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Calculation of the load combinations for the bearing capacity, at persistent or variable situation and accidental and seismic situations, according to CTE DB SE, Art. 4 and EHE-08, Art. 13

Abstract
  • For the correct structure calculations, the CTE code proposes increments for each action with different factors related to the kind of action, and combination of the different actions facored with combination factors according to the kind of action and the verification considered.

  • It is not easy to control at calculation prgrams if the automatic code combinations, and the "default" factors are correctly generated following the CTE. With this utility it is possible to generate the required combination for each structure from the actual loads present, and to check its generation.

  • At structures with many kinds of loads a great amount of load combinations is generated, so it is reccomended to select the exact actions present at the structure.

Calculation
Parameters:
Code to use:CTEThere are differences between the combinations generated with the CTE and the EHE-08. See the author's notes.
 EHE-08
Show all factors:YesIncrement and combination factors are shown instead its product.
Show zero values:YesThe actions with null factors are showed at list. Repeated combinations can be generated. This option is interesting only to check the combinations generation.
Fators before names:YesIt is possible to select the position of the names respect to the action names.
Combination prefixes:  
Persistent or variable situation: 
Extraordinary or eventual situation: 
Seismic situation: 
Permanent actions:ActionsSyncronised(*1)
effect
NameγG,desγG,fabγG,fab
Acc
 
Self weight:1.350.80 
Inner walls weight:1.350.80 
Fachades weight:1.350.80 
Equipment weight:1.350.80 
Soil weight:1.350.80 
Soil push:1.350.70 
Water push:1.20.90 
 Actions NameγP,desγP,fabγP,fab
Acc
 
Pre-stress:(*2)Pre-stressed110 
  Post-stressed 110 
Live loads:(*3)Actions NameγQ,desγQ,fabψ0ψ1ψ2
A1-Residence - Homes or romms at hotels or clinics: 1.500.70.50.3
A2-Residence - depots: 1.500.70.50.3
B-Office: 1.500.70.50.3
C1-Public - Zones with tables and chairs: 1.500.70.70.6
C2-Public - Zones with fixed seats: 1.500.70.70.6
C3-Public - Zones without obstacles (lobbys, halls...): 1.500.70.70.6
C4-Public - Gymnastics: 1.500.70.70.6
C5-Public - Zones of crowding: 1.500.70.70.6
D1-Commercial - Commercial spaces: 1.500.70.70.6
D2-Commercial - Supermarkets or malls: 1.500.70.70.6
E-Use of light vehicles traffic and parking areas (<30kN):(*4) 1.500.70.70.6
G-Use of non accesible roofs (maintaining only):(*5) 1.50000
Snow:Height
> 1000 m
1.500.70.50.2
  Height
<= 1000 m
 1.500.50.20
Wind . X+: 1.500.60.50
Wind . X-:(*6)Change of the
sign to X+
1.500.60.50
Wind . Y+: 1.500.60.50
Wind . Y-:Change of the
sign to Y+
1.500.60.50
Temperature: 1.500.60.50
Soil variable loads: 1.500.70.70.7
Accidental loads:(*7)Actions NameγQ,des
γQ,fab
 
Seismic X:(*8) 1 
Seismic Y: 1 
Seismic Z: 1 
Fire / Firetruck load: 1 
Vehicle impact: 1 
Explosion: 1 
 
(*1)The syncronised effect avoids in the same combination to appear some actions with favourable effect and others with unfavourable effect, but all of them with the same. See author's notes.
(*2)As pre-stress factors are 1 at favourable and unfavourable situations, it presence does not increment the number of cobinations in Ultimate Limit States. But in Serviceable Limit States it increments the number of combinations because it is affected by the factors defined at EHE-08, art. 12.2.
(*3)The live loads has been desglosed according to the points of the CTE DB SE-AE 3.1.1 table 3.1 because following the ap. 8, "Related to the actions combinations, the live loads of each kind of use will be considered as different actions. The items of each point ot the table 3.1 are different types". More information at the first author's note of the "Live loads" utility.
(*4)At CTE DB-SE 4.2.3 table 4.2, at uses notation the letter E has been ommited, being displaced the following uses notation, and without maching with the CTE DB SE-A 3.1.1 table 3.1.
(*5)At accesible roofs the values corresponding to the use of the access will be adopted (CTE DB SE 4.2.3, table 4.1), so it will have to be defined like any other action of the corresponding use.
(*6)When change of sign is active, the name will not appear, but the name of the positive wind will sign changed (Wind X+ or Wind Y+). It is reccommended to change the name of the wind from "WIND X+" to "WIND X", or from "WIND Y+" to "WIND Y" to avoid mistakes. It can be useful not to activate the change of sign at buildings with the opposite facade sheltered, where only exists one pressure positive value, and another suction negative value.
(*7)According the CTE DB SE 4.2.2, accidental actions have to combine with design value Ad, but there is not defined its increment factor. As in EHE-08, 12.1 the increment factors are defined for accidental actions as one, with favorable and unfavorable effect, this is which have been considered. For permanent and prestress actions in accidental combinations according to the CTE, "In accidental situation, all the security factors (γG, γP, γQ), equals zero if favorable effect, and one if unfavorable, with previous terms." See diferences of γP between the CTE and the EHE at Author's notes.
(*8)The horizontal seismic loads combine according to the 30% rule, following the seismic regulation NCSE-2002, art. 3.4.
All the parameters are activated and available for users with an active subscription. (+info)

