地下建筑结构课程设计隧道衬砌设计(英文)

2

Allowable compressive strength:

f

c

=

14.3

N/mm

2

Allowable tensile strength:

f

t

=

1.43

N/mm

2

The type of steel bars: HRB335

Allowable strength:

f

y

= f

y

’

= 300

N/mm

2

Bolt:

Yield strength:

f

By

=

240

N/mm

2

Shear strength:

?

B

=

150N/mm

2

3 Design Method Requirement

(1)How to check member forces:

①

Elastic equation method(option)

②

Force method based on the textbook (must do this)

③

Bedded frame model(Beam element with elastic support)(option)

K

0

P

?

const ant of rotation spring for positive moment at join t=18070

kN

?

m

/

rad

K

0

N

?

constant of rotation spring for negative moment at joint=32100

kN

?

m

/< /p>

rad

< /p>

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(2)How to calculate reinforcement for segmental lining:Limit state method

①

Based on the national code GB50010

-

2002 for reinforcement concrete design.

②

Please choose the grade of concrete and the type of steel rebars.

Bolt:

yield strength

f

By

?

240

MN

/

m

2

shear strength

?

B

?

150

MN

/

m

2

Part Two: Computation by Force Method

1 Load Conditions

(1)Judgment of Tunnel Type (by Terzaghi’s formula)

Figure 1

Judgment of tunnel type

So the designed tunnel is a

shallow tunnel

.

(2)Load Types and Partial Factors

Table 1 shows the loads should be considered in the design and corresponding partial factors.

Table 1

Load Types and Partial Factors

Load Types

Partial Factors

Surcharge

1.4

Dead Load

1.2

Water Pressure

Earth Pressure

1.2

1.2

Subgrade Reaction

1.2

(3)Computation of Loads

Computational element is a 1.2 meter (width of segment) part along the longitudinal direction,

and Figure 2 shows the load condition to compute member forces of the segmental lining.

Figure 2

Load condition of the designed tunnel

①

Vertical Pressure at the Tunnel Crown

Earth Pressure

Water Pressure

②

Vertical Pressure at the Tunnel Bottom

③

Lateral Pressure at the Tunnel Crown

Earth Pressure

Water Pressure

④

Lateral Pressure at the Tunnel Bottom

Where

D

c

?

Computational diameter

?

0

?

t

?

9.5

?

0.4

9.1

m

⑤

Average Self

-

weight

Where

?

c

?

Unit weight of RC segment

?

26

kN

/

m

3

⑥

Lateral Resistance Pressure

Where

?

= Displacement of lining at tunnel spring

?

= Reduction factor of model rigidity = 0.8

E

= Modulus of elasticity of segment =

3.0

?

10

4

N

/< /p>

mm

2

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.

I

= Moment of inertia of area of segment =

1

?

1. 2

?

0.4

3

?

6.4

?

10

?

3

m

4

12

k

= Coefficient of reaction =

60

MN

/

m

3

?

= the angle of measured from the vertical direction around the tunnel

2 Computation of Member Forces

Figure 4 shows the simplified model of the segmental lining.

Figure 3

Simplified model diagram for calculation

(1)Calculation Data

K

?

P

?

18070

kN

g

m

/

rad

(if inside part of lining is tensile)

K

< br>??

?

32100

kN

g

m

/

rad

(if outside part of lining is tensile)

(2)Coefficients Calculation

NOTE:

if the joint just located at 180 degree of the half

-

ring lining, then its stiffness contribution

to the whole structure should be considered as half of the total value.

The value of coefficients by force

-

method equations can be summarized as shown in Table 2.

Table 2

Coefficients in Force

-

method Equations

Coefficients

Values

Then the bending moment and axial force (per 1.2 m) acting at the crown can be obtained by

the following equations:

(3)Member Forces

For loading case 1,

For loading case 2,

For loading case 3,

For loading case 4,

For loading case 5,

For loading case 6,

So the internal forces caused by surrounding pressures can be determined by accumulating

the six loading cases, that is:

Where

M< /p>

pj

,

N

pj< /p>

,

Q

pj

are the bending moment, the axial force and the shear force (per unit

length) under the j

th

loading case, respectively.

Then the total internal forces (i.e. the total bending moment, M, the total axial force, N, the

total

shear

force,

Q)

per

unit

length

(1.2m)

along

the

lining

can

be

obtained

by

the

following

equations:

Where

And with MATLAB software, the maximum (positive and passive) moment, axial force, and

shear force, which is shown in the Table 3. (The original code of MA

TLAB can be

seen in the

addendum.)

Table 3

Member force of the segmental lining