Combinations

 

 

 

Enter the load combination cases to combine the results of static, construction stage, moving load, response spectrum and dynamic time history analyses.

 

MIDAS/Gen supports the following 5 types of dialog box tabs for load combinations.

 

    • General

 

Combine unit load cases to evaluate serviceability or analysis results irrespective of design codes.

 

    • Steel Design

 

Enter the load combinations for designing steel framing members according to the steel design codes.

 

    • Concrete Design

 

Enter the load combinations for designing RC members according to the RC design codes.

 

    • SRC Design

 

Enter the load combinations for designing SRC members according to the SRC design codes.

 

    • Footing Design

 

Enter the load combinations for designing piles and footings.

 

 

 

From the Main Menu select Results > Combinations.

 

Select Results > Combinations in the Menu tab of the Tree Menu.

 

Shortcut key : [Ctrl]+[F9]

 

 

 

 

Load Combinations dialog box

 

 

The entry methods are similar for each dialog box. Refer to Usage of Table Tool and enter as follows:

 

 

To enter new or additional load combinations

 

Enter the load combination cases by the following 4 methods:

 

 1.  The user directly specifies the load combinations

Directly enter the following basic items necessary to define load combinations in the Load Combination List.

 

No: Numbers are sequentially and automatically assigned in the order of the load combination entries.

 

Name: Enter the load combination name.

 

 

Note
In the case of a construction stage analysis for a bridge structure, the loads applied in the construction stage analysis are integrated into the construction stage loads in the analysis. The analysis results are separately stored as the cases below. We can then obtain the analysis results for the load cases and their combinations for each construction stage. Separate load combinations must be specified for the Post CS using the following load cases and/or general load cases. We cannot however verify the auto-generated load cases below.

 

Dead Load (CS): Dead load including Self Weight included in construction stages

 

Erection  Load (CS): Erection load defined by Load Cases to be Distinguished from Dead Load for CS

Output of Construction Stage Analysis Control

 

Tendon Primary (CS): Analysis results due to  prestressing forces in tendons

 

Tendon Secondary (CS): Indeterminate forces resulting from indeterminate condition of the

structure

 

Creep Primary (CS): Results the (imaginary)  loads causing creep strain

 

Creep Secondary (CS): Real member forces resulting from creep strain due to indeterminate

structure

 

Shrinkage Primary (CS): Results for the (imaginary) loads causing shrinkage strain

 

Shrinkage Secondary (CS): Real member forces resulting from shrinkage strain due to indeterminate

structure

 

Summation (CS): Summation of the results of all the cases above

 

Note
The results for creep and shrinkage are separated to check the results individually.


 

Active: Specify Active if the corresponding load combination is applied in design.

 

Inactive: The corresponding load combination is not applied in the post-processing mode.

 

Active: The corresponding load combination is applied in the post-processing mode. (General tab)

 

Strength/Stress: The corresponding load combination is applied in the post-processing mode (Concrete Design tab) except for the serviceability check (crack and fatigue checks).

 

Serviceability: The corresponding load combination is applied in the post-processing mode (Concrete Design tab) except for the auto-design and strength check of beam members.
 

 

Type: Assign the combination types for analysis results.

 

Add: Linear combination of analysis results

L1 + L2 + ... + M1 + M2 + ... + S1 + S2 + ...+ (R1 + R2 + ...) + T + LCB1 + LCB2 + ... + ENV1 + ENV2 + ...

 

Envelope: Maximum, minimum and maximum of absolute values for individual analysis results

 

CBmax: Max (L1, L2, ..., M1, M2, ..., S1, S2, ...,R1, R2, ..., T, LCB1, LCB2, ..., ENV1, ENV2, ...)

 

CBmin: Min (L1, L2, ..., M1, M2, ..., S1, S2, ...,R1, R2, ..., T, LCB1, LCB2, ..., ENV1, ENV2, ...)

 

CBall: Max (|L1|, |L2|, ..., |M1|, |M2|, ..., |S1|, |S2|, ..., |R1|, |R2|, ..., |T|, |LCB1|, |LCB2|, ..., |ENV1|, |ENV2|, ...)

 

Note
The CBall condition produces the maximum of absolute values; the results are produced in non-directional positive (+) values.

 

ABS: Linear combination of the absolute values of analysis results

 

|L1| + |L2| + ... + |M1| + |M2| + ... + |S1| + |S2| + ...+ (|R1| + |R2| + ...) + |T| + |LCB1| + |LCB2| + ... + |ENV1| + |ENV2| + ...

 

SRSS: Linear combination of the SRSS (Square Root of Sum of the Squares) of response

 spectrum analysis results and other analysis results

 

[L12 + L22 + ... + M12 + M22 + ... + S12 + S22 +...+(R12 + R22 +...) + T2 + LCB12 + LCB22 + ... + ENV12 + ENV22 + ...]½

 

where,

L: static analysis results for a unit load case ▼ scale factor

M: static analysis results for a moving load case ▼ scale factor

S: static analysis results for a settlement load case ▼ scale factor

R: dynamic analysis results for a Response Spectrum case ▼ scale factor

T: dynamic analysis results for a Time History Analysis case ▼ scale factor

LCB: Analysis results for a predefined load combination ▼ scale factor

ENV: Analysis results for a predefined envelop conditions ▼ scale factor

 

Note 1
Among the methods of load combinations, Envelope, ABS and SRSS can be applied in General only.

 

Note 2
We can combine 150 load cases or load combinations in a load combination.

 

Note 3
For the method of calculating principal stresses, effective stresses and maximum shear stresses for each load combination type, refer to the explanations at the bottom of the page.

 

Description: Short descriptions for the load combinations

Enter the unit load cases and the corresponding scale factors included in the relevant load combination as many times as desired.

 

 

Load Case: Select the unit load cases from the load case list or the load combinations defined earlier.

 

 

Factor: Enter the load (scale) factors corresponding to the selected unit load cases or load combinations.

 

 2.  Select built-in design standards to automatically generate load combinations

Click at the bottom of the load combinations dialog box. Select the following items in the displayed load combination auto-generation dialog box. If is clicked, the load combinations are automatically entered as per the design code based on the user-defined unit load cases.

 

Note
When accidental torsional moments are considered in Response Spectrum Analysis, load combinations are generated including the accidental torsional moments (Rx (ES), Ry (ES)).

 

 

Auto Generation Dialog box

 

 

Add : Add the generated load combinations to the previously defined load combinations

 

Replace : Replace the previously defined load combinations with the generated load combinations

 

Add Envelope: Envelope of load combinations is auto-generated. This is applicable in the General tab only.

 

Code Selection

 

Steel: Design code for structural steel

 

Concrete: Design code for reinforced concrete

 

SRC: Design code for steel-reinforced concrete composite sections

 

Footing: Design code for reinforced concrete footings

 

Design Code : Select the design code to be used for the auto-generation of load combinations (Refer to Note for design load combinations for different codes)

 

Scale Up Factor : Enter the seismic load scale factor where the seismic load is considered by the response spectrum analysis

 

Manipulation of Construction Stage Load Case: Select a method of auto-generating load combinations when Construction Stage Analysis has been performed.

 

Note
This function becomes activated only when the construction stage analysis data has been created in the model.

 

ST Only: This option generates load combinations using only (general) static load cases (DL (ST), LL (ST)).

 

CS Only: This option generates load combinations using only construction stage load cases (DL (CS), LL (CS)).

 

ST+CS: This option generates load combinations using both (general) static load cases and construction stage load cases together.

 

Note
When we use such general load types as DL and LL in Static Load Case in a construction stage analysis, the program internally creates both static load case (ST) and construction stage load case (CS). There are a number of possibilities for load combinations using such ST and CS cases.

 

If we wish to reflect the results of the construction stage analysis into design, we need to select the CS Only option. If we select the ST+CS option, the load cases used in the construction stage analysis are accounted for twice in the form of both static load case type and construction stage load case type. If we select the ST Only option, only the static analysis results are included in the design load combinations in which case the construction stage analysis results will be excluded from the design load combinations.

 

When we use the construction stage load (CS) type in a construction stage analysis, only the CS type is created after the analysis. In such a case, we need to select the CS Only option. By the same token, we cannot select the ST Only or ST+CS option because ST type loads do not exist.

 

When we distinguish the ST type and CS type loads in the preparation of data for a construction stage analysis, we need to select the ST+CS option to account for all the loads input in the model.

 

Consider Orthogonal Effect: When seismic forces are applied in two orthogonal directions, the combination effect is considered.

 

Set Load Cases for Orthogonal Effect: Set 2 load cases, which will be considered for Orthogonal Effect.

 

Set Load Cases for Orthogonal Effect dialog box

 

 

100% vs. 30%: 100% of seismic load in one direction and 30% of seismic load in the orthogonal direction are summed in absolute values.  

 

SRSS (Square Root of Sum of Square): 100% of seismic loads in both directions are combined in SRSS.

 

Note 1
While generating the load combinations, the Orthogonal Effect can be applied only to the Load Cases that are specified in "Orthogonal Load Group".

 

Note 2
In case where there are three seismic load cases, say EX, EY and EZ, Orthogonal Effect can be applied to EX-EY, EY-EZ and EZ-EX simultaneously, in V720. This feature was disabled in the older version. (This is also applicable to the Response Spectrum Load Case)

 

Coefficients for Serviceability: Define the Live Load and Wind Load factors for serviceability check (This becomes activated only when Eurocode 2 or Eurocode 3 is selected).  

 

Note 1
If serviceability load combinations are generated using Auto Generation, the generated load combinations are automatically categorized according to the load combination type in Design > General Design Parameters > Serviceability Load Combination Type. However, in case when the load combinations are generated manually, the user must manually classify the load combinations into one of three categories, i.e., Quasi-permanent, Frequent & Characteristic.

 

Note 2
For the load factors to be applied to serviceability load combinations, refer to Table A1.1 & A1.4 of prEN 1990:2001.

 

Note 3

For the procedures to be followed to check serviceability as per Eurocode 2 and Eurocode 3, refer to [Procedure for Serviceability Check as per Eurocode 2] in Design > Concrete Code Check > Beam Checking and [ Procedure for Serviceability Check as per Eurocode 3 ] in Design > Steel Code Check, respectively.

 

 

 3.  Enter or modify the load combinations in a Spread Sheet form table

Click in the load combinations dialog box to convert the data into a spreadsheet form table arranging the unit load cases in rows. Enter or modify the items mentioned in Method 1 to add or modify unit load cases.

 

 4.  Import a load combination (fn.lcb) file to generate load combinations

Click in the load combinations dialog box to display the dialog box that imports the load combination files. Select a file containing previously entered load combinations.

 

The fn.LCB file type is as follows:

 

Sequential number, combination method, unit load case i, load factor i, unit load case j, load factor j, ..., load combination k, load factor k, load combination l, load factor l

 

Examples)

1, , 1, 1.0, 2, 1.0

2, , 1, 1.4, 2, 1.7

 

Note Combination methods
 

  blank,0

: Add

  1

: Envelope

  2

: ABS

  3

: SRSS

 

 

: Select desired load combinations from the General tab and a design tab to the right of the [Copy into] button, and click the [Copy into] button. Only the selected load combinations are copied to the corresponding design tab. This functionality can be used only under the General tab.

