固态水(完整版)房屋建筑毕业设计 4外文翻译

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毕业设计

(

论文

)

外文翻译

设计（论文）题目：

宁波天合家园某住宅楼

2

号轴框架结构设计与建筑制图

学

院

名

称：

建筑工程学院

专

业：

土木工程

指

导

教

师：

马永政、陶海燕

2012

年

12

月

10

日

外文原稿

1

Tension Stiffening

in Lightly Reinforced Concrete Slabs

1R. Ian Gilbert1

Abstract:

The

tensile

capacity

of

concrete

is

usually

neglected

when

calculating the strength of a reinforced concrete beam or slab

even though concrete continues to carry tensile stress between the cracks

due

to

the

transfer

of

forces

from

the

tensile

reinforcement

to

the

concrete

through bond. This contribution of the tensile concrete is known as tension

stiffening

and

it

affects

the

member's

stiffness

after

cracking

and or

slab

eventhough

concrete

continues

to

carry

tensile

stress

between

thecracks

due

to the transfer of forces from the tensile reinforcementto the concrete

through bond. This contribution of the tensileconcrete is known as tension

stiffening

and

it

affects

the

member'sstiffness

after

cracking

and amount

permittedby

the relevant building code. For such members

the

flexuralstiffness

of

a

fully

cracked

cross

section

is

many

times

smallerthan that of an uncracked cross section

and

tension

stiffeningcontributes

greatly

to

the

stiffness

after

cracking.

In design

deflectionand

crack

control

at

service-load

levels

are

usually

thegoverning

considerations

and accurate modeling of the stiffnessafter cracking is required.

The

most

commonly

used

approach

in

deflection

calculationsinvolves

determining

an

average

effective

moment

of

inertia

[Ie]for

a

cracked

member.

Several different empirical equations areavailable for Ie

including

the

well-known

equation

developed

byBranson

[1965]

and

recommended in ACI 318 [ACI 2005]. Othermodels for tension stiffening are

included in Eurocode 2 [CEN1992] and the [British Standard BS 8110 1985].

Recently

Bischoff [2005] demonstrated that Branson's equation grossly overestimates

thtie

average

sffness

of

reinforced

concrete

memberscontaining

small

quantities of steel reinforcement

and moment

reaches

the

flexural

tensile

strength

of

the

concrete

or

modulus

of rupture

fr. There is a sudden change in the local stiffness at and immediately

adjacent to this first crack. On the section containing the crack

the flexural stiffness drops significantly

but much of the beam remains uncracked. As load increases

more cracks form and the average flexural stiffness of the entire member

decreases.

If

the

tensile

concrete

in

the

cracked

regions

of

the

beam

carried

no

stress

the load-deflection relationship would follow the dashed line ACD in Fig.

1. If the average extreme fiber tensile stress in the concrete remained at

fr after cracking

the

loaddeflection

relationship

would

follow

the

dashed

the

actual

response lies between these two extremes and is shown in Fig. 1 as the solid

line AB. The difference between the actual response and the zero tension

response is the tension stiffening effect

（

in Fig. 1

）

.

As the load increases

the average tensile stress in the concrete reduces as more cracks develop

and the actual response tends toward the zero tension response

at

least

until

the

crack

pattern

is

fully

developed

and

the

number

of

cracks

deflection calculations.

for Tension Stiffening

The instantaneous deflection of beam or slab at service loads may be

calculated from elastic theory using the elastic modulus of concrete Ec and

an effective moment of inertia

Ie. The value of Ie for the member is the value calculated using Eq. [1]

at

midspan

for

a

simply

supported

member

and

a

weighted

average

value

calculated in the positive and negative moment regions of a continuous span

（

1

）

where Icr=moment of inertia of the cracked transformed section;Ig=moment of

inertia

of

the

gross

cross

section

about

the

centroidal

axis

[but

more

correctly

should

be

the

moment

of

inertia

of

the

uncracked

transformed

section

Iuncr];

Ma=maximum

moment

in

the

member

at

the

stage

deflection

is

computed;

Mcr=cracking moment =(frIg yt); fr=modulus of rupture of concrete (=7.5 fc

in psi and 0.6 fc in Mpa); and yt=distance from the centroidal axis of the

gross section to the extreme fiber in tension.

