Design values of actions

2.8.1 General case

The design value of an action Fd that occurs in a load case is

where Yf

= partial factor for the action according to the limit state under consideration. Table 2.6 indicates the partial factors to be used in the UK for the combinations of representative actions in building structures. yFk may be considered as the representative action, Frep, appropriate to the limit state being considered where y = a factor that converts the characteristic value of an action into a representative value. It adjusts the value of the action to account for the nature of the limit state under consideration and the joint probability of the actions occurring simultaneously. It can assume the value of 1.0 for a permanent action or y0 or or y2 for a variable action. Table 2.7 shows how characteristic values of variable actions are converted into representative values. This table is derived from BS EN 1990[13] and its National Annex[13a]. Fk = characteristic value of an action as defined in Sections 2.2 and 2.3.

Table 2.6 <BS EN 1990

Partial factors (yF) for use in verification of limit states in persistent and transient Table A1.4 & NA design situations >

Table 2.6 <BS EN 1990

Partial factors (yF) for use in verification of limit states in persistent and transient Table A1.4 & NA design situations >

(Gk)

Leading variable action (Qkj)

Accompanying variable actions (Qk,i)d

a) Equilibrium (EQU)

1.10 (0.9)a

1.50 (0.0)a

VQ,I 1.50 (0.0)a

b) Strength at ULS (STR/GEO) not involving geotechnical actions

Either

Exp. (6.10) or worst case of

1.35 (1.0)a

1.5

^01.5

Exp. (6.10a) and

1.35 (1.0)a

1.5

VQ1.5

Exp. (6.10b)

1.25 (1.0)a

1.5

W)1.5

c) Strength at ULS with geotechnical actions (STR/GEO)

Worst case of

Set B and

1.35 (1.0)a

1.5 (0.0)a

Set C

1.0

1.3

d) Serviceability

Characteristic

1.00

1.00

Vq,I 1.00

Frequent Quasi-permanent

1 .00 1.00

y1,1 1.00 ^2>1 1.00

1.00 1.00

e) Accidental design situations

Exp. (6.11a)

1.0

¿db

^1.1 (main) (others)

f) Seismic

Exp. (6.12a/b)

1.0

¿Ed'

Key a Value if favourable (shown in brackets) b Leading accidental action, Ad, is unfactored c Seismic action, AEd d Refer to BS EN 1990 A1.2.2 & NA Notes

1 The values of y are given in Table 2.7.

2 Geotechnical actions given in the table are based on Design Approach 1 in Clause A1.3.1(5) of BS EN 1990, which is recommended in its National Annex.

2.8.2 Design values at ULS

For the ULS of strength (STR), the designer may choose between using Exp. (6.10) or the < BS EN 1990 less favourable of Exp. (6.10a) or Exp. (6.10b). 6.4.3.2(3) >

2.8.2.1 Single variable action

At ULS, the design value of actions is

Either

Exp.

6.10

1.35

Gk + 1.5 Qk,1

worst

case of:

Exp.

6.10a

1.35

Gk + 1.5 Qk,

and

Exp.

6.10b

1.25

Gk + 1.5 Qk,1

Table 2.7 Values of y factors

Action

Vo

Vi

V2

Imposed loads in buildings

Category A: domestic, residential areas

0.7

0.5

0.3

Category B: office areas

0.7

0.5

0.3

Category C: congregation areas

0.7

0.7

0.6

Category D: shopping areas

0.7

0.7

0.6

Category E: storage areas

1.0

0.9

0.8

Category F: traffic (area vehicle

0.7

0.7

0.6

weight < 30 kN)

Category G: traffic area (30 kN <

0.7

0.5

0.3

vehicle weight < 160 kN)

Category H: roofsa

0.7

0.0

0.0

Snow loads where altitude <

0.5

0.2

0.0

1000 m a.m.s.l.a

Wind loadsa

0.5

0.2

0.0

Temperature effects (non-fire)a

0.6

0.5

0.0

Notes

1 The numerical values given above are in accordance with BS EN 1990 and its UK National

Annex.

2 Categories K and L are assumed to be as for Category H Key a On roofs, imposed loads, snow loads and wind loads should not be applied together. < BS

EN 1991-1-1-1 3.3.2>

Expression (6.10) leads to the use of yF = yG = 1.35 for permanent actions and yF = yQ = 1.50 for variable actions (yG for permanent actions is intended to be constant across all spans).

Expression (6.10) is always equal to or more conservative than the less favourable of Expressions (6.10a) and (6.10b). Expression (6.10b) will normally apply when the permanent actions are not greater than 4.5 times the variable actions (except for storage loads, category E in Table 2.7, where Exp. (6.10a) always applies).

