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# 第四章 结构设计方法 Chapter 4 Design Approach

Chapter 4 Design Approach

Questions
1 What working states should be considered for practical structures? 2 How to ensure the safety and serviceability of your design?

3 What factors must be considered to ensure the safety and serviceability?

◆ Design of engineering structures should ensure that the structures are Safe、 Probability and Economical. ◆ A great deal of uncertainties exist in the practical engineering structures.

◆ The objective of design methods for structures
is to study different uncertainty and to find a

balance point between safety and economy.

◆ 工程结构的设计需要保证安全可靠(safety and

probability)、经济合理
◆ 由于实际工程结构中存在多种不确定性
◆ 结构设计方法就是研究工程设计中的各种不确定

◆Allowable Stress Design Method

f ? ? [? ] ? ? Safety coefficient K 安全系数
◆ Safety Coefficient

Material strength 材料强度

K is bigger than 1.0. K，the safety degree of structure

◆ With the increasing of

will increase and the amount of materials used will increase, too.
◆ To find a balance point between safety and economy, It

should select an appropriate K through the consideration of different uncertainties.

◆容许应力设计方法 allowable stress

◆ 安全系数(Safety Coefficient) K 是一个大于1.0的数值 ◆ K 越大，结构安全度就越高，同时结构材料用量也越多

◆ 为取得安全可靠与经济合理的均衡(balance)， 在综合考

◆ What is studied in material mechanics is， linear elastic homogenous material and simple structure. ◆ Practical engineering structure is much complex than it. ◆ Considering the structure safety, the ultimate flexural capacity should be determined for the flexure of RC beam. ◆ It is needed to determine the flexural behavior of this state for controlling the cracks and the deformation during the service time. ◆ Allowable stress design method is not applicable.

◆ ◆ ◆

◆ So according to the structure function, firstly it should have a scientific definition of the safety.
◆ In

addition，it is needed to study the effects of different external influence on the structure.

◆ External

influence：Loads, Temperature change, Settlement, Shrinkage, Creep, Earthquake, Corrosion, Freeze-Thaw.
the variation of the structural sizes and material strength. And then the Structural Reliability can be defined reasonably.

◆ Also

◆ 因此，首先根据工程结构需要满足实际使用的各种

◆ 另一方面，需要尽可能详细了解结构在不同情况下

（施工、使用、破坏）可能受到的各种外界影响的 大小和变化情况

◆ 以及结构尺寸、材料强度等的变异(Variation)情况，

4.1 Functions of Structure
◆ Safety

◎ For M≤Mu， V≤Vu ， N≤Nu

◎ During the predetermined Design Life(50 year),
the structure should support the actions of all

◎ The structure should keep the stability and not

collapse during or after the accident even happens.

4.1 结构的功能

4.1 结构的功能 Functions of Structure ◆ 安全性 Safety
◎ 如（M≤Mu） ◎ 结构在预定的使用期间内（Design Life 一般为50年），

◎ 在偶然事件（如地震、爆炸）发生时和发生后，结构应

4.1 结构的功能

◆ Serviceability
◎ For f ≤[ f ] ◎ During the service time, the structure should

work condition-well.

◆ Durability
◎ For wmax≤[ wmax]

◎ Under the normal service condition, the structure

should have enough durability.
4.1 结构的功能

◆ 适用性 Serviceability ◎ 如（f ≤[ f ]） ◎ 结构在正常使用期间，具有良好的工作性能。如不发生影 响正常使用的过大的变形（挠度、侧移）、振动（频率、 振幅），或产生让使用者感到不安的过大的裂缝宽度。 ◆ 耐久性 Durability ◎ 如（wmax≤[ wmax]） ◎ 结构在正常使用和正常维护条件下，应具有足够的耐久性。 即在各种因素的影响下（混凝土碳化、钢筋锈蚀），结构 的承载力和刚度不应随时间有过大的降低，而导致结构在 其预定使用期间内丧失安全性和适用性，降低使用寿命。

4.1 结构的功能

◆ Reliability

Reliability—A sum of safety, serviceability and durability. Reliability is the ability of accomplishing the predetermined structural functions under the specified condition in the design life. The building cost will increase with the increase of the reliability.

4.1 结构的功能

◆ Structure Reliability 结构的可靠性

■ 结构可靠性越高，建设造价投资越大。 ■

4.1 结构的功能

■ It

is restricted by many factors, such as economic power of one country, design life, maintenance and repair.