 

: The load combinations in the currently activated tab can be output in a text file (*.lcp).

 

 

Note 1

Allow one or more spaces between the commas of Load Combination No. When adding some load combinations to existing load combinations using Import, do not use the same Load Combination No. as that of the existing Load Combination. (Error Message will be displayed)

 

Note 2

For the method of calculating principal stresses, effective stresses and maximum shear stresses for each load combination type, refer to the explanations at the bottom of the page.

 

 

To modify previously defined load combinations

 

Select the load combination to be modified in the load combination list and modify the entry.

 

 

To copy previously defined load combinations

 

Select the load combination to be copied in the load combination list and click .

 

 

To delete previously defined load combinations

 

Select the load combinations to be deleted in the load combination list and click the Delete key.

 

 

Revision of V.7.6.1

 

Note
Auto-generation of load combinations supports the following design codes:

  •  Steel

    Load and Resistance Factor Design of the American Institute of Steel Construction (AISC-LRFD2K, Load & Resistance Factor Design Specification for Structural Steel Buildings, 2000)

    Load combinations for strength verification

    the same with AISC-LRFD93

    Load and Resistance Factor Design of the American Institute of Steel Construction (AISC-LRFD93, Load & Resistance Factor Design Specification for Structural Steel Buildings, 1993)

    Load combinations for strength verification

    1.4*D

    (1.2*D)+(1.6*L)+(0.5*LR)

    (1.2*D)+(0.5*L)+(1.6*LR)

    (1.2*D)+(1.6*L)+(0.5*S)

    (1.2*D)+(0.5*L)+(1.6*S)

    (1.2*D)+(1.6*L)+(0.5*R)

    (1.2*D)+(0.5*L)+(1.6*R)

    (1.2*D)+(1.6*L)+(0.5*IP)

    (1.2*D)+(0.5*L)+(1.6*IP)

    (1.2*D)+(0.5*(L+LR))+(1.3*Wx)

    (1.2*D)+(0.5*(L+LR))+(1.3*Wy)

    (1.2*D)+(0.5*(L+S))+(1.3*Wx)

    (1.2*D)+(0.5*(L+S))+(1.3*Wy)

    (1.2*D)+(0.5*(L+R))+(1.3*Wx)

    (1.2*D)+(0.5*(L+R))+(1.3*Wy)

    (1.2*D)+(0.5*(L+IP))+(1.3*Wx)

    (1.2*D)+(0.5*(L+IP))+(1.3*Wy)

    (1.2*D)+(0.8*Wx)

    (1.2*D)+(0.8*Wy)

    (1.2*D)+(1.3*Wx)

    (1.2*D)+(1.3*Wy)

    (0.9*D)+(1.3*Wx)

    (0.9*D)-(1.3*Wx)

    (0.9*D)+(1.3*Wy)

    (0.9*D)-(1.3*Wy)

    (1.2*D)+(0.5*L)+(1.0*SFx*EspX)+(0.2*S)

    (1.2*D)+(0.5*L)-(1.0*SFx*EspX)+(0.2*S)

    (1.2*D)+(0.5*L)+(1.0*SFy*EspY)+(0.2*S)

    (1.2*D)+(0.5*L)-(1.0*SFy*EspY)+(0.2*S)

    (1.2*D)+(0.5*L)+(1.0*Ex)+(0.2*S)

    (1.2*D)+(0.5*L)-(1.0*Ex)+(0.2*S)

    (1.2*D)+(0.5*L)+(1.0*Ey)+(0.2*S)

    (1.2*D)+(0.5*L)-(1.0*Ey)+(0.2*S)

    (0.9*D)+(1.0*SFx*EspX)

    (0.9*D)-(1.0*SFx*EspX)

    (0.9*D)+(1.0*SFy*EspY)

    (0.9*D)-(1.0*SFy*EspY)

    (0.9*D)+(1.0*Ex)

    (0.9*D)-(1.0*Ex)

    (0.9*D)+(1.0*Ey)

    (0.9*D)-(1.0*Ey)

    (1.2*D)+(1.6*S)

    (1.2*D)+(1.6*R)

    (1.2*D)+(1.6*IP)

    (1.2*D)+(1.6*LR)+(0.8*Wx)

    (1.2*D)+(1.6*LR)+(0.8*Wy)

    (1.2*D)+(1.6*S)+(0.8*Wx)

    (1.2*D)+(1.6*S)+(0.8*Wy)

    (1.2*D)+(1.6*R)+(0.8*Wx)

    (1.2*D)+(1.6*R)+(0.8*Wy)

    (1.2*D)+(1.6*IP)+(0.8*Wx)

    (1.2*D)+(1.6*IP)+(0.8*Wy)

    Allowable Stress Design of the American Institute of Steel Construction (AISC-ASD89, Specification for Structural Steel Buildings: Allowable Stress Design, 1989)

    Load combinations for strength verification

    D+L+LR

    0.75*(D+(L+LR)+Wx)

    0.75*(D+(L+LR)-Wx)

    0.75*(D+(L+LR)+Wy)

    0.75*(D+(L+LR)-Wy)

    0.75*(D+Wx)

    0.75*(D-Wx)

    0.75*(D+Wy)

    0.75*(D-Wy)

    0.75*(D+L+LR+Ex)

    0.75*(D+L+LR-Ex)

    0.75*(D+L+LR+Ey)

    0.75*(D+L+LR-Ey)

    0.75*(D+Ex)

    0.75*(D-Ex)

    0.75*(D+Ey)

    0.75*(D-Ey)

    0.75*(D+L+LR+(SFx*EspX))

    0.75*(D+L+LR-(SFx*EspX))

    0.75*(D+L+LR+(SFy*EspY))

    0.75*(D+L+LR-(SFy*EspY))

    0.75*(D+(SFx*EspX))

    0.75*(D-(SFx*EspX))

    0.75*(D+(SFy*EspY))

    0.75*(D-(SFy*EspY))

    BS5950-90, British Standard, Structural use of steelwork in building: Part 1. Code of practice for design in simple and continuous construction

    Load combinations for strength verification

    (1.4*D)+(1.6*L)

    (1.2*D)+(1.2*L)+(1.2*Wx)

    (1.2*D)+(1.2*L)-(1.2*Wx)

    (1.2*D)+(1.2*L)+(1.2*Wy)

    (1.2*D)+(1.2*L)-(1.2*Wy)

    (1.0*D)+(1.4*Wx)

    (1.0*D)-(1.4*Wx)

    (1.0*D)+(1.4*Wy)

    (1.0*D)-(1.4*Wy)

    (1.2*D)+(1.2*L)+(1.2*Ex)

    (1.2*D)+(1.2*L)-(1.2*Ex)

    (1.2*D)+(1.2*L)+(1.2*Ey)

    (1.2*D)+(1.2*L)-(1.2*Ey)

    (1.0*D)+(1.4*Ex)

    (1.0*D)-(1.4*Ex)

    (1.0*D)+(1.4*Ey)

    (1.0*D)-(1.4*Ey)

    (1.2*D)+(1.2*L)+(1.2*SFx*EspX)

    (1.2*D)+(1.2*L)-(1.2*SFx*EspX)

    (1.2*D)+(1.2*L)+(1.2*SFy*EspY)

    (1.2*D)+(1.2*L)-(1.2*SFy*EspY)

    (1.0*D)+(1.4*SFX*EspX)

    (1.0*D)-(1.4*SFX*EspX)

    (1.0*D)+(1.4*SFY*EspY)

    (1.0*D)-(1.4*SFY*EspY)

    (1.2*D)+(1.2*L)+(1.2*EP)

    (1.0*D)+(1.4*EP)

    (1.2*D)+(1.2*L)+(1.2*WP)

    (1.0*D)+(1.4*WP)

    (1.2*D)+(1.2*L)+(1.2*(EP+WP))

    (1.0*D)+(1.4*(EP+WP))

    [Basic considerations for generating load combinations]

    1. Load combinations for serviceability are generated as per the EN 1990:2002.

    2. The load combinations as per Eurocode 2 are identical to those of Eurocode 3.

     

    ﹥ Load combinations comprising dead load, live load and wind load

    1.35D + 1.5(L+LR)

    1.35D + 1.35(L+LR) ?1.35Wx )

    1.35D + 1.35(L+LR) ?1.35Wy )

    D ?1.5Wx

    D ?1.5Wy

    ﹥ Seismic load combinations

    Ⅱ When Orthogonal Effect is not considered, 16 response spectrum load combinations & 8 static load combinations are generated.

    1.35( D+(L+LR) ?(RSx孰Sx) )

    1.35( D+(L+LR) ?(RSy孰Sy) )

    D + 1.5(RSx孰Sx)

    D + 1.5(RSy孰Sy)

    1.35( D+(L+LR) ?Ex)

    1.35( D+(L+LR) ?Ey)

     D ?1.5Ex

     D ?1.5Ey

    Ⅱ When Orthogonal Effect (with 100:30 Rule applied) is considered, 64 response spectrum load combinations & 24 static load combinations are generated.

    1.35( D+(L+LR) ?{1.0(RSx孰Sx) ?0.3(RSy孰Sy)} )

    1.35( D+(L+LR) ?{1.0(RSy孰Sy) ?0.3(RSx孰Sx)} )

    1.0D ?1.5{1.0(RSx孰Sx) ?0.3(RSy孰Sy)}

    1.0D ?1.5{1.0(RSy孰Sy) ?0.3(RSx孰Sx)}

    1.35( D+(L+LR) ?(1.0EQx?.3EQy) )

    1.35( D+(L+LR) ?(1.0EQy?.3EQx) )

    1.0D ?1.5(1.0EQx?.3EQy) )

    1.0D ?1.5(1.0EQy?.3EQx) )

    Ⅱ When Orthogonal Effect (with SRSS applied) is considered, 16 response spectrum load combinations and 4 static load combinations are generated.