A

modification

of

the

ACI

approach

is

included

in

the

Australian

Standard

concrete may reduce the cracking moment significantly. The cracking moment

is given by Mcr=(fr? fcs)Ig yt

where fcs is maximum shrinkage-induced tensile stress in the uncracked

section at the extreme fibre at which cracking occurs

（

Gilbert 2003

）

.

（

2

）

where

distribution coefficient accounting for moment level and degree of

cracking and is given by

（

3

）

and 1=1.0 for deformed bars and 0.5 for plain bars; 2=1.0 for a single

short- term

load

and

0.5

for

repeated

or

sustained

loading;

sr=stress

in

the

tensile reinforcement at the loading causing first cracking (i.e.

when the moment equals Mcr)

calculated while ignoring concrete in tension; s is reinforcement stress

at loading under consideration (i.e.

when the in-service moment Ms is acting)

calculated while ignoring concrete in tension; cr=curvature at the section

while ignoring concrete in tension; and uncr=curvature on the uncracked

transformed section.

For slabs in pure flexure

if

the

compressive

concrete

and

the

reinforcement

are

both

linear

and

elastic

the ratio sr s in Eq.(3) is equal to the ratio Mcr Ms. Using the notation

of Eq.

（

1

）

Eq.(2) can be reexpressed as

（

4

）

For a flexural member containing deformed bars under shortterm loading

Eq. (3) becomes

=1?

（

Mcr Ms

）

2 and Eq.

（

4

）

can be rearranged to give the

following

alternative

expression

for

Ie

for

short-term

deflection

calculations

(5)

This approach

which .

4parison with Experimental Data

To test the applicability of the ACI 318

Eurocode 2

and BS 8110 approaches for lightly reinforced concrete members

[recently

proposed

by

Bischoff

(2005)]:

the measured moment versus deflection response for 11 simply supported

singly reinforced one-way slabs containing tensile steel quantities in the

range 0.0018<<0.01 are compared with the calculated responses. The slabs

(designated S1 to S3

S8

SS2 to SS4

and Z1 to Z4) were all prismatic

of rectangular section

850 mm wide

and contained a single layer of longitudinal tensile steel reinforcement

at an effective depth d (with Es=200

000 MPa and the nominal yield stress fsy=500 Mpa). Details of each slab are

given in Table 1

including relevant geometric and material properties.

The predicted and measured deflections at midspan for each slab when the

moment at midspan equals 1.1

1.2

and

1.3

Mcr

are

presented

in

Table

2.

The

measured

moment

versus

instantaneousdeflection

response

at

midspan

of

two

of

the

slabs

(SS2

and

Z3)

are compared with the calculated responses obtained using the three code

approaches

in

Fig.

2. Also

shown

are

the

responses

if

cracking did

not

occur

and if tension stiffening was ignored.

sion of Results

It is evident that for these lightly reinforced slabs

tension stiffening is very significant

providing a large proportion of the postcracking stiffness. From Table 2

the

ratio

of

the

midspan

deflection

obtained

by

ignoring

tension

stiffening

to

the

measured

midspan

deflection

(over

the

moment

range

Mcr

to

1.3

Mcr

)is

in the range 1.38-3.69 with a mean value of 2.12. That is

on average

tension

stiffening

contributes

more

than

50%

of

the

instantaneous

stiffness

of a lightly reinforced slab after cracking at service load.

For every slab

the ACI 318 approach underestimates the instantaneous deflection after

cracking

particularly so for lightly reinforced slabs. In addition

ACI

318

does

not

model

the

abrupt

change

in

direction

of

the

moment-deflection response at first cracking

nor

does

it

predict

the

correct

shape

of

the

postcracking

moment- deflection

curve.

