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Membranes, slabs and shells

Units: kN, m, MPa. See the conventions for signs.

EN 1992-1-1:2023, Annex G

Code reference: uls2023.annex_g, uls2023.membrane_check.eurocode2_membrane_check, uls2023.slab_design.eurocode2_slab_check, uls2023.shell_check.eurocode2_shell_check

from eurocodepy.ec2 import uls2023
from eurocodepy.ec2.uls2023 import annex_g as g

g.membrane_optimum(5.0, 3.0, 2.0)          # Table G.1: cot θ*, ftdx*, ftdy*, σcd*
r = uls2023.eurocode2_membrane_check(
    uls2023.MembraneInput(n_xx=100, n_yy=50, n_xy=20, fck=30, fyk=500, thickness=0.2))
r.asx, r.asy, r.crushing                    # σcd ≤ ν·fcd (ν = 0,4, or nu_mode="strain")

s = uls2023.slab_design.eurocode2_slab_check(uls2023.slab_design.SlabInput(
    m_x=50, m_y=30, m_xy=10, fck=30, fyk=500, thickness=0.2,
    cover_bot_x=0.03, cover_bot_y=0.04, cover_top_x=0.03, cover_top_y=0.04))
s.asx_bot, s.details["m_rdx"]               # Tables G.2/G.3 optimum capacities

Tension and sagging moments are positive. slab_design takes the design moments of the element (it is not a drop-in for uls.slab_check, which takes Wood-Armer moments). SlabInput.method is "auto" (default): Tables G.2/G.3 where |mxy| < 0,07·d²·fcd and nEd = 0, the sandwich model (G.4(1)) otherwise — two layers t = 2·c apart by z = h − t, each designed as a membrane, σcd ≤ ν·fcd checked per layer (details["crushing"]); "optimum" and "sandwich" force one of them. In-plane forces go in n_x, n_y, n_xy.

EN 1992-1-1:2004 and EN 1992-2 (Annex F, 6.109, Annex LL)

Slabs and membranes

Code reference: uls.slab_check.eurocode2_slab_check, uls.membrane_check.eurocode2_membrane_check, uls.shell.strut_limit

uls.slab_check takes Wood-Armer moments (SlabInput.min_reinf="demand" by default: a face with no tension gets zero reinforcement). strip_reinforcement is the underlying strip design. The 2004 code does not limit mxy; the Wood-Armer tables of EN 1992-1-1:2023 (G.4(5)) are valid for |mxy| ≤ 0,07·d²·fcd.

uls.eurocode2_membrane_check limits the concrete strut with MembraneInput.strut_model:

from eurocodepy.ec2.uls import shell

sx, sy, txy, fck, fcd, cot = -10.0, -5.0, 2.0, 30.0, 20.0, 2.0      # MPa
shell.strut_limit("annex_f", sx, sy, txy, fck, fcd, cot)     # F.1(3)-(4): σ ≤ fcd, or ν·fcd, ν = 0,6(1 − fck/250)
shell.strut_limit("6.109", sx, sy, txy, fck, fcd, cot)       # EN 1992-2 6.109(103): Eqs. 6.110 and 6.112
shell.principal_stresses(sx, sy, txy); shell.elastic_compression_angle(sx, sy, txy)
shell.deformation_capacity_ok_2004(1.0, 1.0, sx, sy, txy)  # 6.109(105) check of the reinforcement ductility

Shell elements (sandwich model, both editions)

Code reference: uls.shell_check.eurocode2_shell_check, uls2023.shell_check.eurocode2_shell_check, uls.shell.calc_reinf_shell

from eurocodepy.ec2 import uls, uls2023

inp = dict(n_xx=100, n_yy=50, n_xy=20, m_xx=20, m_yy=10, m_xy=5,      # kN/m and kNm/m
           fck=30, fyk=500, thickness=0.2, cover=0.04)
r = uls.eurocode2_shell_check(uls.ShellInput(**inp))                  # 2004: strut ≤ ν·fcd, ν = 0,6(1 − fck/250)
r23 = uls2023.eurocode2_shell_check(uls2023.ShellInput(**inp))        # 2023: Annex G.4, ν = 0,4 or G.9
r.asx_bot, r.asy_bot, r.asx_top, r.asy_top, r.crushing               # m²/m

Two layers of thickness t = 2·cover at z = h − t (EN 1992-2 Annex LL); each layer is a membrane (Table G.1 / Annex F); ftd·t/fyd gives the area and the strut of each layer is checked against ν·fcd. Sagging moments put the bottom layer in tension (EN 1992-2 Annex LL: the "top" layer of calc_reinf_shell is the upper one, +m/z).

Cracking (EN 1992-2 Annex LL (102)–(104), (107)): with check_cracking=True (default) the principal stresses of the uncracked section are evaluated through the thickness (shell_stresses_at_level) and the element is cracked where the Ottosen criterion (ottosen_phi, LL.101; fctm or Table 3.1) is exceeded. An element that is not cracked gets zero areas and only σmin ≤ fcd is checked: details["cracked"] is False. check_cracking=False designs it as cracked. shell_cracking(n, m, h, fck, v, f_ctm) returns the check on its own.

Out-of-plane shear: pass v_x, v_y (kN/m) to ShellInput (and to SlabInput in uls2023). The principal shear vEd0 = √(vx² + vy²) is verified as a beam of unit width — 2004: inner layer of Annex LL (109)–(111) with ρl = ρx·cos²φ0 + ρy·sin²φ0; 2023: clause 8.2 (G.4(4)). Where stirrups are needed (r.asw_s, m²/m²), the chord force vEd0·cot θ of the truss is added to the outer layers and the shell is redesigned; r.details["shear"] has the checks and a crushed shear strut sets r.crushing. check_shear=False skips it. uls.slab_check returns asw_s too, but the chord force is not added to the Wood-Armer bars.