    1.35( D+(L+LR) ?SQRT{(RSx孰Sx)^2+(RSy孰Sy)^2} )

    1.0D ?1.5SQRT{(RSx孰Sx)^2+(RSy孰Sy)^2} )

    1.35( D+(L+LR) ?SQRT{Ex^2+Ey^2} )

    1.0D ?1.5SQRT{Ex^2+Ey^2} )

    ﹥ Load combinations for serviceability

    Ⅱ Load Factors

    Live Load        份1,1         份1,2       份1,3

                        Wind Load     份2,1          份2,2       份2,3

     

    [An example of generation of load combinations in case of the presence of three Live Loads]

    Ⅱ Characteristic Load Combination

    1.0D + 1.0LL1 + 份1,1LL2 + 份1,1LL3 ?份2,1Wx

    1.0D + 份1,1LL1 + 1.0LL2 + 份1,1LL3 ?份2,1Wx

    1.0D + 份1,1LL1 + 份1,1LL2 + 1.0LL3 ?份2,1Wx

    1.0D + 份1,1LL1 + 份1,1LL2 + 份1,1LL3 ?1.0Wx

    1.0D + 1.0LL1 + 份1,1LL2 + 份1,1LL3 ?份2,1Wy

    1.0D + 份1,1LL1 + 1.0LL2 + 份1,1LL3 ?份2,1Wy

    1.0D + 份1,1LL1 + 份1,1LL2 + 1.0LL3 ?份2,1Wy

    1.0D + 份1,1LL1 + 份1,1LL2 + 份1,1LL3 ?1.0Wy

    Ⅱ Frequent Load Combination

    1.0D + 份1,2LL1 + 份1,3LL2 + 份1,3LL3 ?份2,3Wx

    1.0D + 份1,3LL1 + 份1,2LL2 + 份1,3LL3 ?份2,3Wx

    1.0D + 份1,3LL1 + 份1,3LL2 + 份1,2LL3 ?份2,3Wx

    1.0D + 份1,3LL1 + 份1,3LL2 + 份1,3LL3 ?份2,2Wx

    1.0D + 份1,2LL1 + 份1,3LL2 + 份1,3LL3 ?份2,3Wy

    1.0D + 份1,3LL1 + 份1,2LL2 + 份1,3LL3 ?份2,3Wy

    1.0D + 份1,3LL1 + 份1,3LL2 + 份1,2LL3 ?份2,3Wy

    1.0D + 份1,3LL1 + 份1,3LL2 + 份1,3LL3 ?份2,2Wy

    Ⅱ Quasi-permanent Load Combination

    1.0D + 份1,3LL1 + 份1,3LL2 + 份1,3LL3 ?份2,3Wx

    1.0D + 份1,3LL1 + 份1,3LL2 + 份1,3LL3 ?份2,3Wy

    Eurocode 3, ENV 1993-1-1 Eurocode3, Design of steel structures : Part 1.1 General Rules and Rules for Building

    [Basic considerations for generating load combinations]

    1. Load combinations for serviceability are generated as per the EN 1990:2002.

    2. The load combinations as per Eurocode 2 are identical to those of Eurocode 3.

     

    ﹥ Load combinations comprising dead load, live load and wind load

    1.35D + 1.5(L+LR)

    1.35D + 1.35(L+LR) ▽ 1.35Wx )

    1.35D + 1.35(L+LR) ▽ 1.35Wy )

    D ▽ 1.5Wx

    D ▽ 1.5Wy

    ﹥ Seismic load combinations

    Ⅱ When Orthogonal Effect is not considered, 16 response spectrum load combinations & 8 static load combinations are generated.

    1.35( D+(L+LR) ▽ (RSx▽ESx) )

    1.35( D+(L+LR) ▽ (RSy▽ESy) )

    D + 1.5(RSx▽ESx)

    D + 1.5(RSy▽ESy)

    1.35( D+(L+LR) ▽ Ex)

    1.35( D+(L+LR) ▽ Ey)

     D ▽ 1.5Ex

     D ▽ 1.5Ey

    Ⅱ When Orthogonal Effect (with 100:30 Rule applied) is considered, 64 response spectrum load combinations & 24 static load combinations are generated.

    1.35( D+(L+LR) ▽ {1.0(RSx▽ESx) ▽ 0.3(RSy▽ESy)} )

    1.35( D+(L+LR) ▽ {1.0(RSy▽ESy) ▽ 0.3(RSx▽ESx)} )

    1.0D ▽ 1.5{1.0(RSx▽ESx) ▽ 0.3(RSy▽ESy)}

    1.0D ▽ 1.5{1.0(RSy▽ESy) ▽ 0.3(RSx▽ESx)}

    1.35( D+(L+LR) ▽ (1.0EQx▽0.3EQy) )

    1.35( D+(L+LR) ▽ (1.0EQy▽0.3EQx) )

    1.0D ▽ 1.5(1.0EQx▽0.3EQy) )

    1.0D ▽ 1.5(1.0EQy▽0.3EQx) )

    Ⅱ When Orthogonal Effect (with SRSS applied) is considered, 16 response spectrum load combinations and 4 static load combinations are generated.

    1.35( D+(L+LR) ▽ SQRT{(RSx▽ESx)^2+(RSy▽ESy)^2} )

    1.0D ▽ 1.5SQRT{(RSx▽ESx)^2+(RSy▽ESy)^2} )

    1.35( D+(L+LR) ▽ SQRT{Ex^2+Ey^2} )

    1.0D ▽ 1.5SQRT{Ex^2+Ey^2} )

    ﹥ Load combinations for serviceability

    Ⅱ Load Factors

    Live Load

    Live Load        份1,1         份1,2       份1,3

                        Wind Load     份2,1          份2,2       份2,3

     

    [An example of generation of load combinations in case of the presence of three Live Loads]

    Ⅱ Characteristic Load Combination

    1.0D + 1.0LL1 + 份1,1LL2 + 份1,1LL3 ▽ 份2,1Wx

    1.0D + 份1,1LL1 + 1.0LL2 + 份1,1LL3 ▽ 份2,1Wx

    1.0D + 份1,1LL1 + 份1,1LL2 + 1.0LL3 ▽ 份2,1Wx

    1.0D + 份1,1LL1 + 份1,1LL2 + 份1,1LL3 ▽ 1.0Wx

    1.0D + 1.0LL1 + 份1,1LL2 + 份1,1LL3 ▽ 份2,1Wy

    1.0D + 份1,1LL1 + 1.0LL2 + 份1,1LL3 ▽ 份2,1Wy

    1.0D + 份1,1LL1 + 份1,1LL2 + 1.0LL3 ▽ 份2,1Wy

    1.0D + 份1,1LL1 + 份1,1LL2 + 份1,1LL3 ▽ 1.0Wy

    Ⅱ Frequent Load Combination

    1.0D + 份1,2LL1 + 份1,3LL2 + 份1,3LL3 ▽ 份2,3Wx

    1.0D + 份1,3LL1 + 份1,2LL2 + 份1,3LL3 ▽ 份2,3Wx

    1.0D + 份1,3LL1 + 份1,3LL2 + 份1,2LL3 ▽ 份2,3Wx

    1.0D + 份1,3LL1 + 份1,3LL2 + 份1,3LL3 ▽ 份2,2Wx

    1.0D + 份1,2LL1 + 份1,3LL2 + 份1,3LL3 ▽ 份2,3Wy

    1.0D + 份1,3LL1 + 份1,2LL2 + 份1,3LL3 ▽ 份2,3Wy

    1.0D + 份1,3LL1 + 份1,3LL2 + 份1,2LL3 ▽ 份2,3Wy

    1.0D + 份1,3LL1 + 份1,3LL2 + 份1,3LL3 ▽ 份2,2Wy

    Ⅱ Quasi-permanent Load Combination

    1.0D + 份1,3LL1 + 份1,3LL2 + 份1,3LL3 ▽ 份2,3Wx

    1.0D + 份1,3LL1 + 份1,3LL2 + 份1,3LL3 ▽ 份2,3Wy

     

     

    CSA-S16-01, Canadian Standards Association, Limit States Design of Steel Structures, 2001

    Load combinations for strength verification

    1.25D + 1.5(L+LR)

    0.85D + 1.5Wx

    0.85D - 1.5Wx

    0.85D + 1.5Wy

    0.85D - 1.5Wy

    1.25D + 1.25T

    1.25D + 0.7(1.5(L+LR) + 1.5Wx)

    1.25D + 0.7(1.5(L+LR) - 1.5Wx)

    1.25D + 0.7(1.5(L+LR) + 1.5Wy)        

    1.25D + 0.7(1.5(L+LR) - 1.5Wy)        

    1.25D + 0.7(1.5(L+LR) + 1.25T)        

    1.25D + 0.7(1.5Wx + 1.25T)        

    1.25D + 0.7(1.5Wy + 1.25T)        

    1.25D + 0.6(1.5(L+LR) + 1.5Wx + 1.25T)

    1.25D + 0.6(1.5(L+LR) - 1.5Wx + 1.25T)

    1.25D + 0.6(1.5(L+LR) + 1.5Wy + 1.25T)

    1.25D + 0.6(1.5(L+LR) - 1.5Wy + 1.25T)

    1.0D + 1.0Ex                     

    1.0D - 1.0Ex                     

    1.0D + 1.0Ey               

    1.0D - 1.0Ey               

    1.0D + 0.5(L+LR) + 1.0Ex        

    1.0D + 0.5(L+LR) - 1.0Ex        

    1.0D + 0.5(L+LR) + 1.0Ey          

    1.0D + 0.5(L+LR) - 1.0Ey          

    1.0D + 1.0(SFx*EspX)         

    1.0D - 1.0(SFx*EspX)         

    1.0D + 1.0(SFy*EspY)         

    1.0D - 1.0(SFy*EspY)         

    1.0D + 0.5(L+LR) + 1.0(SFx*EspX)  

    1.0D + 0.5(L+LR) - 1.0(SFx*EspX)  

    1.0D + 0.5(L+LR) + 1.0(SFy*EspY)  

    1.0D + 0.5(L+LR) - 1.0(SFy*EspY)

    AISI-CFSD86, American Iron and Steel Institute, Cold-Formed Steel Design, 1986

    Load combinations for strength verification

    D+L+LR

    0.75*(D+L+LR+Wx)

    0.75*(D+L+LR-Wx)

    0.75*(D+L+LR+Wy)

    0.75*(D+L+LR-Wy)

    0.75*(D+Wx)

    0.75*(D-Wx)

    0.75*(D+Wy)

    0.75*(D-Wy)

    0.75*(D+L+LR+Ex)

    0.75*(D+L+LR-Ex)

    0.75*(D+L+LR+Ey)

    0.75*(D+L+LR-Ey)

    0.75*(D+Ex)

    0.75*(D-Ex)

    0.75*(D+Ey)

    0.75*(D-Ey)

    0.75*(D+L+LR+(SFx*EspX))

    0.75*(D+L+LR-(SFx*EspX))

    0.75*(D+L+LR+(SFy*EspY))

    0.75*(D+L+LR-(SFy*EspY))

    0.75*(D+(SFx*EspX))

    0.75*(D-(SFx*EspX))

    0.75*(D+(SFy*EspY))

    0.75*(D-(SFy*EspY))

    Revision of V.7.6.1

    IS:800-2007, Indian Standard, Code of Practice for General Construction in Steel, 2007

    Partial Safety Factors For Loads (乓f ) (Normal Structures)  (IS 800 : 2007)

     

    Combination

    Limit State of Strength

    DL

    LL

    WL/EL

    AL

    DL (unfavorable effects)

    1.50

    -

    -

    -

    DL + LL

    1.50

    1.50

    -

    -

    DL + LL + WL/EL

    1.20

    1.20

    0.60

    -

    DL + WL/EL

    1.50 (0.9)

    1.20

    -

    -

    DL + ER

    1.20 (0.9)

    1.20

    -

    -

    DL + LL + AL

    1.00

    0.35

    -

    1.00

     

    DL = Dead Load , LL = Live Load

    CL = Crane Load (Vertical / Horizontal)

    WL = Wind Load , EL = Earthquake Load

    ER = Erection Load , AL = Accidental Load

     

