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Design approaches Design approaches according to Eurocode 7according to Eurocode 7
October 2010October 2010Structural Engineering Master program - Irina Structural Engineering Master program - Irina
LunguLungu
Faculty of Civil Engineering and Building Faculty of Civil Engineering and Building Services IasiServices Iasi
Geotechnical restrictionGeotechnical restriction
Ed <= Rd Ed = γE * Ek Md = Mk / γM Rd = Rk / γR
Parameters with their real values, without safety factors, are named characteristic values with an index k: Ek = characteristic actions, Rk = characteristic resistances.
Parameters with safety factors are named design values with an index d: Ed = design actions, Rd = design resistances.
For the GEO and STR limit states, the three possible design approaches use different sets of partial safety factors:
Design approach 1 with two combinations: Combination 1: A1 + M1 (= 1) + R1 (= 1) → safety factors on
loads Combination 2: A2 (= 1) + M2 + R1 (= 1) → safety factors on
materials (soil) for piles: Combination 1: A1 + M1 (= 1) + R1 (= 1) Combination 2: A2 (= 1) + (M1 (= 1) or M2) + R4 (M1 for pile resistance, M2 for unfavorable actions like negative skin
friction or transversal loads)
Design approach 2: A1 + M1 (= 1) + R2 → safety factors on loads and resistances
Design approach 3: A2 (= 1) + M2 + R3 (= 1) (A1 for loads from the structure without influence of soil material
parameters)
Design exampleDesign example 1 – spread foundation 1 – spread foundationProposal within Evaluation of Eurocode 7Proposal within Evaluation of Eurocode 7
Stiff till
Square pad foundation
GEO GEO ultimate limit stateultimate limit state – – bearing resistance failurebearing resistance failure
Vd ≤ Rd
Vd – design vertical loadRd – design bearing resistance
Short term safety – undrained conditions for soilLong term safety – drained soil condition for soil
partial safety factors onpartial safety factors on Actions - A Actions - A
Actions A1 A2
Permanent loads, unfavorable 1.35 1.00
Permanent loads, favorable 1.00 1.00
Variable loads, unfavorable 1.50 1.30
Variable loads, favorable 0.00 0.00
partial safety factors onpartial safety factors on Materials - M Materials - M
Materials M1 M2
Angle of internal friction tan(ϕ) 1.00 1.25
Cohesion c 1.00 1.25
Undrained cohesion cu 1.00 1.40
Unit weight γ 1.00 1.00
partial safety factors onpartial safety factors on Resistances - R Resistances - R
Resistances R1 R2 R3 R4
Sliding resictance 1.00 1.40 1.00
Bearing capacity resistance 1.00 1.10 1.00
Passive earth pressure 1.00 1.40 1.00
End bearing for bore piles 1.25 1.10 1.00 1.60
Skin friction for bore piles, compress. 1.00 1.10 1.00 1.30
Skin friction for bore piles, tension 1.25 1.15 1.10 1.60
Vertical loadsVertical loads
Vd = γG (Gk + Gpad,k) + γQ Qk
= γG (Gk + A γc d) + γQ Qk
Vd = γG (900 + B2 x 24 x 0.8) + γQ x 600
Undrained condition Undrained condition – short term safety– short term safety
Rd/A’ = Rd/A = pcr = ((π + 2) cu,d bc sc ic + qd) /γR = ((π + 2) cu,d sc + qd) /γR
b – base inclination factor, bc = 1.00
i – load inclination factor, ic = 1.00
s – shape factor, sc = 1.20A’ = A, centric loading case
Rd = pcr x A = B2 x ((π + 2) cu,d sc + qd) /γR = B2 ((π +2)(200/γM)+22 x 0.8)/ γR
DA1 – combination 1DA1 – combination 1
A1 + M1 (= 1) + R1 (= 1) → safety factors on loads
Vd = 1.35 (900 + B2 x 24 x 0.8) + 1.5 x 600
Rd = B2 ((π +2)(200/1.00)+22 x 0.8)/1.00
→ B = ?
DA1 – combination 2DA1 – combination 2
A2 (= 1) + M2 + R1 (= 1) → safety factors on materials (soil)
Vd = 1.0 (900 + B2 x 24 x 0.8) + 1.3 x 600
Rd = B2 ((π +2)(200/1.4)+22 x 0.8)/1.00
→ B = ?
DA2DA2
A1 + M1 (= 1) + R2 → safety factors on loads and resistances
Vd = 1.35 (900 + B2 x 24 x 0.8) + 1.5 x 600
Rd = B2 ((π +2)(200/1.00)+22 x 0.8)/1.40
→ B = ?