Results:
Persistent or variabe situation:38 
Accidental or seismic situation:8 
Extraordinary or eventual situation:14 
Total:60Combinations 

ULS01:SLFW*1.35+PARTW*1.35+A1_HOME*1.5+WINDX+*0.9 
ULS02:SLFW*1.35+PARTW*1.35+A1_HOME*1.5-WINDX+*0.9 
ULS03:SLFW*1.35+PARTW*1.35+A1_HOME*1.5 
ULS04:SLFW*1.35+PARTW*1.35+WINDX+*0.9 
ULS05:SLFW*1.35+PARTW*1.35-WINDX+*0.9 
ULS06:SLFW*1.35+PARTW*1.35 
ULS07:SLFW*1.35+PARTW*1.35+G_ROOFNA*1.5+A1_HOME*1.05+WINDX+*0.9
ULS08:SLFW*1.35+PARTW*1.35+G_ROOFNA*1.5+A1_HOME*1.05-WINDX+*0.9
ULS09:SLFW*1.35+PARTW*1.35+G_ROOFNA*1.5+A1_HOME*1.05 
ULS10:SLFW*1.35+PARTW*1.35+G_ROOFNA*1.5+WINDX+*0.9 
ULS11:SLFW*1.35+PARTW*1.35+G_ROOFNA*1.5-WINDX+*0.9 
ULS12:SLFW*1.35+PARTW*1.35+G_ROOFNA*1.5 
ULS13:SLFW*1.35+PARTW*1.35+A1_HOME*1.05+WINDX+*0.9 
ULS14:SLFW*1.35+PARTW*1.35+A1_HOME*1.05-WINDX+*0.9 
ULS15:SLFW*1.35+PARTW*1.35+A1_HOME*1.05 
ULS16:SLFW*1.35+PARTW*1.35+WINDX+*1.5+A1_HOME*1.05 
ULS17:SLFW*1.35+PARTW*1.35-WINDX+*1.5+A1_HOME*1.05 
ULS18:SLFW*1.35+PARTW*1.35+WINDX+*1.5 
ULS19:SLFW*1.35+PARTW*1.35-WINDX+*1.5 
ULS20:SLFW*0.8+PARTW*0.8+A1_HOME*1.5+WINDX+*0.9 
ULS21:SLFW*0.8+PARTW*0.8+A1_HOME*1.5-WINDX+*0.9 
ULS22:SLFW*0.8+PARTW*0.8+A1_HOME*1.5 
ULS23:SLFW*0.8+PARTW*0.8+WINDX+*0.9 
ULS24:SLFW*0.8+PARTW*0.8-WINDX+*0.9 
ULS25:SLFW*0.8+PARTW*0.8 
ULS26:SLFW*0.8+PARTW*0.8+G_ROOFNA*1.5+A1_HOME*1.05+WINDX+*0.9
ULS27:SLFW*0.8+PARTW*0.8+G_ROOFNA*1.5+A1_HOME*1.05-WINDX+*0.9
ULS28:SLFW*0.8+PARTW*0.8+G_ROOFNA*1.5+A1_HOME*1.05 
ULS29:SLFW*0.8+PARTW*0.8+G_ROOFNA*1.5+WINDX+*0.9 
ULS30:SLFW*0.8+PARTW*0.8+G_ROOFNA*1.5-WINDX+*0.9 
ULS31:SLFW*0.8+PARTW*0.8+G_ROOFNA*1.5 
ULS32:SLFW*0.8+PARTW*0.8+A1_HOME*1.05+WINDX+*0.9 
ULS33:SLFW*0.8+PARTW*0.8+A1_HOME*1.05-WINDX+*0.9 
ULS34:SLFW*0.8+PARTW*0.8+A1_HOME*1.05 
ULS35:SLFW*0.8+PARTW*0.8+WINDX+*1.5+A1_HOME*1.05 
ULS36:SLFW*0.8+PARTW*0.8-WINDX+*1.5+A1_HOME*1.05 
ULS37:SLFW*0.8+PARTW*0.8+WINDX+*1.5 
ULS38:SLFW*0.8+PARTW*0.8-WINDX+*1.5 
SIS39:SLFW*1+PARTW*1+QUAKEX*1+A1_HOME*0.45 
SIS40:SLFW*1+PARTW*1+QUAKEX*1 
SIS41:SLFW*1+PARTW*1-QUAKEX*1+A1_HOME*0.45 
SIS42:SLFW*1+PARTW*1-QUAKEX*1 
SIS43:QUAKEX*1+A1_HOME*0.45 
SIS44:QUAKEX*1 
SIS45:QUAKEX*-1+A1_HOME*0.45 
SIS46:QUAKEX*-1 
ACC47:SLFW*1+PARTW*1+EXPLO*1+A1_HOME*0.75 
ACC48:SLFW*1+PARTW*1+EXPLO*1 
ACC49:SLFW*1+PARTW*1+EXPLO*1+A1_HOME*0.45 
ACC50:SLFW*1+PARTW*1+EXPLO*1+WINDX+*0.75+A1_HOME*0.45
ACC51:SLFW*1+PARTW*1+EXPLO*1-WINDX+*0.75+A1_HOME*0.45
ACC52:SLFW*1+PARTW*1+EXPLO*1+WINDX+*0.75 
ACC53:SLFW*1+PARTW*1+EXPLO*1-WINDX+*0.75 
ACC54:EXPLO*1+A1_HOME*0.75 
ACC55:EXPLO*1 
ACC56:EXPLO*1+A1_HOME*0.45 
ACC57:EXPLO*1+WINDX+*0.75+A1_HOME*0.45 
ACC58:EXPLO*1-WINDX+*0.75+A1_HOME*0.45 
ACC59:EXPLO*1+WINDX+*0.75 
ACC60:EXPLO*1-WINDX+*0.75 


