Load case combinations according to EC

SCIA Engineer makes no distinction between primary and secondary variable load case. The algorithm takes one load case (in turn) as the primary one and all the others are considered secondary. The coefficients Psi0 are assigned accordingly. Doing this in turns, all the possible combinations are exploited. No combination should contain two variable load cases with the full coefficient 1.5 (one of them is always reduced by the corresponding Psi0).

It may happen, under some special circumstances, that this approach is not the most economical one (if the primary load is small (insignificant) and the secondary one is large - there is the difference if the coefficient Psi0=0.5 is applied to the large load or the small one). However, this is based on the assumption that the large load is usually taken as the primary one.

Let us consider the following load cases, groups and combinations.

Load cases:

Name	Description	Action type	Load group	Load type	Specification	Direction	Duration	Master load case
LC1	self weight	Permanent	LG1	Self weight		-Z
LC2	live load (20 kNm)	Variable	LG2	Static	Standard		Long	None
LC3	snow load (10 kNm)	Variable	LG3	Static	Standard		Long	None

Load groups:

Name	Load	Relation	Coeff 2
LG1	Permanent
LG2	Variable	Standard	Cat E: Storage
LG3	Variable	Standard	Snow load H < 1000 m a.s.l.

Combinations:

Name	Description	Type	Load cases	Coeff [1]
CO1	(1)	EN - ULS Fundamental (STR)	LC1 - self weight	1.00
			LC2 - live load (20 kNm)	1.00
			LC3 - snow load (10 kNm)	1.00
CO2	(7)	EN - ULS Accidential - Psi 1	LC1 - self weight	1.00
			LC2 - live load (20 kNm)	1.00
			LC3 - snow load (10 kNm)	1.00
CO3	(1)	EN - ULS Accidential - Psi 2	LC1 - self weight	1.00
			LC2 - live load (20 kNm)	1.00
			LC3 - snow load (10 kNm)	1.00

Let us use the following combinations setup:

 

We get the following envelope combinations:

C1.1	(118)	Envelope – ultimate	LC1 – self weight	1.35
C1.2	(119)	Envelope – ultimate	LC1 – self weight LC2 - live load (20 kNm) LC3 – snow load (10 kNm)	1.35 1.50 0.75
C1.3	(120)	Envelope – ultimate	LC1 – self weight LC2 - live load (20 kNm) LC3 – snow load (10 kNm)	1.00 1.50 0.75
C1.4	(121)	Envelope – ultimate	LC1 – self weight LC2 - live load (20 kNm) LC3 – snow load (10 kNm)	1.35 1.50 1.50
C1.5	(122)	Envelope – ultimate	LC1 – self weight LC2 - live load (20 kNm) LC3 – snow load (10 kNm)	1.00 1.50 1.50
C2.1	(123)	Envelope – ultimate	LC1 – self weight	1.00
C2.2	(124)	Envelope – ultimate	LC1 – self weight LC2 - live load (20 kNm) LC3 – snow load (10 kNm)	1.00 0.90 0.00
C2.3	(125)	Envelope – ultimate	LC1 – self weight LC2 - live load (20 kNm) LC3 – snow load (10 kNm)	1.00 0.80 0.20
C3.1	(126)	Envelope – ultimate	LC1 – self weight	1.00
C3.2	(127)	Envelope – ultimate	LC1 – self weight LC2 - live load (20 kNm) LC3 – snow load (10 kNm)	1.00 0.80 0.00
C3.3	(128)	Envelope – ultimate	LC1 – self weight LC2 - live load (20 kNm) LC3 – snow load (10 kNm)	1.00 0.80 0.00

Let us review the already stated:

LC1 – permanent => LG 1

LC2-variable (live load (20kNm)) => LG2 (Cat E : Storage) => from setup: Psi 0 =1.0, Psi1=0.9, Psi2=0.8

LC3–variable (snow load (10kNm) ) => LG3 (Snow load H < 1000 m a.s.l.") => from setup: Psi 0 =0.5, Psi1=0.2, Psi2=0.0

Combination C01 (EN - ULS Fundamental(STR)) : LC1+LC2+LC3

We use Eq.6.10

It is not specified at the load case if it is the primary or secondary load case. Therefore, always one load case (group) in turn is taken as the primary one and the rest is considered secondary. This is repeated until all the load cases are used for the primary one.