■ The design method of the specification is the minimum requirements. ■ Designer may improve the design level and the reliability of the structure according to different conditions.

4.1 结构的功能

■ 显然这种可靠与经济的均衡受到多方面的影响，如国家

■ 规范规定的设计方法，是这种均衡的最低限度，也是国

■ 设计人员可以根据具体工程的重要程度、使用环境和情

4.1 结构的功能

4.2 Limit State A limit state is that loading condition which, if exceeded, will render the structure unserviceable.

M < Mu f < [f]

M = Mu f = [f]

M > Mu f > [f]

wmax< [wmax] wmax= [wmax] wmax> [wmax]
4.2 极限状态

4.2 极限状态

Limit State

◆ 结构能够满足功能要求而良好地工作，则称结构是“可靠”

◆ 区分结构“可靠”与“失效”的临界工作状态称为“极限

M < Mu f < [f]

M = Mu f = [f]

M > Mu f > [f]

wmax< [wmax] wmax= [wmax] wmax> [wmax]
4.2 极限状态

3.2 极限状态 Limit State (P.35)
◆ 结构能够满足功能要求而良好地工作，则称结构是“可靠”

◆ 区分结构“可靠”与“失效”的临界工作状态称为“极限

A limit state is that loading condition which, if exceeded, will render the structure unserviceable. 安全性 承载力能力极限状态 正常使用极限状态 不安全 不适用性 不耐久性
3.2 极限状态

Ultimate Limit State
If exceeded this state, the structure will unsafe. An ultimate limit state occurs at the collapse, or partial collapse, of a structure. ◆ Maximum load capacity occurs in the structure or members. ◆ Structure or part of it is overbalance. ◆ The plastic deformation is too big to service normally. ◆ The structure becomes an automotive system. ◆ Structure or part of it is unstable.
4.2 极限状态

Ultimate Limit State

An ultimate limit state occurs at the collapse, or partial collapse,
of a structure. ◆ 结构或构件达到最大承载力（包括疲劳）

◆ 结构整体或其中一部分作为刚体失去平衡（如倾覆、滑移）
◆ 结构塑性变形过大而不适于继续使用 ◆ 结构形成几何可变体系（超静定结构中出现足够多塑性铰） ◆ 结构或构件丧失稳定（如细长受压构件的压曲失稳）

4.2 极限状态

Serviceability Limit State
An serviceability limit state is produced by
excessive the deflection, cracking, or vibration.

◆ Excessive deformation or lateral displacement;
◆ Excessive cracks; ◆ Excessive vibration; ◆ Others

4.2 极限状态

Limit State

An serviceability limit state is produced by excessive the
deflection, cracking, or vibration.
◆ 过大的变形、侧移（影响非结构构件、不安全感、不能正

◆ 过大的裂缝（钢筋锈蚀、不安全感、漏水等）； ◆ 过大的振动（不舒适）； ◆ 其他正常使用要求。

4.2 极限状态

An ultimate limit state is necessary to determine the maximum load carrying capacity of a structure.

An serviceability limit state is necessary to ensure satisfactory behavior under working load condition.

4.2 极限状态

S < R Reliable

Expression of structural function

S——Action Effect Effects of the action applied to the structures like bending moment M, axial force N, shear force V, moment of torsion T, deflection f, crack width w.

S = R limit state S > R Unreliable

S = S(Q)

M ?

1 2 pl 8

Refers to Structural Mechanics

R——Resistance The ability to resist the effects of the structure like Mu, Vu, [f], [w].

R = R(fc, fy, A, h0, As, …)
Primary content of this course

f y As ? ? M u ? f y As ? ?h0 ? (1 ? k2 ) ? ? k1 ? f c ? b ? ?
4.2 极限状态

S < R 可靠
S = R 极限状态 S > R 失效 S——作用效应 Action Effect 结构上的作用（使结构产生内力和变形的原因，如荷载、 不均匀沉降、温度变形、收缩变形、地震等）引起的效应 如弯矩M、轴力N、剪力V、扭矩T、挠度 f、裂缝宽度 w 等 1 2 S = S(Q) M ? pl 结构力学的主要内容 8 R——结构抗力 Resistance 结构抵抗作用效应的能力，如受弯承载力Mu、受剪承载 力Vu、容许挠度[f]、容许裂缝宽度[w]

R = R(fc, fy, A, h0, As, …) M ? f A ? ?h ? (1 ? k ) ? f y As ? u y s ? 0 2 ?