Author's notes
  • Its common at calculation models to define all the permanent acctions in the same load case. This simplify cannot be accurate at all cases and generate unfavorable situations respect to the combinations generated with this program. For example, at buildings with the facade at the small cantilever's extreme, this load is favorable for the beams or slabs and is being considered as unfavorable at usual cases.
    On the other side, at EHE-08, Art. 12.1, it says "...For the permanent actions, the consideration of favorable or unfavorable effect is obtained factoring all the actions of the same origin with the same factor, showed at table 12.1.a", and at CTE DB SE 4.2.2, ap. c it says "The security factors values ... are shown at table 4.1 for each kind of action, considering for resisance checkings if it effect is unfaorable or favorable, globally considered."; Those confusing paragraphs could mean that all the gravitatory loads have to be considered with syncronized effect. In author's opinion, the regulation is not clear enough in how is required to distribute the permanent loads, with the corresponding increment in the number of combinations; and in other side, the traditional calculations with the permanent actions grouped does not seem to generate mistaken or unsure results, so the groupig has to be left to the designer critera.

  • In most of the calculation programs, the combinations are the same for all the structure members. This makes calculations mistaken or unoptimized at structures with steel and concrete members, because the combinations obtained with the CTE and with the EHE-08 are different. At mixed structures with programs that can't associate the combinations with the materials, it is required to make two calculations with two combination sets,one for concrete (EHE combinations) and other for steel (CTE combinatios). The points that make different combinations at each regulation are:
         CTE        EHE    
    Self weight favorable effect γQ,fab:0.8 (4.2.3)1 (12.1)
    Soil push favorable effect γQ,fab:0.7 (4.2.3)1 (12.1)
    Water pressure favorable effect γQ,fab:0.9 (4.2.3)1 (12.1)
    Water pressure unfavorable effect γQ,des:1.2 (4.2.3)1.35 (12.1)
    Dead load favorabe effect in accidental situation γQ,fab,acc:0 (4.2.2)1 (12.1)
    Prestress favorable effect in accidental situation γP,fab,acc:0 (4.2.2)1 (12.1)
    Different fators for stability checkings for dead loads at CTE.

  • Most of the calculation programs let introduce user defined combinations, so with this program, will be possible to copy and paste the combinaion into a spreadsheet for it introduction into a calculation program. Keep in mind that some calculation programs let define combinations but not to add new load cases, so it is possible that all the regulation combinations couldn't be introduced correctly.

  • The author didn't find any commercial program generting and applying accurately the combinations following the regulation. Usually at combination list of persistent or variable situation, the wind and the snow appears only in a few combinations, while according to the CTE or the EHE-08, the wind and the snow will have to appear the same times as any other variable load, as the formulation does not specify the kind of variaable loads..

Version 29/05/2013







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