : Area of compression reinforcement

- fy : Specified yield strength of tension reinforcement

- f'y : Specified yield strength of compression reinforcement

- ds : Distance from extreme compression fiber to the centiod of nonprestressed tension reinforcement

- d : Distance from extreme tension fiber to the centriod of nonprestressed tension reinforcement

- d's : Distance from extreme compression fiber to the centriod of compression reinforcement

- a : Depth of the equivalent stress block = c β1

- c : Distance from neutral axis to the extreme compression fiber = [Asfy-A'sf'y]/(0.85f'cβ1b)

Specified yield strength of tension reinforcement fy 400 MPa

Specified yield strength of compression reinforcement f'y 400 MPa

Specified compressive strength of concrete f'c 30 MPa

Modulus of elasticity of steel Es 200,000 MPa

Modulus of elasticity of concrete Ec 29,440 MPa

Project: Trung Luong - My Thuan Expressway

Mcr = frIg/yt

- Modulus of rupture of concrete fr = 0.63f'c

0.5

3.45 Mpa

- Moment of inertia of gross concrete section Ig : 3,572,916,667 mm4

- Distance from neutral axis to the extreme tension fiber yt: 175 mm

7 Checking for maximum reinforcement :

The maximum amount of nonprestressed reinforcement shall be such that :

c/de ≤ 0.42Where:

de = (As*fy*ds)/(As*fy)

- de : the corresponding effective depth from the extreme compression fiber to the centriod of the tensile force in the tensile reinforcement (mm)

8 Checking for minimum reinforcement :

The minimum amount of nonprestressed reinforcement shall be such that :

ρmin ≥ 0.03f'c/f'y

− ρmin : ratio of tension reinforcement and effective concrete area ρmin=As/Ac

- Area of tension reinforcement As = 3,927 mm2

- Effective area of concrete Ac = 283,500 mm2

ρmin=As/Ac 0.0139 0.03f'c/f'y = 0.0023

9 Control cracking by distribution of reinforcement:

Checking load combination is Service load

Condition:

fs≤ fsa = Z/(dcA)1/3 ≤ 0.6 f'y

Project: Trung Luong - My Thuan Expressway

dc: depth of concrete measured from extreme tension fiber to center of bar located closest hereto, for calculation purpose, the thickness

of clear cover used to compute dc shall not be taken to be greater than 50mm

A: Area of concrete surrounding tension reinforcement

Z: crack width parameter

+ 30 kN/mm for members in moderate exposure conditions

+ 23 kN/mm for members in severe exposure conditions

+ 17.5 kN/mm for buried structures

+ f'y : Specified yield strength of compression reinforcement 400 Mpa

10 Checking axial compression:

Axial resistance of components shall be taken as: P r = ϕ P n

For members with spiral reinforcement:

For members with tie reinforcement: Pn = 0.8 [0.85f'c(Ag-Ast) + fyAst]

ϕ: axial compression factor 0.75

Ag: gross area of section 350,000.0 mm2

Ast: total area of longitudinal reinforcement 7,854.0 mm2

Pn: nominal axial resistance 9,493,052.9 N

Pr: calculation axial resistance 7,119,789.67 N

Pn = 0.85 [0.85f'c(Ag-Ast) + fyAst]

Item Box Culvert 4x4M Section: Bottom Slab (Checking to X axis - cross section of box culvert )

CHECKING SHEAR RESISTANCE

Materials

Elastic modulus of Prestressing Steel Ep 197,000 MPa Elastic modulus of Reinforcement Es 200,000 MPa

Compress strength of concrete f' c 30 MPa

+ V s : nominal shear resistance of reinforcement A y *f y *d v *(cosq+cosa)*sina)/s

Distance from extreme tension fiber to the centroid tensile reinforcement

- Quantity

Distance from extreme compression fiber to the centroid tensile reinforcement

* α : angle of inclination of transverse reinforcement to longitudinal axis

* b : factor indicating ability of diagonally cracked concrete to transmit tension

* q : inclination angle of diagonal compressive stress

Xác định b & q Factor indicating ability of diagonally cracked concrete to transmit tension β 3.8

V p Component of effective prestresed force in the direction of the applied shear V p 0N

Checking region requiring transverse reinforcement: V u và 0.5ϕ(V c +V p ) Unncessary

Minimum tranverse reinforcement within distance s s: A v 170.479 mm2

Data of transverse reinforcement

- Area of cross section of shear reinforcement A v1 - mm2

Nominal shear resistance of reinforcement V s1 - N

Item Box Culvert 4x4M Section: Bottom Slab (Checking to X axis - cross section of box culvert )

- Area of cross section of shear reinforcement A v2 - mm2

Nominal shear resistance of reinforcement V s2 - N

Checking: V r = 395,636 > V u = 162,846 Satisfactory

Project: Trung Luong - My Thuan Expressway

CHECKING FLEXURAL & AXIAL RESISTANCE

The factored flexural resistance Mr shall be taken as: M r =ϕM n

Where :