?

k1 ? f c ? b ?

4.2 极限状态

4.3 Uncertainties and unexpected deviations factor in Design

1 M ? ( g ? q )l 2 8

★ Dead Load g is related to the member sizes and the material density. ★ Live Load q changes from time to time. ★ The inaccuracy of the span l . ★Variability of material strength fy and fc ★Construction error of sectional sizes h0 and b . ★Stress-strain relationship coefficient k1 and k2

f y As ? ? M u ? f y As ? ?h0 ? (1 ? k2 ) ? ? k1 ? f c ? b ? ?

M ? Mu
No always means safety

4.3 结构中的不确定性

4.3 结构设计中的不确定性
Uncertainties and unexpected deviations factor in Design

1 M ? ( g ? q )l 2 8

★ 计算跨度 l 的不准确

f y As ? ? M u ? f y As ? ?h0 ? (1 ? k2 ) ? ? k1 ? f c ? b ? ?

★材料强度 fy 和 fc 的离散 ★截面尺寸h0和 b 的施工误差 ★应力-应变关系参数 k1 和 k2

M ? Mu

4.3 结构中的不确定性

4.4 Design Methods
A great deal of uncertainties exist in the practical engineering structures. The objective of design methods of structures is to study different uncertainty and to find a balance point between safety and economy.
◆ Allowable

Stress Design

f ? ? [? ] ? k
The working stress design method is adequate when material stresses are low. The method models the behavior of a member under service loads satisfactorily but provides an unsatisfactory indication of conditions as loading increases and failure approaches.
4.4 结构设计方法

4.4 结构设计方法

f ? ? [? ] ? k
4.4 结构设计方法

4.4 Design Methods
A great deal of uncertainties exist in the practical engineering structures. The objective of design methods of structures is to study different uncertainty and to find a balance point between safety and economy.
◆ Allowable

Stress Design
f ? ? [? ] ? k

◎ The structural behavior of RC members is not elastic； ◎ Once a point of the structure reaches the allowable stress, it is considered to be fail； ◎ Safety coefficient is defined from experience.
4.4 结构设计方法

◎ No take into account the multiplicity of the structural function；

4.4 结构设计方法

f ? ? [? ] ? k
◎ 钢筋混凝土结构的受力性能不是弹性的； ◎ 结构中一点达到容许应力，结构即认为失效；

◎ 没有考虑结构功能的多样性要求；
◎ 安全系数是凭经验确定的，缺乏科学依据。
4.4 结构设计方法

◆ Design for damage stage

Mu M ? K
It is considered to be fail only when the whole section reaches the ultimate load capacity. And it takes into account the plastic behavior of the materials makes the most of the strength. The ultimate load can be testified by the experiment and the whole safety of the member is definite. ◎ Safety coefficient is also defined from experience. ◎ No take into account the multiplicity of the structural function.

4.4 结构设计方法

◆ 破损阶段设计法

Mu M ? K

◎没有考虑结构功能的多样性要求的问题。

4.4 结构设计方法

◆Limit State Design It is required the design of not only limit state of bearing capacity, but limit state of serviceability. For the former one, it selects different safety coefficients for different situations.

f ck f sk M (? kqi qik ) ? M u ( ， ，As，b，h0， ) ? kc k s

4.4 结构设计方法

◆极限状态设计法(Limit State Design)

f ck f sk M (? kqi qik ) ? M u ( ， ，As，b，h0， ) ? kc k s
◎ 材料强度 fck 和 fsk 是根据统计后按一定保证率取其下限分 位值，反映的材料强度的变异性。 ◎ 荷载值 qik 也尽可能根据各种荷载的统计资料，按一定保证 率取其上限分位值。 ◎ 荷载系数 kqi ，材料强度系数 kc 和 ks 仍按经验确定，但对 于不同荷载的变异大小，可取不同的荷载系数。
4.4 结构设计方法

◆ Limit State Design Based on the Probability Theory
Because of the uncertainties in the practical structures, all the structures have the possibility of unreliable. The probability theory is reasonable to express the reliability.

