GGU-FOOTING: Differences between DIN 1054 (old) and DIN 1054:2005/EC 7

The differences between DIN 1054 (old) and 1054:2005 or EC 7 are minor for bearing capacity analysis.

The failure load, or, using partial safety factors, the characteristic bearing capacity (R_k) is determined identically. This value is subsequently divided by the bearing capacity partial safety factor _{bearing capacity} (Table 3 in DIN 1054:2005). This is 1.40 for load case 1, 1.30 for load case 2 and 1.20 for load case 3. This leads to the bearing capacity design value R_d

R_d = R_k / γ_{bearing capacity}

This value is compared to the design value for the present load (action) V_d. The design value is given by the load present or, using partial safety factors, by the characteristic action V_k multiplied by the partial safety factor for the actions γ_G (permanent) and γ_Q (changeable). According to Table 2 (DIN 1054:2005), the following partial safety factors must be adopted:

Permanent actions: (1.35 LC 1, 1.20 LC 2 and 1.00 LC 3)

Unfavourable changeable actions: (1.50 LC 1, 1.30 LC 2 and 1.00 LC 3)

If the characteristic action consists of a permanent (index G) and a changeable (index Q) action, the design value V_d is

V_d = γ_G · V_k,G + γ_Q · V_k,Q

The bearing capacity has been verified if

V_d ≤ R_d

is shown. A safety factor η according to the global safety factor concept

η = failure load/present load

is currently not envisaged. However, the safety factor η according to the global safety factor concept has the great advantage that the distance to safe conditions is documented with a single number.

e.g. for load case 1 according to the global safety factor concept:

η = 2.01 = just adhered to for allowable η = 2.00

or

η = 16.26 = generously dimensioned for allowable η = 2.00

So a utilisation factor μ is defined by

µ = V_d / R_d

A value of μ smaller than 1.0 therefore indicates stable conditions.

A simple example (load case 1) will demonstrate the differences between DIN 1054 (old) and DIN 1054:2005.

• DIN 1054 (old)
  pres. V = 1000 kN
  V_Failure = 2100 kN (via bearing capacity analysis)
  η = 2100/1000 = 2.10 > allow. η = 2.00

• DIN 1054:2005
  V_k,G = 400 kN (permanent) = characteristic permanent load
  V_k,Q = 600 kN (changeable) = characteristic changeable load
  V_d = γ_G · V_k,G + γ_Q · V_k,Q = 1,35 · 400 + 1,50 · 600 = 1440 kN
  V_d = 1,440 kN = load design value
  R_k = V_Failure (according to DIN 1054 (old)) = 2,100 kN (via bearing capacity analysis)
  R_k = characteristic bearing capacity
  R_d = R_k / γ_{Bearing capacity} = 2,100/1.40 = 1,500
  R_d = bearing capacity design value
  μ = V_d / R_d = 1,440/1,500 = 0.96

An utilisation factor in accordance with the partial safety factor concept can be acquired for the global safety factor concept by dividing the allowable safety factor by the present safety factor.

μ (DIN 1054 (old)) = allow. η (DIN 1054 (old)/pres. η (DIN 1054 (old) = 2,00/2,10 = 0,95

This value roughly corresponds to the value for the partial safety factor concept. In principle, then, nothing has changed.

From the relationship for the utilisation factor according to the partial safety factor concept

μ = V_d / R_d

an allowable load can be computed if the utilisation factor is set to μ = 1.0.

μ = (γ_G · V_k,G + γ_Q · V_k,Q) / (R_k / γ_{Bearing capacity})
1,0 = (γ_G · V_k,G + γ_Q · V_k,Q) / (R_k / γ_{Bearing capacity})
V_k,G = permanent loads
V_k,Q = changeable loads

If, as in the example, the changeable loads component p is more than 60% of total loads

p = V_k,Q / (V_k,G + V_k,Q) = 600 / (600 + 400)= 0,60 [= 60%]

the equation can be simplified as follows:

1,0 = (γ_G · (1 – p) · V_k + γ_Q · p · V_k) / (R_k / γ_{Bearing capacity})
1,0 = (γ_G · (1 – p) + γ_Q · p) · V_k / (R_k / γ_{Bearing capacity})
(γ_G · (1 – p) + γ_Q · p) · V_k = R_k / γ_{Bearing capacity}
allow. V_k = R_k / [(γ_G · (1 – p) + γ_Q · p) · γ_{Bearing capacity}]

According to the partial safety factor concept, the characteristic bearing capacity value R_k is calculated identically to DIN 1054 (old).

The equivalent relationship from DIN 1054 (old) is:

allow. V = V_Failure / η

According to the partial safety factor concept, in load case 1, γ_G = 1.35, γ_Q = 1.50 and γ_{Bearing capacity} = 1.40 . Depending on the proportion p of the variable loads in the total loads, the values shown in the following table result for the expression

(γ_G · (1 – p) + γ_Q · p) · γ_{Bearing capacity}

The third column in the table can be compared to the constant safety factor according to DIN 1054 (old) of 2.0 (load case 1). The comparison demonstrates that this not noticeably different to the global safety factor of 2.00. This was also the laudable intention of the authors of the partial safety factor concept. If the load component p is around 50%, almost precisely the same results are achieved.

In analogy to the DIN 1054 (old), the DIN 1054:2005 contains tables with allowable footing pressures for various systems in Annex A. The tables and table values are identical with the values in the old standard. This may appear strange at first glance. But here, too, the authors of the partial safety factor concept have orientated themselves to proven systems and analysis concepts. The allowable footing pressures given here may be compared to existing footing pressures, determined using characteristic loads, i.e. with loads not increased by partial safety factors.

This concept is also utilised by the program when footing analysis diagrams ("Multiple footings" check box in menu item "File/New" activated) are calculated. You then define, in addition to the old standard, the ration of changeable loads p to the total loads, using the menu item "Edit/System parameters"

p = V_k,Q / (V_k,G + V_k,Q)

Using this, the program can compute a substitute global safety factor η':

η' = (γ_G · (1 – p) + γ_Q · p) · γ_{Bearing capacity}

For example, for load case 1:

η' = (1.35 · (1 – p) + 1.50 · p) · 1.40

Ask the structural engineer for the proportion of changeable loads in the permanent loads. If you get no answer, set p to 0.5 (50 %, approximately corresponds to the old standard). If you are very unsure, select p = 1.0 (100 %). You then get the allowable footing pressures, which are around 5% [2.00/(1.50 · 1.40) = 2.00/2.10 = 0.95] below the old standards values for load case 1.

If footing analysis diagrams are computed ("Multiple footings" check box in menu item "File/New" activated), the program determines the settlements under total load (as previously).

In all, it is shown that bearing capacity analysis according to the partial safety factor concept does not contain anything new. Unfortunately, it has only become a lot more unclear.