    1.5D

    1.5D + 1.5L

    1.2D + 1.2L + 0.6Wx

    1.2D + 1.2L - 0.6Wx

    1.2D + 1.2L + 0.6Wy

    1.2D + 1.2L - 0.6Wy

    1.2D + 1.2L + 0.6Ex

    1.2D + 1.2L - 0.6Ex

    1.2D + 1.2L + 0.6Ey

    1.2D + 1.2L - 0.6Ey

    1.5(0.9)D + 1.5Wx

    1.5(0.9)D - 1.5Wx

    1.5(0.9)D + 1.5Wy

    1.5(0.9)D - 1.5Wy

    1.5(0.9)D + 1.5Ex

    1.5(0.9)D - 1.5Ex

    1.5(0.9)D + 1.5Ey

    1.5(0.9)D - 1.5Ey

    1.2D + 1.2L + 0.6((SFx)RSx)

    1.2D + 1.2L - 0.6((SFx)RSx)

    1.2D + 1.2L + 0.6((SFx)RSy)

    1.2D + 1.2L - 0.6((SFx)RSy)

    1.5(0.9)D + 1.5((SFx)RSx)

    1.5(0.9)D - 1.5((SFx)RSx)

    1.5(0.9)D + 1.5((SFx)RSy)

    1.5(0.9)D - 1.5((SFx)RSy)

    1.2(0.9)D + 1.2ER

    1.0D + 0.35L + 1.0AL

     

    Additional Load Combinations

     

    Combination

    Limit State of Strength

    DL

    LL

    EL

    DL + LL + EL

    1.20

    0.50

    2.50

    DL + EL

    1.50

    -

    1.50

     

     

    1.2D + 0.5L + 2.5Ex

    1.2D + 0.5L - 2.5Ex

    1.2D + 0.5L + 2.5Ey

    1.2D + 0.5L - 2.5Ey

    1.5D + 1.5Ex

    1.5D - 1.5Ex

    1.5D + 1.5Ey

    1.5D - 1.5Ey

    1.2D + 0.5L + 2.5((SFx)RSx)

    1.2D + 0.5L - 2.5((SFx)RSx)

    1.2D + 0.5L + 2.5((SFx)RSy)

    1.2D + 0.5L - 2.5((SFx)RSy)

    1.5D + 1.5((SFx)RSx)

    1.5D - 1.5((SFx)RSx)

    1.5D + 1.5((SFx)RSy)

    1.5D - 1.5((SFx)RSy)

     

    Partial Safety Factors For Loads Serviceability (乓f ) (Normal Structures)  (IS 800 : 2007)

     

    Combination

    Limit State of Strength

    DL

    LL

    WL/EL

    AL

    DL (unfavorable effects)

    -

    -

    -

    -

    DL + LL

    1.00

    1.00

    -

    -

    DL + LL + WL/EL

    1.00

    0.80

    0.80

    -

    DL + WL/EL

    1.00

    -

    1.00

    -

    DL + ER

    -

    1.20

    -

    -

    DL + LL + AL

    -

    -

    -

    -

     

     

    1.0D + 1.0L

    1.0D + 0.8L + 0.8Wx

    1.0D + 0.8L - 0.8Wx

    1.0D + 0.8L + 0.8Wy

    1.0D + 0.8L - 0.8Wy

    1.0D + 0.8L + 0.8Ex

    1.0D + 0.8L - 0.8Ex

    1.0D + 0.8L + 0.8Ey

    1.0D + 0.8L - 0.8Ey

    1.0D + 1.0Wx

    1.0D - 1.0Wx

    1.0D + 1.0Wy

    1.0D - 1.0Wy

    1.0D + 1.0Ex

    1.0D - 1.0Ex

    1.0D + 1.0Ey

    1.0D - 1.0Ey

    1.0D + 0.8L + 0.8((SFx)RSx)

    1.0D + 0.8L - 0.8((SFx)RSx)

    1.0D + 0.8L + 0.8((SFx)RSy)

    1.0D + 0.8L - 0.8((SFx)RSy)

    1.0D + 1.0((SFx)RSx)

    1.0D - 1.0((SFx)RSx)

    1.0D + 1.0((SFx)RSy)

    1.0D - 1.0((SFx)RSy)

    IS:800-1984, Indian Standard, Code of Practice for General Construction in Steel (Second Revision), 1984

    D

    D + L

    D + L + Wx

    D + L + Wy

    D + L - Wx

    D + L - Wy

    D + Wx

    D + Wy

    D - Wx

    D - Wy

    D + L + Ex

    D + L + Ey

    D + L - Ex

    D + L - Ey

    D + Ex

    D + Ey

    D - Ex

    D - Ey

    D + L + ((SFx)RSx)

    D + L + ((SFx)RSy)

    D + L - ((SFx)RSx)

    D + L - ((SFx)RSy)

    D + ((SFx)RSx)

    D + ((SFx)RSy)

    D - ((SFx)RSx)

    D - ((SFx)RSy)

    TWN-ASD90, Taiwan Standard, Allowable Stress Design Specification and Commentary for Structural Steel Building, 2001

    D + (L+LR)

    0.75(D + (L+LR) ▽ T)

    0.75(D ▽ T)

    0.75(D + (L+LR) ▽ 1.25Wx )

    0.75(D + (L+LR) ▽ 1.25Wy )

    0.75(D ▽ 1.25Wx)

    0.75(D ▽ 1.25Wy)

    0.75(D ▽ 1.25Wx + T)

    0.75(D ▽ 1.25Wy + T)

    0.66(D + (L+LR) ▽ 1.25Wx  + T)

    0.66(D + (L+LR) ▽ 1.25Wy  + T)

    0.75( (D+(L+LR)) ▽ (1.0ESx▽0.3ESy) )

    0.75( (D+(L+LR)) ▽ (1.0ESy▽0.3ESx) )

    0.75( D ▽ (1.0EQx▽0.3EQy) )

    0.75( D ▽ (1.0EQy▽0.3EQx) )

    0.75( (D+(L+LR)) ▽ {1.0(RSx▽ESx) ▽ 0.3(RSy▽ESy)} )

    0.75( (D+(L+LR)) ▽ {1.0(RSy▽ESy) ▽ 0.3(RSx▽ESx)} )

    0.75( D ▽ {1.0(RSx▽ESx) ▽ 0.3(RSy▽ESy)} )

    0.75( D ▽ {1.0(RSy▽ESy) ▽ 0.3(RSx▽ESx)} )

    0.75( D ▽ (1.0EQx▽0.3EQy) + T)

    0.75( D ▽ (1.0EQy▽0.3EQx) + T)

    0.75( D ▽ {1.0(RSx▽ESx) ▽ 0.3(RSy▽ESy)} + T)

    0.75( D ▽ {1.0(RSy▽ESy) ▽ 0.3(RSx▽ESx)} + T)

    0.66( (D+(L+LR)) ▽ (1.0ESx▽ESy) + T)

    0.66( (D+(L+LR)) ▽ (1.0ESy▽ESx) + T)

    TWN-LSD90, Taiwan Standard, Limit States Design Specification and Commentary for Structural Steel Building, 2001

    1.4D

    1.2D+1.6(L+LR)

    1.2D + 0.5(L+LR) ▽ 1.25Wx

    1.2D + 0.5(L+LR) ▽ 1.25Wy

    0.9D ▽ 1.6Wx

    0.9D ▽ 1.6Wy

    1.2D + 0.5(L+LR) ▽ (1.0ESx▽0.3ESy)

    1.2D + 0.5(L+LR) ▽ (1.0ESy▽0.3ESx)

    1.2D + 0.5(L+LR) ▽ {1.0(RSx▽ESx) ▽ 0.3(RSy▽ESy)}

    1.2D + 0.5(L+LR) ▽ {1.0(RSy▽ESy) ▽ 0.3(RSx▽ESx)}

    0.9D ▽ (1.0ESx▽0.3ESy)

    0.9D ▽ (1.0ESy▽0.3ESx)

    0.9D ▽ {1.0(RSx▽ESx) ▽ 0.3(RSy▽ESy)}

    0.9D ▽ {1.0(RSy▽ESy) ▽ 0.3(RSx▽ESx)}}

    GB50017-03, Chinese Code for design of steel structures, 2003

    GBJ17-88, Chinese Code for design of steel structures, 1988

    1.35D + 1.4(0.7)(L+LR)

    1.2D + 1.4(L+LR)

    1.0D + 1.4(L+LR)

    1.2D + 1.4Wx

    1.2D + 1.4Wy

    1.2D - 1.4Wx

    1.2D - 1.4Wy

    1.0D + 1.4Wx

    1.0D + 1.4Wy

    1.0D - 1.4Wx

    1.0D - 1.4Wy

    1.2D + 1.4(L+LR) + 1.4(0.6)Wx

    1.2D + 1.4(L+LR) + 1.4(0.6)Wy

    1.2D + 1.4(L+LR) - 1.4(0.6)Wx

    1.2D + 1.4(L+LR) - 1.4(0.6)Wy

    1.0D + 1.4(L+LR) + 1.4(0.6)Wx

    1.0D + 1.4(L+LR) + 1.4(0.6)Wy

    1.0D + 1.4(L+LR) - 1.4(0.6)Wx

    1.0D + 1.4(L+LR) - 1.4(0.6)Wy

    1.2D + 1.4(0.7)(L+LR) + 1.4Wx

    1.2D + 1.4(0.7)(L+LR) + 1.4Wy

    1.2D + 1.4(0.7)(L+LR) - 1.4Wx

    1.2D + 1.4(0.7)(L+LR) - 1.4Wy

    1.0D + 1.4(0.7)(L+LR) + 1.4Wx

    1.0D + 1.4(0.7)(L+LR) + 1.4Wy

    1.0D + 1.4(0.7)(L+LR) - 1.4Wx

    1.0D + 1.4(0.7)(L+LR) - 1.4Wy

    1.2(D+0.5(L+LR)) + 1.3Ex

    1.2(D+0.5(L+LR)) + 1.3Ey

    1.2(D+0.5(L+LR)) - 1.3Ex

    1.2(D+0.5(L+LR)) - 1.3Ey

    1.0(D+0.5(L+LR)) + 1.3Ex

    1.0(D+0.5(L+LR)) + 1.3Ey

    1.0(D+0.5(L+LR)) - 1.3Ex

    1.0(D+0.5(L+LR)) - 1.3Ey

    1.2(D+0.5(L+LR)) + 1.3(SFx)*RSx

    1.2(D+0.5(L+LR)) + 1.3(SFy)*RSy

    1.2(D+0.5(L+LR)) - 1.3(SFx)*RSx

    1.2(D+0.5(L+LR)) - 1.3(SFy)*RSy

    1.0(D+0.5(L+LR)) + 1.3(SFx)*RSx

    1.0(D+0.5(L+LR)) + 1.3(SFy)*RSy

    1.0(D+0.5(L+LR)) - 1.3(SFx)*RSx

    1.0(D+0.5(L+LR)) - 1.3(SFy)*RSy

    1.35D + 1.4(0.7)(L+S)

    1.2D + 1.4(L+S)

    1.0D + 1.4(L+S)