Failure Probability

Pf = P (S > R)

Failure probability decreases when the structure’s reliability increases. The measuring of structural reliability in probability is Reliability Degree. When the failure probability Pf is less than some value, it is then considered the structure is reliable. And this value is called Allowable Failure Probability [Pf].
4.4 结构设计方法

◆以概率理论为基础的极限状态设计法

Failure Probability

Pf = P (S > R)

Structural function expression
Z=R-S

f(Z)

b?z

Pf =P (S >R) =P(Z< 0)

?Z Pf ? b ? mZ
b?值

Pf

mz

Z=R- S

b —Reliability Index
3.2 6.9×10-4 3.7 1.1×10-4 4.2 1.3×10-5

4.4 结构设计方法

f(Z)

b?z

?Z Pf ? b ? mZ

Pf

mz

Z=R- S

b —可靠指标 Reliability Index
b?值

4.4 结构设计方法

◆ According to the statistics, the death rate per year of

electroshock is 6×10-6

◆ When b =3.7，Pf=1.1×10-4，design life is 50 years， then the failure probability per year is1.1×104/50=2.2×10-6

◆ Structure will not failure instantly after 50 years and its failure probability will increase.
4.4 结构设计方法

◆ 根据统计，触电的年死亡率为6×10-6 ◆ b?=3.7时，Pf=1.1×10-4，按设计基准期50年考虑，

◆ 50年后并不是结构就失效，而是失效概率增加。

◆ 我国对于一般工程结构，当为延性破坏时，其可

◆ 对于重要的工程结构，应提高可靠指标。

4.4 结构设计方法

◆ 作用：使结构产生内力和变形的原因，分为直接作用和间接作 用两种。

★偶然荷载（作用）：爆炸力、撞击力。 桥梁：P.312 ◆ 作用效应(S)：结构上的作用使结构产生的内力（弯矩、剪力、 扭矩）和变形、裂缝的统称。

3.4 结构设计方法

δ ?

σ

m

m?

?x
i ?1

n

i

n

??

( m ? xi ) 2 ? n
3.2.3 极限状态设计法

◆材料强度标准值：根据统计分析可以确定一个具有一定保证 率（95%）的下限强度分位值，该特征值称为材料强度标准值

（符号fc，fs）。材料强度标准值=μ-1.645σ

P.58

3.2.3 结构设计方法

◆分项系数:考虑目标可靠指标的等价作用。P.59 荷载设计值=荷载标准值*荷载分项系数( 恒载分项系数一般取γG

= 1.2，活载分项系数一般取γQ = 1.4） ； P.60

3.4 结构设计方法

Standard Value Sk of Action Effects
◆ The uncertainties of the effects S is determined by the uncertainties of the action Q. ★Dead Load G S ? C ?Q ★Live Load Q S ? C ? G ? C ? Q1 ? ? ★Accidental Load
G Q1

Accidental action consist of fire, explosion, severe earthquake. 4.4 结构设计方法

◆ 作用效应S的不确定性就主要取决于结构上作用Q的不确定性 ★永久荷载G S ? C ?Q ★可变荷载Q S ? CG ? G ? CQ1 ? Q1 ? ? ★偶然荷载（作用） ★永久荷载G

★可变荷载Q

★偶然荷载（作用）

Accidental action consist of fire, explosion, severe earthquake.
4.4 结构设计方法

Standard Value Sk of Action Effects
◆ The uncertainties of the effects S is determined by the uncertainties of the action Q.

S ? C ?Q

S ? CG ? G ? CQ1 ? Q1 ? ?

S k ? CG ? Gk ? CQ1 ? Q1k ? ?? Qi ? CQi ? Qik
i ?2

n

4.4 结构设计方法

◆ 作用效应S的不确定性就主要取决于结构上作用Q的不确定性 ★永久荷载G S ? C ?Q ★可变荷载Q S ? CG ? G ? CQ1 ? Q1 ? ? ★偶然荷载（作用） ◆ 不同的荷载，其变异情况不同。根据统计分析可以确定一个 具有一定保证率（如95%）的上限荷载分位值，该特征值称 为荷载标准值（符号Gk，Qik）。 ◆ 按荷载标准值确定的荷载效应，称为荷载效应标准值Sk ◆ 有多个可变荷载同时作用的情况，考虑到它们同时达到标准 值的可能性较小，考虑荷载组合系数?，