Figure 2.5

Figure 2.5

Therefore, except in the case of concrete structures supporting storage loads where = 1.0, or for mixed use, Exp. (6.10b) will usually apply. Thus, for members supporting vertical actions at ULS, 1.25Gk + 1.5Q will be appropriate for most situations and applicable to most concrete structures. See Figure 2.5

Compared with the use of Exp. (6.10), the use of either Exp. (6.10a) or (6.10b) leads to a more consistent reliability index across lightweight and heavyweight materials.

2.8.2.2 Accompanying variable actions

Again the designer may choose between using Exp. (6.10) or the less favourable of Exp. (6.10a) or (6.10b).

Either:

1.35 Gk + 1.5 Qk,1 + 1^0,i 1.5 Qk,i 1.35 Gk + y0,i 1.5 Qk,1 + 1.5 Qk,i 1.25 Gk - 1.5 Qk,1 + Iy0,i 1.5 Qk,i

In the above, Qk,1 refers to the leading variable action and Qk,i refers to accompanying independent variable actions. In general the distinction between the two types of actions will be obvious (see Figure 2.6); where it is not, each load should in turn be treated as the leading action. Also the numerical values for partial factors given in the UK National Annex[13a] are used in the equations above. The value of depends on the use of the building and should be obtained from the UK National Annex for BS EN 1990 (see Table 2.7).

Figure 2.6 Independent variable actions

Generally the variable actions on a typical office block would be considered as being three sets of independent variable actions:

1. Imposed office loads on the office floors

2. Roof imposed load

3. Wind load

Figure 2.6 Independent variable actions

The expressions take into account the probability of joint occurrence of loads by applying the ^0,i factor to the accompanying variable action. The probability that these combined actions will be exceeded is deemed to be similar to the probability of a single action being exceeded.

If the two independent variable actions Qk,1 and Q<,2 are associated with different spans and the use of Exp. (6.10b) is appropriate, then in one set of analyses 1.25Gk + 1.5Qk,1 should be applied to the 'Qk,1' spans with 1.25Gk + ^0,i 1.5Qi<,2 applied to the 'Qj<,2' spans. In associated analyses, 1.25Gk + ^0,i 1.5Qk,1 should be applied to the 'Q<,1' spans and 1.25Gk + 1.5Q<,2 to the 'Q<,2' spans. See Example 2.11.2 (2 variable actions).

2.8.3 Design values at SLS

There are three combinations of actions at SLS (or Load combination at SLS). These are given in Table 2.8. The combination and value to be used depends on the nature of the limit state being checked. Quasi-permanent combinations are <BS EN 1990 6.5, Table associated with deformation, crack widths and crack control. Frequent A1.4>

combinations may be used to determine whether a section is cracked or not. The numeric values of y 0, y 1 and y 2 are given in Table 2.7.

Table 2.8

Partial factors to be applied in the verification of the SLS

Combination

Permanent actions Gk

Variable actions Q.k

Unfavourablea

Favourablea

Leadingb

Othersb

Characteristic

Gk,sup

Gk,inf

Qk,1

^0,iOk,i

Frequent

Gk,sup

Gk,inf

^2,iQk,i

Quasi-permanent

Gk,sup

Gk,inf

^2,iQk,i

Key a Generally Gk,sup and Gk,inf may be taken as Gk b y factors are given in Table 2.7

See Section 2.4

2.8.4 Design values for other limit states

Load combinations are given in Table 2.6 for a) Equilibrium (EQU), b) Strength at ULS with geotechnical actions (GEO), e) Accidental and f) Seismic design situations.

2.8.5 Variations in permanent actions

When the variation of a permanent action is not small then the upper (Gkj,sup) and the (Gkj;inf) characteristic values (the 95 and 5 percentile values respectively) should be established. This procedure is only necessary when the coefficient of variation (= 100 x standard deviation/mean) is greater than 10. In terms of permanent actions, variations in the self-weight of concrete in concrete frames are considered small.

At ULS where the variation is not small, yGk,sup should be used with Gkj,sup and yGk,inf with Gkj;inf. Similarly, where the variation is not small, at SLS Gkj,sup should be used where actions are unfavourable and Gkj;inf used where favourable.

Where checks, notably checks on static equilibrium (EQU), are very sensitive to variation of the magnitude of a permanent action from one place to another the favourable and unfavourable parts of this action should be considered as individual actions. yG,sup and yG;inf should be used in such 'very sensitive' verifications.

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