    1.2D + 1.4(L+S) + 1.4(0.6)Wx

    1.2D + 1.4(L+S) + 1.4(0.6)Wy

    1.2D + 1.4(L+S) - 1.4(0.6)Wx

    1.2D + 1.4(L+S) - 1.4(0.6)Wy

    1.0D + 1.4(L+S) + 1.4(0.6)Wx

    1.0D + 1.4(L+S) + 1.4(0.6)Wy

    1.0D + 1.4(L+S) - 1.4(0.6)Wx

    1.0D + 1.4(L+S) - 1.4(0.6)Wy

    1.2D + 1.4(0.7)(L+S) + 1.4Wx

    1.2D + 1.4(0.7)(L+S) + 1.4Wy

    1.2D + 1.4(0.7)(L+S) - 1.4Wx

    1.2D + 1.4(0.7)(L+S) - 1.4Wy

    1.0D + 1.4(0.7)(L+S) + 1.4Wx

    1.0D + 1.4(0.7)(L+S) + 1.4Wy

    1.0D + 1.4(0.7)(L+S) - 1.4Wx

    1.0D + 1.4(0.7)(L+S) - 1.4Wy

    1.2(D+0.5(L+S)) + 1.3Ex

    1.2(D+0.5(L+S)) + 1.3Ey

    1.2(D+0.5(L+S)) - 1.3Ex

    1.2(D+0.5(L+S)) - 1.3Ey

    1.0(D+0.5(L+S)) + 1.3Ex

    1.0(D+0.5(L+S)) + 1.3Ey

    1.0(D+0.5(L+S)) - 1.3Ex

    1.0(D+0.5(L+S)) - 1.3Ey

    1.2(D+0.5(L+S)) + 1.3(SFx)*RSx

    1.2(D+0.5(L+S)) + 1.3(SFy)*RSy

    1.2(D+0.5(L+S)) - 1.3(SFx)*RSx

    1.2(D+0.5(L+S)) - 1.3(SFy)*RSy

    1.0(D+0.5(L+S)) + 1.3(SFx)*RSx

    1.0(D+0.5(L+S)) + 1.3(SFy)*RSy

    1.0(D+0.5(L+S)) - 1.3(SFx)*RSx

    1.0(D+0.5(L+S)) - 1.3(SFy)*RSy

     

  •  Concrete

    RC Structures Design Codes of the American Concrete Institute (ACI318-02, Building Code Requirements for Reinforced Concrete, 2002)

    Load combinations for strength verification

    1.4D + 1.50Fp

    1.2(D+Fp+(T+CR+SH)) + 1.6(L+(EP+WP)) + 0.5LR

    1.2(D+Fp+(T+CR+SH)) + 1.6(L+(EP+WP)) + 0.5S

    1.2(D+Fp+(T+CR+SH)) + 1.6(L+(EP+WP)) + 0.5R

    1.2D + 1.6LR + 1.0L

    1.2D + 1.6LR + 0.8Wx

    1.2D + 1.6LR - 0.8Wx

    1.2D + 1.6LR + 0.8Wy

    1.2D + 1.6LR - 0.8Wy

    1.2D + 1.6S + 1.0L

    1.2D + 1.6S + 0.8Wx

    1.2D + 1.6S - 0.8Wx

    1.2D + 1.6S + 0.8Wy

    1.2D + 1.6S - 0.8Wy

    1.2D + 1.6R + 1.0L

    1.2D + 1.6R + 0.8Wx

    1.2D + 1.6R - 0.8Wx

    1.2D + 1.6R + 0.8Wy

    1.2D + 1.6R - 0.8Wy

    1.2D + 1.6Wx + 1.0L + 0.5LR

    1.2D - 1.6Wx + 1.0L + 0.5LR

    1.2D + 1.6Wy + 1.0L + 0.5LR

    1.2D - 1.6Wy + 1.0L + 0.5LR

    1.2D + 1.6Wx + 1.0L + 0.5S

    1.2D - 1.6Wx + 1.0L + 0.5S

    1.2D + 1.6Wy + 1.0L + 0.5S

    1.2D - 1.6Wy + 1.0L + 0.5S

    1.2D + 1.6Wx + 1.0L + 0.5R

    1.2D - 1.6Wx + 1.0L + 0.5R

    1.2D + 1.6Wy + 1.0L + 0.5R

    1.2D - 1.6Wy + 1.0L + 0.5R

    1.2D + 1.0Ex + 1.0L + 0.2S

    1.2D - 1.0Ex + 1.0L + 0.2S

    1.2D + 1.0Ey + 1.0L + 0.2S

    1.2D - 1.0Ey + 1.0L + 0.2S

    0.9D + 1.6Wx + 1.6(EP+WP)

    0.9D - 1.6Wx + 1.6(EP+WP)

    0.9D + 1.6Wy + 1.6(EP+WP)

    0.9D - 1.6Wy + 1.6(EP+WP)

    0.9D + 1.0Ex + 1.6(EP+WP)

    0.9D - 1.0Ex + 1.6(EP+WP)

    0.9D + 1.0Ey + 1.6(EP+WP)

    0.9D - 1.0Ey + 1.6(Ep+Wp)

    1.2D + 1.0(SFx*EspX) + 1.0L + 0.2S

    1.2D - 1.0(SFx*EspX) + 1.0L + 0.2S

    1.2D + 1.0(SFy*EspY) + 1.0L + 0.2S

    1.2D - 1.0(SFy*EspY) + 1.0L + 0.2S

    0.9D + 1.0(SFx*EspX) + 1.6(Ep+WP)

    0.9D - 1.0(SFx*EspX) + 1.6(Ep+WP)

    0.9D + 1.0(SFy*EspY) + 1.6(Ep+WP)

    0.9D - 1.0(SFy*EspY) + 1.6(Ep+WP)

    RC Structures Design Codes of the American Concrete Institute (ACI318-89, 95, 99, Building Code Requirements for Reinforced Concrete, 1989, 1995, 1999)

    Load combinations for strength verification

    (1.4*D)+(1.7*(L+LR))

    (1.05*D)+(1.275*(L+LR))+(1.275*Wx)

    (1.05*D)+(1.275*(L+LR))-(1.275*Wx)

    (1.05*D)+(1.275*(L+LR))+(1.275*Wy)

    (1.05*D)+(1.275*(L+LR))-(1.275*Wy)

    (0.9*D)+(1.3*Wx)

    (0.9*D)-(1.3*Wx)

    (0.9*D)+(1.3*Wy)

    (0.9*D)-(1.3*Wy)

    (1.05*D)+(1.275*(L+LR))+(1.4025*Ex)

    (1.05*D)+(1.275*(L+LR))-(1.4025*Ex)

    (1.05*D)+(1.275*(L+LR))+(1.4025*Ey)

    (1.05*D)+(1.275*(L+LR))-(1.4025*Ey)

    (0.9*D)+(1.43*Ex)

    (0.9*D)-(1.43*Ex)

    (0.9*D)+(1.43*Ey)

    (0.9*D)-(1.43*Ey)

    (1.05*D)+(1.275*(L+LR))+(1.4025*SFx*EspX)

    (1.05*D)+(1.275*(L+LR))-(1.4025*SFx*EspX)

    (1.05*D)+(1.275*(L+LR))+(1.4025*SFy*EspY)

    (1.05*D)+(1.275*(L+LR))-(1.4025*SFy*EspY)

    (0.9*D)+(1.43*SFx*EspX)

    (0.9*D)-(1.43*SFx*EspX)

    (0.9*D)+(1.43*SFy*EspY)

    (0.9*D)-(1.43*SFy*EspY)

    (1.05*D)+(1.275*(L+LR))+(1.05*T)

    (1.4*D)+(1.4*T)

    (1.4*D)+(1.7*(L+LR))+(1.7*EP)

    (0.9*D)+(1.7*(L+LR))+(1.7*EP)

    (0.9*D)+(1.7*EP)

    (1.4*D)+(1.7*(L+LR))+(1.7*WP)

    (0.9*D)+(1.7*(L+LR))+(1.7*WP)

    (0.9*D)+(1.7*WP)

    (1.4*D)+(1.7*(L+LR))+(1.7*(EP+WP))

    (0.9*D)+(1.7*(L+LR))+(1.7*(EP+WP))

    (0.9*D)+(1.7*(EP+WP))

    (1.05*D)+(1.275*(L+LR))+(1.05*SH)

    (1.4*D)+(1.4*SH)

    (1.05*D)+(1.275*(L+LR))+(1.05*CR)

    (1.4*D)+(1.4*CR)

    CSA-A23.3-94, Canadian Standards Association, Design of Concrete Structures, 1994

    Load combinations for strength verification

    1.25D + 1.5L

    0.85D + 1.5Wx

    0.85D - 1.5Wx

    0.85D + 1.5Wy

    0.85D - 1.5Wy

    1.25D + 1.25T

    1.25D + 0.7(1.5L + 1.5Wx)

    1.25D + 0.7(1.5L - 1.5Wx)

    1.25D + 0.7(1.5L + 1.5Wy)        

    1.25D + 0.7(1.5L - 1.5Wy)        

    1.25D + 0.7(1.5L + 1.25T)        

    1.25D + 0.7(1.5L + 1.25T)        

    1.25D + 0.6(1.5L + 1.5Wx + 1.25(T+CR+SH))

    1.25D + 0.6(1.5L - 1.5Wx + 1.25(T+CR+SH))

    1.25D + 0.6(1.5L + 1.5Wy + 1.25(T+CR+SH))

    1.25D + 0.6(1.5L - 1.5Wy + 1.25(T+CR+SH))

    1.0D + 1.0Ex                     

    1.0D - 1.0Ex                     

    1.0D + 1.0Ey               

    1.0D - 1.0Ey               

    1.0D + 0.5L + 1.0Ex        

    1.0D + 0.5L - 1.0Ex        

    1.0D + 0.5L + 1.0Ey          

    1.0D + 0.5L - 1.0Ey          

    1.0D + 1.0(SFx*EspX)         

    1.0D - 1.0(SFx*EspX)         

    1.0D + 1.0(SFy*EspY)         

    1.0D - 1.0(SFy*EspY)         

    1.0D + 0.5L + 1.0(SFx*EspX)  

    1.0D + 0.5L - 1.0(SFx*EspX)  

    1.0D + 0.5L + 1.0(SFy*EspY)  

    1.0D + 0.5L - 1.0(SFy*EspY)

    BS8110-97, British Standard, Structural use of concrete: Part 1. Code of practice for design and construction, 1997

    Load combinations for strength verification

    (1.4*D)+(1.6*L)

    (1.2*D)+(1.2*L)+(1.2*Wx)

    (1.2*D)+(1.2*L)-(1.2*Wx)

    (1.2*D)+(1.2*L)+(1.2*Wy)

    (1.2*D)+(1.2*L)-(1.2*Wy)

    (1.0*D)+(1.4*Wx)

    (1.0*D)-(1.4*Wx)

    (1.0*D)+(1.4*Wy)

    (1.0*D)-(1.4*Wy)

    (1.2*D)+(1.2*L)+(1.2*Ex)

    (1.2*D)+(1.2*L)-(1.2*Ex)

    (1.2*D)+(1.2*L)+(1.2*Ey)

    (1.2*D)+(1.2*L)-(1.2*Ey)

