Slenderness and load-bearing capacity of masonry wall

A masonry wall must be checked for slenderness (λ ≤ 27) and for load-bearing capacity N_Rd = Φ·f_d·A. Here is the Eurocode 6 method step by step.

Introduction

A masonry wall's bearing capacity under vertical loads is checked in three steps: effective height slenderness and capacity. All three come from EN 1996-1-1 and the Danish national annex.

Step 1 — effective height and slenderness

Fig. Slankhed er forholdet mellem effektiv højde h_ef og effektiv tykkelse t_ef — højt og tyndt = slankt

Step 2 — capacity reduction factor Φ

Φ depends on slenderness and eccentricity. High slenderness and large eccentricity markedly reduce bearing capacity.

Step 3 — load capacity N_Rd

Slenderness ratios ρ_n

Den effektive højde h_ef = ρ_n · h afhænger af, hvordan væggen er fastholdt langs sine kanter (EN 1996-1-1 pkt. 5.5.1). Reglen er enkel: jo flere og jo bedre fastholdte rande, jo mindre ρ, jo kortere effektiv højde og jo mindre slank væg.

01ρ2 = 0,75 — væg fastholdt for oven og forneden af stive dæk (fx betondæk der spænder ind til væggen). Standardtilfældet for en etagevæg.
02Weak or one-sided fixing — ρ approaches 1.0 (or more at a free end) because the wall can move freely at the top.
03ρ3 and ρ4 — the wall is also supported along one and two vertical edges respectively (cross walls/pilasters). ρ is further reduced, calculated from the ratio of cross wall spacing to height.
04Free vertical edge — removes the bracing on that side and increases ρ; a free-standing wall is treated as a cantilever.

Eccentricity — the load rarely hits in the middle

A brick wall is almost never loaded exactly centrally. EN 1996-1-1 (section 6.1.2.2) adds several eccentricity contributions together, because together they determine how much the load-bearing capacity is reduced:

01e_i (top/bund) — excentricitet fra selve lastindføringen ved etagedækket, fx et dæk der kun hviler på en del af væggens tykkelse (e_i = M_id/N_id).
02e_hm — eccentricity from horizontal load (wind pressure/suction) taken at wall centre.
03e_init — an unintended built-in eccentricity from execution tolerances, set to h_ef/450.
04e_k — creep eccentricity that can be added for slender walls.

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