DA3DA3
A1 + M2 + R3 (= 1)
A1 for loads from the structure without influence of soil material parameters
Vd = 1.35 (900 + B2 x 24 x 0.8) + 1.5 x 600 Rd = B2 ((π +2)(200/1.40)+22 x 0.8)/1.00
→ B = ?
Drained condition – Drained condition – long term safetylong term safety
Rd/A’ = c’ Nc bc sc ic + q’ Nq bq sq iq + 0.5 γ’ B’ Nγ bγ sγ iγ
c’ = 0 q’ = 0.8 x (γ - γw) = 0.8 x (22 – 9.81) = 9.75kPa A’ = A = B2; B’ = B i = all 1.00 b = all 1.00 sγ = 0.7; sq = 1 + sin Φ’
Rd = A (q’ Nq sq + 0.5 γ’ B Nγ 0.7) = B2 (9.75 x Nq x sq + 0.5 x 12.19 x B x Nγ x 0.7
DA1 – combination 1DA1 – combination 1 A1 + M1 (= 1) + R1 (= 1) → safety factors on loads
Vd = 1.35 (900 + B2 x (24 – 9.81) x 0.8) + 1.5 x 600 Rd = B2 (9.75 x Nq x sq + 0.5 x 12.19 x B x Nγ x 0.7
Nq = eπ x tanφ’tan2(π/4 + φ'/2) = eπtan35tan2(π/4 + 35.0/2) = 33.30
Nγ = 2(Nq - 1) tanφ' = 2(33.3 – 1) tan35 = 45.23 sq = 1 + sinφ' = 1 + sin35 = 1.57 Rd = B2 (9.75 x 33.3 x 1.57 + 0.5 x 12.19 x B x 45.23
x 0.7)/1.00
→ B = ?
DA1 – combination 2DA1 – combination 2 A2 (= 1) + M2 + R1 (= 1) → safety factors on
materials (soil) Vd = 1.0 (900 + B2 x (24 – 9.81) x 0.8) + 1.3 x 600 Rd = B2 (9.75 x Nq x sq + 0.5 x 12.19 x B x Nγ x 0.7
φ'd = tan-1(tan φ'k)/γM = tan-1(tan35/1.25) = 29.30 Nq = eπ x tanφ’tan2(π/4 + φ'/2) = eπtan29.3tan2(π/4 + 29.3/2)
= 16.92 Nγ = 2(Nq - 1) tanφ' = 2(16.92 – 1) tan29.3 = 17.84 sq = 1 + sinφ' = 1 + sin29.3 = 1.49
Rd = B2 (9.75 x 16.92 x 1.49 + 0.5 x 12.19 x B x 17.84 x 0.7)/1.00
→ B = ?
DA2DA2 A1 + M1 (= 1) + R2 → safety factors on loads and
resistances
Vd = 1.35 (900 + B2 x (24-9.81) x 0.8) + 1.5 x 600 Rd = B2 (9.75 x Nq x sq + 0.5 x 12.19 x B x Nγ x 0.7
Nq = eπ x tanφ’tan2(π/4 + φ'/2) = eπtan35tan2(π/4 + 35.0/2) = 33.30
Nγ = 2(Nq - 1) tanφ' = 2(33.3 – 1) tan35 = 45.23 sq = 1 + sinφ' = 1 + sin35 = 1.57 Rd = B2 (9.75 x 33.3 x 1.57 + 0.5 x 12.19 x B x 45.23 x
0.7)/1.40
→ B = ?
DA3DA3A1 + M2 + R3 (= 1)
A1 for loads from the structure without influence of soil material parameters
Vd = 1.35 (900 + B2 x (24 - 9.81) x 0.8) + 1.5 x 600 Rd = B2 (9.75 x Nq x sq + 0.5 x 12.19 x B x Nγ x 0.7
φ'd = tan-1(tan φ'k)/γM = tan-1(tan35/1.25) = 29.30 Nq = eπ x tanφ’tan2(π/4 + φ'/2) = eπtan29.3tan2(π/4 + 29.3/2) = 16.92 Nγ = 2(Nq - 1) tanφ' = 2(16.92 – 1) tan29.3 = 17.84 sq = 1 + sinφ' = 1 + sin29.3 = 1.49
Rd = B2 (9.75 x 16.92 x 1.49 + 0.5 x 12.19 x B x 17.84 x 0.7)/1.00
→ B = ?
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