    (1.0*D)+(1.4*Ex)

    (1.0*D)-(1.4*Ex)

    (1.0*D)+(1.4*Ey)

    (1.0*D)-(1.4*Ey)

    (1.2*D)+(1.2*L)+(1.2*SFx*EspX)

    (1.2*D)+(1.2*L)-(1.2*SFx*EspX)

    (1.2*D)+(1.2*L)+(1.2*SFy*EspY)

    (1.2*D)+(1.2*L)-(1.2*SFy*EspY)

    (1.0*D)+(1.4*SFx*EspX)

    (1.0*D)-(1.4*SFx*EspX)

    (1.0*D)+(1.4*SFy*EspY)

    (1.0*D)-(1.4*SFy*EspY)

    (1.2*D)+(1.2*L)+(1.2*EP)

    (1.0*D)+(1.4*EP)

    (1.2*D)+(1.2*L)+(1.2*WP)

    (1.0*D)+(1.4*WP)

    (1.2*D)+(1.2*L)+(1.2*(EP+WP))

    (1.0*D)+(1.4*(EP+WP))

     

    ENV 1992-1-1 Eurocode2, Design of concrete structures: Part 1. General Rules and Rules for Building

    [Basic considerations for generating load combinations]

    1. Load combinations for serviceability are generated as per EN 1990:2002.

    2. The load combinations as per Eurocode 2 are identical to those of Eurocode 3.    

     

    ﹥ Load combinations comprising dead load, live load and wind load

    1.35D + 1.5(L+LR)

    1.35D + 1.35(L+LR) ▽ 1.35Wx )

    1.35D + 1.35(L+LR) ▽ 1.35Wy )

    D ▽ 1.5Wx

    D ▽ 1.5Wy

     

    ﹥ Seismic load combinations

    ⅡWhen Orthogonal Effect is not considered, 16 response spectrum load combinations & 8 static load combinations are generated.

    1.35( D+(L+LR) ▽ (RSx▽ESx) )

    1.35( D+(L+LR) ▽ (RSy▽ESy) )

    D + 1.5(RSx▽ESx)

    D +1.5(RSy▽ESy)

    1.35( D+(L+LR) ▽ Ex)

    1.35( D+(L+LR) ▽ Ey)

     D ▽ 1.5Ex

     D ▽ 1.5Ey

    ⅡWhen Orthogonal Effect (with 100:30 Rule applied) is considered, 64 response spectrum load combinations & 24 static load combinations are generated.

    1.35( D+(L+LR) ▽ {1.0(RSx▽ESx) ▽ 0.3(RSy▽ESy)} )

    1.35( D+(L+LR) ▽ {1.0(RSy▽ESy) ▽ 0.3(RSx▽ESx)} )

    1.0D ▽ 1.5{1.0(RSx▽ESx) ▽ 0.3(RSy▽ESy)}

    1.0D ▽ 1.5{1.0(RSy▽ESy) ▽ 0.3(RSx▽ESx)}

    1.35( D+(L+LR) ▽ (1.0EQx▽0.3EQy) )

    1.35( D+(L+LR) ▽ (1.0EQy▽0.3EQx) )

    1.0D ▽ 1.5(1.0EQx▽0.3EQy) )

    1.0D ▽ 1.5(1.0EQy▽0.3EQx) )

    ⅡWhen Orthogonal Effect (with SRSS applied) is considered, 16 response spectrum load combinations and 4 static load combinations are generated.

    1.35( D+(L+LR) ▽ SQRT{(RSx▽ESx)^2+(RSy▽ESy)^2} )

    1.0D ▽ 1.5SQRT{(RSx▽ESx)^2+(RSy▽ESy)^2} )

    1.35( D+(L+LR) ▽ SQRT{Ex^2+Ey^2} )

    1.0D ▽ 1.5SQRT{Ex^2+Ey^2} )

    ﹥ Load combinations for serviceability

    ⅡLoad Factors

    Live Load             份1,1             份1,2             份1,3

    Wind Load           份2,1             份2,2             份2,3

     

    [An example of generation of load combinations in case of the presence of three Live Loads]

    Ⅱ Characteristic Load Combination

    1.0D + 1.0LL1 + 份1,1LL2 + 份1,1LL3 ▽ 份2,1Wx

    1.0D + 份1,1LL1 + 1.0LL2 + 份1,1LL3 ▽ 份2,1Wx

    1.0D + 份1,1LL1 + 份1,1LL2 + 1.0LL3 ▽ 份2,1Wx

    1.0D + 份1,1LL1 + 份1,1LL2 + 份1,1LL3 ▽ 1.0Wx

    1.0D + 1.0LL1 + 份1,1LL2 + 份1,1LL3 ▽ 份2,1Wy

    1.0D + 份1,1LL1 + 1.0LL2 + 份1,1LL3 ▽ 份2,1Wy

    1.0D + 份1,1LL1 + 份1,1LL2 + 1.0LL3 ▽ 份2,1Wy

    1.0D + 份1,1LL1 + 份1,1LL2 + 份1,1LL3 ▽ 1.0Wy

    Ⅱ Frequent Load Combination

    1.0D + 份1,2LL1 + 份1,3LL2 + 份1,3LL3 ▽ 份2,3Wx

    1.0D + 份1,3LL1 + 份1,2LL2 + 份1,3LL3 ▽ 份2,3Wx

    1.0D + 份1,3LL1 + 份1,3LL2 + 份1,2LL3 ▽ 份2,3Wx

    1.0D + 份1,3LL1 + 份1,3LL2 + 份1,3LL3 ▽ 份2,2Wx

    1.0D + 份1,2LL1 + 份1,3LL2 + 份1,3LL3 ▽ 份2,3Wy

    1.0D + 份1,3LL1 + 份1,2LL2 + 份1,3LL3 ▽ 份2,3Wy

    1.0D + 份1,3LL1 + 份1,3LL2 + 份1,2LL3 ▽ 份2,3Wy

    1.0D + 份1,3LL1 + 份1,3LL2 + 份1,3LL3 ▽ 份2,2Wy

    Ⅱ Quasi-permanent Load Combination

    1.0D + 份1,3LL1 + 份1,3LL2 + 份1,3LL3 ▽ 份2,3Wx

    1.0D + 份1,3LL1 + 份1,3LL2 + 份1,3LL3 ▽ 份2,3Wy

     

     

     

     

     

    IS456:2000, Indian Standard, Plain and Reinforced Concrete Code of Practice (Fourth Revision), 2000

    1.5(D + L)

    1.2(D + L + Wx)

    1.2(D + L + Wy)

    1.2(D + L - Wx)

    1.2(D + L - Wy)

    1.5(D + Wx)

    1.5(D + Wy)

    1.5(D - Wx)

    1.5(D - Wy)

    0.9D + 1.5Wx

    0.9D + 1.5Wy

    0.9D - 1.5Wx

    0.9D - 1.5Wy

    1.2(D + L + Ex)

    1.2(D + L + Ey)

    1.2(D + L - Ex)

    1.2(D + L - Ey)

    1.5(D + Ex)

    1.5(D + Ey)

    1.5(D - Ex)

    1.5(D - Ey)

    0.9D + 1.5Ex

    0.9D + 1.5Ey

    0.9D - 1.5Ex

    0.9D - 1.5Ey

    1.2(D + L + (SFx)RSx)

    1.2(D + L + (SFy)RSy)

    1.2(D + L - (SFx)RSx)

    1.2(D + L - (SFy)RSy)

    1.5(D + (SFx)RSx)

    1.5(D + (SFy)RSy)

    1.5(D - (SFx)RSx)

    1.5(D - (SFy)RSy)

    0.9D + 1.5(SFx)RSx

    0.9D + 1.5(SFy)RSy

    0.9D - 1.5(SFx)RSx

    0.9D - 1.5(SFy)RSy

     

    TWN-USD92, Taiwan Standard, Design Specification and Commentary for Concrete Structures, 2003

    1.4D + 1.7(L+LR)

    1.4D + 1.7(L+LR) + 1.7H

    0.9D + 1.7(L+LR) + 1.7H

    1.4D + 1.7H

    0.9D + 1.7H

    0.75(1.4D + 1.7(L+LR) ▽ 1.7Wx )

    0.75(1.4D + 1.7(L+LR) ▽ 1.7Wy )

    0.75( 1.4D + 1.7(L+LR) ▽ 1.87(1.0ESx▽0.3ESy) )

    0.75( 1.4D + 1.7(L+LR) ▽ 1.87(1.0ESy▽0.3ESx) )

    0.9D ▽ 1.43(1.0EQx▽0.3EQy) )

    0.9D ▽ 1.43(1.0EQy▽0.3EQx) )

    0.75( 1.4D + 1.7(L+LR) ▽ 1.87{1.0(RSx▽ESx) ▽ 0.3(RSy▽ESy)} )

    0.75( 1.4D + 1.7(L+LR) ▽ 1.87{1.0(RSy▽ESy) ▽ 0.3(RSx▽ESx)} )

    0.9D ▽ 1.43{1.0(RSx▽ESx) ▽ 0.3(RSy▽ESy)}

    0.9D ▽ 1.43{1.0(RSy▽ESy) ▽ 0.3(RSx▽ESx)}

    GB50010-02, Chinese Code for design of concrete structures, 2002

    1.35(D+CR+SH) + 1.4(0.7)(L+LR)

    1.2(D+CR+SH) + 1.4(L+LR)

    1.0(D+CR+SH) + 1.4(L+LR)