We get the following combinations:

First of all, we get the combination with just the permanent load cases

C1.1 1.35 * LC1

Secondly, one variable load case is taken as primary one (1.5) and the rest as secondary (1.5 * Psi0) + the permanent load is either favourable (1.0) or unfavourable (1.35)

The combinations obtained are:

Permanent load case LC1 is unfavourable (1.35) and LC2 is the primary load.

C1.2 1.35*LC1 + 1.5*LC2 + 1.5*Psi0*LC3 = 1.35*LC1 + 1.5*LC2 + (1.5*0.5)*LC3 = 1.35*LC1 + 1.5*LC2 + 0.75*LC3

(Psi0 = 0.5; LG3 is (Snow load H < 1000 m a.s.l.") )

Permanent load case LC1is favourable (1.00) and LC2 is the primary load.

C1.3 1.0*LC1 + 1.5*LC2 + 1.5*Psi0*LC3 = 1.0*LC1 + 1.5*LC2 + (1.5*0.5)*LC3 = 1.0*LC1 + 1.5*LC2 + 0.75*LC3

(Psi0 = 0.5; LG3 is (Snow load H < 1000 m a.s.l.") )

Permanent load case LC1 is unfavourable (1.35) and LC3 is the primary load.

C1.4 1.35*LC1 + 1.5*LC3 + 1.5*Psi0*LC2 = 1.35*LC1 + 1.5*LC3 + (1.5*1.0)*LC2 = 1.35*LC1 + 1.5*LC3 + 1.5*LC2

(Psi0 = 1.0; LG2 is Category E )

Permanent load case LC1 is favourable (1.00) and LC3 is the primary load.

C1.5 1.0*LC1 + 1.5*LC3 + 1.5*Psi0 = 1.0*LC1 + 1.5*LC3 + (1.5*1.0)*LC2 = 1.0*LC1 + 1.5*LC3 + 1.5*LC2

(Psi0 = 1.0; LG2 is Category E )

Then we have combinations C2 and C3 that are created using these rules:

The choice between 1,l or 2,l is done by the user. Default is 1,l.

C02 - EN - ULS Accidental - Psi 1 : LC1+LC2+LC3

First of all, we get the combination with just the permanent load cases

C2.1 1.0 * LC1

Second, the combination rule applies Psi1 to one load case and Psi2 to the other one.

C2.2 1.0 * LC1 + Psi1*LC2 + Psi2*LC3 = 1.0 * LC1 + 0.9*LC2 + 0.0*LC3

C2.3 1.0 * LC1 + Psi2(LG2) *LC2 + Psi1(LG3)*LC3 = 1.0 * LC1 + 0.8*LC2 + 0.2*LC3

C03 - EN - ULS Accidental - Psi 2 : LC1+LC2+LC3

First of all, we get the combination with just the permanent load cases

C3.1 1.0 * LC1

Second, the combination rule applies Psi1 to one load case and Psi2 to the other one.

C3.2 1.0 * LC1 + Psi2*LC2 + Psi2*LC3 = 1.0 * LC1 + 0.8*LC2 + 0.0*LC3

C3.3 1.0 * LC1 + Psi2(LG2) *LC2 + Psi2(LG3)*LC3 = 1.0 * LC1 + 0.8*LC2 + 0.0*LC3

In addition, the combinations setup dialogue makes it possible to say that instead of Eq.6.10, formulas Eq.6.10a & Eq.6.10b should be used and the rule for the combination is:

The choice between Eq.6.10 and (Eq.6.10a & Eq.6.10.b) is done in the National Annex.

The default is Eq.6.10.