S k ? CG ? Gk ? CQ1 ? Q1k ? ?? Qi ? CQi ? Qik
i ?2
4.4 结构设计方法

n

Standard Value Rk of Structure Reactance

Rk ? R( f ck，f sk，As，b，h0， ) ?
fck、fsk are standard strength value of rebar and concrete,
respectively. The value of b、h0 and As is design value.
f(S) f(R)

Sk

S

Rk
4.4 结构设计方法

R

Rk ? R( f ck，f sk，As，b，h0， ) ?
fck、fsk分别为混凝土和钢筋的强度标准值，截面尺寸b、h0和 配筋As取设计值。
f(S) f(R)

Sk

S

Rk
4.4 结构设计方法

R

Design Expression
f (S)，f (R)

Rk

Sk

S，R

4.5 结构设计方法

Design Expression
f (S)，f (R)

SkRk

S，R

4.5 结构设计方法

Design Expression
f (S)，f (R)

Sk

Rk

S，R

Pf = [ Pf]
4.5 结构设计方法

◆以概率理论为基础的极限状态设计法
f (S)，f (R)

μR-μS

S
S*

R

μS

R*

μR

S，R

P.59 图4-5

Pf = [ Pf]
3.5 结构设计方法

S* ? R *
S* ? ? S ? Sk

Pf ? [Pf ]

Design value of effects，?S Sub coefficient of effects Load factor
n

S * ? ? S ? S k ? ? G ? CG ? Gk ? ? Q1 ? CQ1 ? Q1k ? ?? Qi ? ? Qi ? CQi ? Qik
i ?2

R* ?

?R

Rk

Design value of structure reactance，?R Sub coefficient of structure reactance

Strength reduction factor

R* ?

?R

Rk

f ck f sk ? R( ， ，As，b，h0， ) ?

?c ?s

4.5 结构设计方法

S* ? R *
S* ? ? S ? Sk

Pf ? [Pf ]

n

S * ? ? S ? S k ? ? G ? CG ? Gk ? ? Q1 ? CQ1 ? Q1k ? ?? Qi ? ? Qi ? CQi ? Qik
i ?2

R* ?

?R

Rk

Strength reduction factor

R* ?

?R

Rk

f ck f sk ? R( ， ，As，b，h0， ) ?

?c ?s

4.5 结构设计方法

Load factor compensate the following factors: ? The unfavorable deviation of the loading from the nominal value ? Uncertainties in the methods of analysis ? Unexpected deviations in structural behavior ? The reduced probability of the full nominal loads, in a combination of loads, being present simultaneously

Strength reduction factor compensate the following factors: ? The possibility of adverse variations in material strength ? Dimensional inaccuracies ? Inadquate workmanship ? The strength of the material in the structure being less than that of the control specimens ? The degree of importance of the member to the integrity of the structure

Expression from Specification
n f f ? ? ? 0 ? ? G ? CG ? Gk ? ? Q1 ? CQ1 ? Q1k ? ?? Qi ? ? Qi ? CQi ? Qik ? ? R( ck ，sk ，A，b，h0， ) ? ?c ?s i ?2 ? ?

?0 ——Structure Importance Coefficient

?G ?Q

In the Serviceability Limit State, all of the sub coefficient are 1.0.
4.5 结构设计方法

n f f ? ? ? 0 ? ? G ? CG ? Gk ? ? Q1 ? CQ1 ? Q1k ? ?? Qi ? ? Qi ? CQi ? Qik ? ? R( ck ，sk ，A，b，h0， ) ? ?c ?s i ?2 ? ?

?0 ——结构重要性系数

?G ?Q

4.5 结构设计方法

Design Value of Material Strength

fc ?

?c

f ck

fy ?

f yk

?s

f y?

4.5 结构设计方法

210 300 360

fc ?

?c

f ck

fy ?

f yk

?s
C40 19.1 1.71 C80 35.9 2.22
f y?

4.5 结构设计方法

210 300 360

Key notes
1 Limit states: Ultimate and Serviceability 2 Reliability of structure 3 Failure probability ---- Degree of reliability 4 Action and action results ---- Design value 5 Resistance ---- design value 6 Practical design formula

★基本述语（45-46）
★作用、材料强度的标准值（47） ；作用效应、

★失效概率、可靠指标（40）

★极限状态：点→截面→构件→结构
★结构可靠度——可靠性的概率度量

★失效概率、可靠指标
★作用—— ★作用效应—— ★作用效应设计值—— ★结构抗力——

★材料强度设计值——