    1.2(D+CR+SH) + 1.4Wx

    1.2(D+CR+SH) + 1.4Wy

    1.2(D+CR+SH) - 1.4Wx

    1.2(D+CR+SH) - 1.4Wy

    1.0(D+CR+SH) + 1.4Wx

    1.0(D+CR+SH) + 1.4Wy

    1.0(D+CR+SH) - 1.4Wx

    1.0(D+CR+SH) - 1.4Wy

    1.2(D+CR+SH) + 1.4(L+LR) + 1.4(0.6)Wx

    1.2(D+CR+SH) + 1.4(L+LR) + 1.4(0.6)Wy

    1.2(D+CR+SH) + 1.4(L+LR) - 1.4(0.6)Wx

    1.2(D+CR+SH) + 1.4(L+LR) - 1.4(0.6)Wy

    1.0(D+CR+SH) + 1.4(L+LR) + 1.4(0.6)Wx

    1.0(D+CR+SH) + 1.4(L+LR) + 1.4(0.6)Wy

    1.0(D+CR+SH) + 1.4(L+LR) - 1.4(0.6)Wx

    1.0(D+CR+SH) + 1.4(L+LR) - 1.4(0.6)Wy

    1.2(D+CR+SH) + 1.4(0.7)(L+LR) + 1.4Wx

    1.2(D+CR+SH) + 1.4(0.7)(L+LR) + 1.4Wy

    1.2(D+CR+SH) + 1.4(0.7)(L+LR) - 1.4Wx

    1.2(D+CR+SH) + 1.4(0.7)(L+LR) - 1.4Wy

    1.0(D+CR+SH) + 1.4(0.7)(L+LR) + 1.4Wx

    1.0(D+CR+SH) + 1.4(0.7)(L+LR) + 1.4Wy

    1.0(D+CR+SH) + 1.4(0.7)(L+LR) - 1.4Wx

    1.0(D+CR+SH) + 1.4(0.7)(L+LR) - 1.4Wy

    1.2((D+CR+SH)+0.5(L+LR)) + 1.3Ex

    1.2((D+CR+SH)+0.5(L+LR)) + 1.3Ey

    1.2((D+CR+SH)+0.5(L+LR)) - 1.3Ex

    1.2((D+CR+SH)+0.5(L+LR)) - 1.3Ey

    1.0((D+CR+SH)+0.5(L+LR)) + 1.3Ex

    1.0((D+CR+SH)+0.5(L+LR)) + 1.3Ey

    1.0((D+CR+SH)+0.5(L+LR)) - 1.3Ex

    1.0((D+CR+SH)+0.5(L+LR)) - 1.3Ey

    1.2((D+CR+SH)+0.5(L+LR)) + 1.3(SFx)RSx

    1.2((D+CR+SH)+0.5(L+LR)) + 1.3(SFy)RSy

    1.2((D+CR+SH)+0.5(L+LR)) - 1.3(SFx)RSx

    1.2((D+CR+SH)+0.5(L+LR)) - 1.3(SFy)RSy

    1.0((D+CR+SH)+0.5(L+LR)) + 1.3(SFx)RSx

    1.0((D+CR+SH)+0.5(L+LR)) + 1.3(SFy)RSy

    1.0((D+CR+SH)+0.5(L+LR)) - 1.3(SFx)RSx

    1.0((D+CR+SH)+0.5(L+LR)) - 1.3(SFy)RSy

    1.35(D+CR+SH) + 1.4(0.7)(L+S)

    1.2(D+CR+SH) + 1.4(L+S)

    1.0(D+CR+SH) + 1.4(L+S)

    1.2(D+CR+SH) + 1.4(L+S) + 1.4(0.6)Wx

    1.2(D+CR+SH) + 1.4(L+S) + 1.4(0.6)Wy

    1.2(D+CR+SH) + 1.4(L+S) - 1.4(0.6)Wx

    1.2(D+CR+SH) + 1.4(L+S) - 1.4(0.6)Wy

    1.0(D+CR+SH) + 1.4(L+S) + 1.4(0.6)Wx

    1.0(D+CR+SH) + 1.4(L+S) + 1.4(0.6)Wy

    1.0(D+CR+SH) + 1.4(L+S) - 1.4(0.6)Wx

    1.0(D+CR+SH) + 1.4(L+S) - 1.4(0.6)Wy

    1.2(D+CR+SH) + 1.4(0.7)(L+S) + 1.4Wx

    1.2(D+CR+SH) + 1.4(0.7)(L+S) + 1.4Wy

    1.2(D+CR+SH) + 1.4(0.7)(L+S) - 1.4Wx

    1.2(D+CR+SH) + 1.4(0.7)(L+S) - 1.4Wy

    1.0(D+CR+SH) + 1.4(0.7)(L+S) + 1.4Wx

    1.0(D+CR+SH) + 1.4(0.7)(L+S) + 1.4Wy

    1.0(D+CR+SH) + 1.4(0.7)(L+S) - 1.4Wx

    1.0(D+CR+SH) + 1.4(0.7)(L+S) - 1.4Wy

    1.2((D+CR+SH)+0.5(L+S)) + 1.3Ex

    1.2((D+CR+SH)+0.5(L+S)) + 1.3Ey

    1.2((D+CR+SH)+0.5(L+S)) - 1.3Ex

    1.2((D+CR+SH)+0.5(L+S)) - 1.3Ey

    1.0((D+CR+SH)+0.5(L+S)) + 1.3Ex

    1.0((D+CR+SH)+0.5(L+S)) + 1.3Ey

    1.0((D+CR+SH)+0.5(L+S)) - 1.3Ex

    1.0((D+CR+SH)+0.5(L+S)) - 1.3Ey

    1.2((D+CR+SH)+0.5(L+S)) + 1.3(SFx)RSx

    1.2((D+CR+SH)+0.5(L+S)) + 1.3(SFy)RSy

    1.2((D+CR+SH)+0.5(L+S)) - 1.3(SFx)RSx

    1.2((D+CR+SH)+0.5(L+S)) - 1.3(SFy)RSy

    1.0((D+CR+SH)+0.5(L+S)) + 1.3(SFx)RSx

    1.0((D+CR+SH)+0.5(L+S)) + 1.3(SFy)RSy

    1.0((D+CR+SH)+0.5(L+S)) - 1.3(SFx)RSx

    1.0((D+CR+SH)+0.5(L+S)) - 1.3(SFy)RSy

  •  SRC

    SSRC79, Structural Stability Research Council, A Specification for the Design of Steel-Concrete Composite Columns, 1979

    Load combinations for strength verification

    D+L+LR

    0.75*(D+L+LR+Wx)

    0.75*(D+L+LR-Wx)

    0.75*(D+L+LR+Wy)

    0.75*(D+L+LR-Wy)

    0.75*(D+Wx)

    0.75*(D-Wx)

    0.75*(D+Wy)

    0.75*(D-Wy)

    0.75*(D+L+LR+Ex)

    0.75*(D+L+LR-Ex)

    0.75*(D+L+LR+Ey)

    0.75*(D+L+LR-Ey)

    0.75*(D+Ex)

    0.75*(D-Ex)

    0.75*(D+Ey)

    0.75*(D-Ey)

    0.75*(D+L+LR+(SFx*EspX))

    0.75*(D+L+LR-(SFx*EspX))

    0.75*(D+L+LR+(SFy*EspY))

    0.75*(D+L+LR-(SFy*EspY))

    0.75*(D+(SFx*EspX))

    0.75*(D-(SFx*EspX))

    0.75*(D+(SFy*EspY))

    0.75*(D-(SFy*EspY))

    TWN-SRC93, Taiwan Standard, Design Specification and Commentary for Steel Reinforced Concrete Structures, 2003

    1.4D

    1.2(D+T) + 1.6(L+H) + 0.5LR

    1.2(D+T) + 1.6(L+H) + 0.5S

    1.2(D+T) + 1.6(L+H) + 0.5R

    1.2D + 1.6LR + 1.0L

    1.2D + 1.6S + 1.0L

    1.2D + 1.6R + 1.0L

    1.2D + 1.6LR ▽ 0.8Wx

    1.2D + 1.6LR ▽ 0.8Wy

    1.2D + 1.6S ▽ 0.8Wx

    1.2D + 1.6S ▽ 0.8Wy

    1.2D + 1.6R ▽ 0.8Wx

    1.2D + 1.6R ▽ 0.8Wy

    1.2D ▽ 1.6Wx + 1.0L + 0.5LR

    1.2D ▽ 1.6Wy + 1.0L + 0.5LR

    1.2D ▽ 1.6Wx + 1.0L + 0.5S

    1.2D ▽ 1.6Wy + 1.0L + 0.5S

    1.2D ▽ 1.6Wx + 1.0L + 0.5R

    1.2D ▽ 1.6Wy + 1.0L + 0.5R

    0.9D ▽ 1.6Wx + 1.6H

    0.9D ▽ 1.6Wy + 1.6H

    1.2D ▽ 1.0(1.0ESx▽0.3ESy) + 1.0L + 0.2S

    1.2D ▽ 1.0(1.0ESy▽0.3ESx) + 1.0L + 0.2S

    1.2D ▽ 1.0{1.0(RSx▽ESx) ▽ 0.3(RSy▽ESy)} + 1.0L + 0.2S

    1.2D ▽ 1.0{1.0(RSy▽ESy) ▽ 0.3(RSx▽ESx)} + 1.0L + 0.2S

    0.9D ▽ 1.0(1.0ESx▽0.3ESy) + 1.6H

    0.9D ▽ 1.0(1.0ESy▽0.3ESx) + 1.6H

    0.9D ▽ 1.0{1.0(RSx▽ESx) ▽ 0.3(RSy▽ESy)} + 1.6H

    0.9D ▽ 1.0{1.0(RSy▽ESy) ▽ 0.3(RSx▽ESx)} + 1.6H

    JGJ138-01, Chinese Technical specification for steel reinforced concrete composite structures, 2001

    1.35(D+CR+SH) + 1.4(0.7)(L+LR)

    1.2(D+CR+SH) + 1.4(L+LR)

    1.0(D+CR+SH) + 1.4(L+LR)

    1.2(D+CR+SH) + 1.4Wx

    1.2(D+CR+SH) + 1.4Wy

    1.2(D+CR+SH) - 1.4Wx

    1.2(D+CR+SH) - 1.4Wy

    1.0(D+CR+SH) + 1.4Wx

    1.0(D+CR+SH) + 1.4Wy

    1.0(D+CR+SH) - 1.4Wx

    1.0(D+CR+SH) - 1.4Wy

    1.2(D+CR+SH) + 1.4(L+LR) + 1.4(0.6)Wx

    1.2(D+CR+SH) + 1.4(L+LR) + 1.4(0.6)Wy

    1.2(D+CR+SH) + 1.4(L+LR) - 1.4(0.6)Wx

    1.2(D+CR+SH) + 1.4(L+LR) - 1.4(0.6)Wy

    1.0(D+CR+SH) + 1.4(L+LR) + 1.4(0.6)Wx

    1.0(D+CR+SH) + 1.4(L+LR) + 1.4(0.6)Wy

    1.0(D+CR+SH) + 1.4(L+LR) - 1.4(0.6)Wx

    1.0(D+CR+SH) + 1.4(L+LR) - 1.4(0.6)Wy

    1.2(D+CR+SH) + 1.4(0.7)(L+LR) + 1.4Wx

    1.2(D+CR+SH) + 1.4(0.7)(L+LR) + 1.4Wy

    1.2(D+CR+SH) + 1.4(0.7)(L+LR) - 1.4Wx

    1.2(D+CR+SH) + 1.4(0.7)(L+LR) - 1.4Wy

    1.0(D+CR+SH) + 1.4(0.7)(L+LR) + 1.4Wx

    1.0(D+CR+SH) + 1.4(0.7)(L+LR) + 1.4Wy

    1.0(D+CR+SH) + 1.4(0.7)(L+LR) - 1.4Wx

    1.0(D+CR+SH) + 1.4(0.7)(L+LR) - 1.4Wy

    1.2((D+CR+SH)+0.5(L+LR)) + 1.3Ex

    1.2((D+CR+SH)+0.5(L+LR)) + 1.3Ey

    1.2((D+CR+SH)+0.5(L+LR)) - 1.3Ex

    1.2((D+CR+SH)+0.5(L+LR)) - 1.3Ey

    1.0((D+CR+SH)+0.5(L+LR)) + 1.3Ex

    1.0((D+CR+SH)+0.5(L+LR)) + 1.3Ey

    1.0((D+CR+SH)+0.5(L+LR)) - 1.3Ex

    1.0((D+CR+SH)+0.5(L+LR)) - 1.3Ey

    1.2((D+CR+SH)+0.5(L+LR)) + 1.3(SFx)RSx

    1.2((D+CR+SH)+0.5(L+LR)) + 1.3(SFy)RSy

    1.2((D+CR+SH)+0.5(L+LR)) - 1.3(SFx)RSx

    1.2((D+CR+SH)+0.5(L+LR)) - 1.3(SFy)RSy

    1.0((D+CR+SH)+0.5(L+LR)) + 1.3(SFx)RSx

    1.0((D+CR+SH)+0.5(L+LR)) + 1.3(SFy)RSy

    1.0((D+CR+SH)+0.5(L+LR)) - 1.3(SFx)RSx

    1.0((D+CR+SH)+0.5(L+LR)) - 1.3(SFy)RSy

    1.35(D+CR+SH) + 1.4(0.7)(L+S)