- Mn : Nominal resistance

- ϕ : Resistance factor as specified in Article 5.5.4.2

- As : Area of nonprestressed tension reinforcement

- A's : Area of compression reinforcement

- fy : Specified yield strength of tension reinforcement

- f'y : Specified yield strength of compression reinforcement

- ds : Distance from extreme compression fiber to the centiod of nonprestressed tension reinforcement

- d : Distance from extreme tension fiber to the centriod of nonprestressed tension reinforcement

- d's : Distance from extreme compression fiber to the centriod of compression reinforcement

- a : Depth of the equivalent stress block = c β1

- c : Distance from neutral axis to the extreme compression fiber = [Asfy-A'sf'y]/(0.85f'cβ1b)

Specified yield strength of tension reinforcement fy 400 MPa

Specified yield strength of compression reinforcement f'y 400 MPa

Specified compressive strength of concrete f'c 30 MPa

Modulus of elasticity of steel Es 200,000 MPa

Modulus of elasticity of concrete Ec 29,440 MPa

Project: Trung Luong - My Thuan Expressway

Mcr = frIg/yt

- Modulus of rupture of concrete fr = 0.63f'c

0.5

3.45 Mpa

- Moment of inertia of gross concrete section Ig : 3,572,916,667 mm4

- Distance from neutral axis to the extreme tension fiber yt: 175 mm

7 Checking for maximum reinforcement :

The maximum amount of nonprestressed reinforcement shall be such that :

c/de ≤ 0.42Where:

de = (As*fy*ds)/(As*fy)

- de : the corresponding effective depth from the extreme compression fiber to the centriod of the tensile force in the tensile reinforcement (mm)

8 Checking for minimum reinforcement :

The minimum amount of nonprestressed reinforcement shall be such that :

ρmin ≥ 0.03f'c/f'y

− ρmin : ratio of tension reinforcement and effective concrete area ρmin=As/Ac

- Area of tension reinforcement As = 565 mm2

- Effective area of concrete Ac = 240,000 mm2

ρmin=As/Ac 0.0024 0.03f'c/f'y = 0.0023

9 Control cracking by distribution of reinforcement:

Checking load combination is Service load

Condition:

fs≤ fsa = Z/(dcA)1/3 ≤ 0.6 f'y

Project: Trung Luong - My Thuan Expressway

dc: depth of concrete measured from extreme tension fiber to center of bar located closest hereto, for calculation purpose, the thickness

of clear cover used to compute dc shall not be taken to be greater than 50mm

A: Area of concrete surrounding tension reinforcement

Z: crack width parameter

+ 30 kN/mm for members in moderate exposure conditions

+ 23 kN/mm for members in severe exposure conditions

+ 17.5 kN/mm for buried structures

+ f'y : Specified yield strength of compression reinforcement 400 Mpa

10 Checking axial compression:

Axial resistance of components shall be taken as: P r = ϕ P n

For members with spiral reinforcement:

For members with tie reinforcement: Pn = 0.8 [0.85f'c(Ag-Ast) + fyAst]

ϕ: axial compression factor 0.75

Ag: gross area of section 350,000.0 mm2

Ast: total area of longitudinal reinforcement 1,131.0 mm2

Pn: nominal axial resistance 7,478,839.6 N

Pr: calculation axial resistance 5,609,129.71 N

Pn = 0.85 [0.85f'c(Ag-Ast) + fyAst]

Item Box Culvert 4x4M Section: Bottom Slab (Checking to Y axis - longitudinal section of box culvert )

CHECKING SHEAR RESISTANCE

Materials

Elastic modulus of Prestressing Steel Ep 197,000 MPa Elastic modulus of Reinforcement Es 200,000 MPa

Compress strength of concrete f' c 30 MPa

+ V c : nominal shear resistance of concrete 0.083*b*(f' c )^0.5*b w *d v

+ V s : nominal shear resistance of reinforcement A y *f y *d v *(cosq+cosa)*sina)/s

Distance from extreme tension fiber to the centroid tensile reinforcement

- Quantity

Distance from extreme compression fiber to the centroid tensile reinforcement

* α : angle of inclination of transverse reinforcement to longitudinal axis

* b : factor indicating ability of diagonally cracked concrete to transmit tension

* q : inclination angle of diagonal compressive stress

Xác định b & q Factor indicating ability of diagonally cracked concrete to transmit tension β 3.7

V p Component of effective prestresed force in the direction of the applied shear V p 0N

Checking region requiring transverse reinforcement: V u và 0.5ϕ(V c +V p ) Unncessary

Minimum tranverse reinforcement within distance s s: A v 170.479 mm2

Data of transverse reinforcement

Angle of inclination of transverse reinforcement to longitudinal axis

+ V p : component of effective prestresed force in the direction of the applied shear

Angle of inclination of transverse reinforcement to longitudinal axis

- Quantity

Item Box Culvert 4x4M Section: Bottom Slab (Checking to Y axis - longitudinal section of box culvert )

- Area of cross section of shear reinforcement A v2 - mm2

Nominal shear resistance of reinforcement V s2 - N

Checking: V r = 384,117 > V u = 27,468 Satisfactory