The underestimation of short-term deflection using the ACI318 model is

considerably

greater

in

practice

than

that

indicated

by

the

laboratory

tests

reported nature of cracking

the agreement between the Eurocode 2 predictions and the test results over

such a wide range of tensile reinforcement ratios is quite remarkable. With

the ratio of () in Table 2 varying between 0.80 and 1.39 with a mean value

of 1.07

the Eurocode 2 approach certainly provides a better estimate of short-term

behavior than either ACI 318 or BS8110.

sions

Although tension stiffening 11 laboratory tests on slabs containing

varying quantities of steel reinforcement. The Eurocode 2 approach

（

Eq.

（

5

）

并在一个有效深度载有纵向拉伸单层钢筋

d(Es=200000MPa

和屈服应力

=500M Pa)

每个板块的详细情况见表

1

包括有关的几何和材料特性

在每个板跨中挠度的预测结果与实测时

在跨中力矩等于

1.1

1.2

和

1.3Mcr

列出在表

2

与瞬时变形响应的测量力矩的两跨中的板

（

SS2 and Z3

）进行比较和计算结果获得图

2

使用三个代码方式同时显示的结果

如果没有出现开裂

如果张力加劲被忽略

5.

讨论结果

很明显

这些轻型钢筋板

张力加劲非常显著

提供一个大比例的开裂后刚度

从表

2

跨中挠度的比例得到了加劲

对测量张 力跨中挠度忽视（在

Mcr

和

1.3M cr

范围）是在

1.38-3.69

范 围

取平均值

2.12

也就是说

平均而言

张力加劲超过

50

％的一个轻型钢筋板在屈服荷载的瞬间开裂< /p>

对于每一个板

在

ACI 318

的方法低估了瞬间挠度后开裂

特别是对于轻型钢筋板

此外

在这一时刻

ACI 318

突然不成模型

在起初开裂处

突然改变力矩偏转结果的方向

也没有预测的正确形状矩挠度曲线

在短期挠度的低估使用

ACI

318

模式是经化验报告在这里在表示实践中相当大的

比

不同于

Eurocode 2

和

BS 8110

ACI 318

模型不承认或为在开裂的力矩

这将不可避免地减少在实践中出现的由于张力引起的混凝土干燥收缩或热变形

对于许多板

因早期干燥或温度变化在数周内将发生铸件的开裂

以及经常暴露之前

其板全方位服务的负荷

通过限制混凝土拉伸应力水平的拉伸筋只有

1.0 MPa

BS 8110

的方法对测试板的上下挠度和立即高于开裂力矩的高估

由于约束的早期收缩和热变形

这并非不合理和占损失的刚度发生在实践中

不过

BS 8110

提供了一个相对较差模型刚度

并错误地认为

平均拉力混凝土裂缝进行了实际调高

M

增大和中性轴的上升

因此

BS 8110

开裂后力矩偏转斜率图甚至超过了所有板测量斜坡

这种方法使用比

Eurocode 2

或

ACI

两种方式更繁琐

在所有情况下

Eurocode 2

挠度计算

[EPS.(3)-(5)]

是在更接近与实测挠度在整个负载范围内协议

可以看出在图

2

荷载

-

挠度曲线的形状并使用

Eurocode 2

是一个比这更好的代表性实际曲线结果

使用

EP.(1)

考虑到具体的变异材料性能影响的板

该协议

Eurocode 2

在运行特 征和对开裂的随机性之间的预测和试验结果在如此广泛

的受拉钢筋比率是相当显著的

在图

2

（）

0.80

和

1.39

之间的值平均值为

1.07

Eurocode 2

的方法提供了

ACI 318

或

BS 8110

更好地估计短期行为

6.

结论

虽然张力加劲只对重钢筋梁挠度的影响相对较小

这是非常重要的对于

Iuncr ICR

的比例很高的轻型钢筋构件

例如作为最实用的钢筋混凝土楼板

加劲张力的模型纳入

ACI(2005)

Eurocode 2(CEN1993)

和

BS 8110(1985)

已提交并且轻型钢筋混凝土楼板的适用性已进行评估