    1.2(D+CR+SH) + 1.4(L+S)

    1.0(D+CR+SH) + 1.4(L+S)

    1.2(D+CR+SH) + 1.4(L+S) + 1.4(0.6)Wx

    1.2(D+CR+SH) + 1.4(L+S) + 1.4(0.6)Wy

    1.2(D+CR+SH) + 1.4(L+S) - 1.4(0.6)Wx

    1.2(D+CR+SH) + 1.4(L+S) - 1.4(0.6)Wy

    1.0(D+CR+SH) + 1.4(L+S) + 1.4(0.6)Wx

    1.0(D+CR+SH) + 1.4(L+S) + 1.4(0.6)Wy

    1.0(D+CR+SH) + 1.4(L+S) - 1.4(0.6)Wx

    1.0(D+CR+SH) + 1.4(L+S) - 1.4(0.6)Wy

    1.2(D+CR+SH) + 1.4(0.7)(L+S) + 1.4Wx

    1.2(D+CR+SH) + 1.4(0.7)(L+S) + 1.4Wy

    1.2(D+CR+SH) + 1.4(0.7)(L+S) - 1.4Wx

    1.2(D+CR+SH) + 1.4(0.7)(L+S) - 1.4Wy

    1.0(D+CR+SH) + 1.4(0.7)(L+S) + 1.4Wx

    1.0(D+CR+SH) + 1.4(0.7)(L+S) + 1.4Wy

    1.0(D+CR+SH) + 1.4(0.7)(L+S) - 1.4Wx

    1.0(D+CR+SH) + 1.4(0.7)(L+S) - 1.4Wy

    1.2((D+CR+SH)+0.5(L+S)) + 1.3Ex

    1.2((D+CR+SH)+0.5(L+S)) + 1.3Ey

    1.2((D+CR+SH)+0.5(L+S)) - 1.3Ex

    1.2((D+CR+SH)+0.5(L+S)) - 1.3Ey

    1.0((D+CR+SH)+0.5(L+S)) + 1.3Ex

    1.0((D+CR+SH)+0.5(L+S)) + 1.3Ey

    1.0((D+CR+SH)+0.5(L+S)) - 1.3Ex

    1.0((D+CR+SH)+0.5(L+S)) - 1.3Ey

    1.2((D+CR+SH)+0.5(L+S)) + 1.3(SFx)RSx

    1.2((D+CR+SH)+0.5(L+S)) + 1.3(SFy)RSy

    1.2((D+CR+SH)+0.5(L+S)) - 1.3(SFx)RSx

    1.2((D+CR+SH)+0.5(L+S)) - 1.3(SFy)RSy

    1.0((D+CR+SH)+0.5(L+S)) + 1.3(SFx)RSx

    1.0((D+CR+SH)+0.5(L+S)) + 1.3(SFy)RSy

    1.0((D+CR+SH)+0.5(L+S)) - 1.3(SFx)RSx

    1.0((D+CR+SH)+0.5(L+S)) - 1.3(SFy)RSy

     

    AIJ-ASD02, Architectural Institute of Japan, Allowable Stress Design, 2002 (available upon request)

    Load combinations for strength verification

    D+L+LR

    D+L+LR+Wx

    D+L+LR-Wx

    D+L+LR+Wy

    D+L+LR-Wy

    D+L+LR+Ex

    D+L+LR-Ex

    D+L+LR+Ey

    D+L+LR-Ey

    D+Ex

    D-Ex

    D+Ey

    D-Ey

    D+L+LR+(SFx*EspX)

    D+L+LR-(SFx*EspX)

    D+L+LR+(SFy*EspY)

    D+L+LR-(SFy*EspY)

    D+(SFx*EspX)

    D-(SFx*EspX)

    D+(SFy*EspY)

    D-(SFy*EspY)

     

    AIJ-WSD99, Architectural Institute of Japan, Working Stress Design, 1999 (available upon request)Load combinations for strength verification

    D+L+LR

    D+L+LR+Wx

    D+L+LR-Wx

    D+L+LR+Wy

    D+L+LR-Wy

    D+Wx

    D-Wx

    D+Wy

    D-Wy

    D+L+LR+Ex

    D+L+LR-Ex

    D+L+LR+Ey

    D+L+LR-Ey

    D+Ex

    D-Ex

    D+Ey

    D-Ey

    D+L+LR+(SFx*EspX)

    D+L+LR-(SFx*EspX)

    D+L+LR+(SFy*EspY)

    D+L+LR-(SFy*EspY)

    D+(SFx*EspX)

    D-(SFx*EspX)

    D+(SFy*EspY)

    D-(SFy*EspY)

    AIJ-SRC01. Architectural Institute of Japan, Allowable Stress Design, 2001 (available upon request)

    Load combinations for strength verification

    D+L+LR

    D+L+LR+Wx

    D+L+LR-Wx

    D+L+LR+Wy

    D+L+LR-Wy

    D+L+LR+Ex

    D+L+LR-Ex

    D+L+LR+Ey

    D+L+LR-Ey

    D+Ex

    D-Ex

    D+Ey

    D-Ey

    D+Wx

    D-Wx

    D+Wy

    D-Wy

    D+L+LR+(SFx*EspX)

    D+L+LR-(SFx*EspX)

    D+L+LR(SFy*EspY)

    D+L+LR-(SFy*EspY)

    D+(SFx*EspX)

    D-(SFx*EspX)

    D+(SFy*EspY)+

    D-(SFy*EspY)

     

 

< Static Load >

1

D

Dead Load  

2

L

Live Load

3

LR

Roof Live Load

4

Wx

Wind Load on Structure in X-direction

5

Wy

Wind Load on Structure in Y-direction

6

Ex

Earthquake in X-direction

7

Ey

Earthquake in Y-direction

8

EVT

Earthquake in Z-direction

9

T

Temperature

10

S

Snow Load

11

R

Rain Load

12

EP

Earth Pressure

13

WP

Steam Flow Pressure

14

FP

Fluid Pressure

15

SH

Shrinkage

16

CR

Creep

17

PS

Prestress

18

IP

Ice Pressure

 

< Dynamic Load >

1

RSx

Response Spectrum in X-direction

2

RSy

Response Spectrum in Y-direction

3

RSz

Response Spectrum in Z-direction

4

ESx

Accidental Torsional Moment for Response Spectrum in X-direction

5

ESy

Accidental Torsional Moment for Response Spectrum in Y-direction

6

ESz

Accidental Torsional Moment for Response Spectrum in Z-direction

 

< Factor >

1

SFx

Scale up factor of X-Direction

2

SFy

Scale up factor in Y-direction

3

SFz

Scale up factor of Z-Direction

 

 

Calculations of Principal Stresses, Effective Stresses and Maximum Shear Stresses for each Load Combination Type

1. Available Force Components

 

Result Type

Component

Plate Force/Moment

Fmax, Fmin, Mmax, Mmin

Plane-Stress/Plate Stress

Sig-max, Sig-min, Sig-EFF, Max-Shear

Plane Strain

Sig-P1, Sig-P2, Sig-P3, Max-Shear, Sig-EFF

Solid

Sig-P1, Sig-P2, Sig-P3, Max-Shear, Sig-EFF

Axisymmetric

Sig-P1, Sig-P2, Sig-P3, Max-Shear, Sig-EFF

 

2. Examples - for each Load Case/Load Combination

 

Load Cases

LC1, LC2, LC3, LC4

 

Load Combination

Name

Type

Cases

CB1

Add

LC1 + LC2

ENV1

Envelope

LC2, LC3, LC4

CB2

Add

CB1 + ENV1

ENV2

Envelope

CB1, CB2, LC4

 

a. The load combination CB1 is an Add type and the types of displayed results are identical to those of general load cases.

 

b. ENV1 and 2 are Envelope type load combinations and the results are classified into Max, Min and All.

 

c. CB2 is an Add type load combination but includes an Envelope type load combination ENV1. Therefore, the results are classified into Max, Min and All.

 

d. "Max" displays the maximum of the results, "Min" displays the minimum and "All" displays the absolute maximum.

Check the option in the Preference menu to produce the "All" type results with signs instead of the absolute values.

 

 

3. Calculation of CB1 stresses (Add type load combination that includes general load cases)

 

 

 

 

Ｃ CB1 = LC1 + LC2

a. Principal stress: Add the stresses of all load cases for each stress component and then recalculate the principal stress based on the sum of the stresses for each stress component.

 

b. Sig-EFF & Max-Shear: Calculate based on the principal stress calculated from above (*Note: The principal stress, effective stress and maximum shear stress of CB1 are not calculated simply by summing the results of LC1 and LC2.)

 

 

4. Calculation of ENV1 stresses (Envelope type load combination that includes general Load Cases or Add type load combinations)

 

 

 

 

Ｃ ENV1 = Envelope (LC2, LC3, LC4)

    Principal stress & Sig-EFF & Max-Shear: Display the maximum, minimum and absolute maximum values among the principal stresses of LC2, LC3 and LC4. The same goes for Sig-EFF & Max-Shear.

 

 

5. Calculation of CB2 stresses (Add type load combination that includes Envelope type load combinations)

 

 

 

Ｃ CB2_max = CB1+ENV1_max

     CB2_min = CB1+ENV1_min

     CB2_all = CB1+ENV1_all

 

a. Based on the stresses of 'CB2_max' 'CB2_min' and 'CB2_all' for each stress component, Sig-Max, Sig-Min, Sig-EFF and Max-Shear are recalculated.

 

b. CB2 load combination includes Envelope type load combinations, but it is an Add type load combination. First, calculate the sum of the stresses of all load cases for each stress component and recalculate the principal stress, effective stress, etc based on the sum of the stresses for each stress component.

 

 

6. Calculation of ENV2 stresses (Envelope type load combination that includes Envelope type load combinations) - The calculation method is identical to that for ENV1.

 

Ｃ ENV2_max = MAX[LC4, CB1, max(CB2)]

     ENV2_min = MIN[LC4, CB1, min(CB2)]

     ENV2_all = MAX[abs(LC4), abs(CB1), all(CB2)]

 

Note
1. This calculation method is identically applicable to the load combination that includes the load cases whose results are classified into max, min and all, i.e., the load cases such as moving load cases, settlement load cases and time history load cases.

 

2. The 'all' condition of an Envelope type load combination or an Add type load combination that includes an Envelope type load combination produces the maximum of absolute values. Whether to produce the values with signs or without signs can be determined from the Tools>Preferences.