Part 1-1: General Rules for Reinforced and Unreinforced Masonry Structures
Structural Analysis Methods
Eurocode 6 Part 1-1 specifies that structural analysis of masonry structures shall comply with the principles outlined in EN 1990, with linear elastic methods forming the basis for both ultimate limit state (ULS) and serviceability limit state (SLS) verifications.[2] This approach assumes a linear relationship between stress and strain, utilizing the short-term secant modulus of elasticity, and presumes that plane sections remain plane after deformation.[2] For ULS and SLS, the analysis yields internal forces such as axial loads, shear forces, and bending moments, which are then used in subsequent design checks.[2]
Various methods are permitted depending on structural complexity. For buildings within scope, simplified methods may be applied if assumptions are stated and justified, such as frame analysis for regular multi-storey structures.[2] More rigorous approaches, like finite element analysis, are recommended for irregular geometries, substantial openings, or heights exceeding three times the building width, accounting for the orthotropic behavior of masonry.[2] In finite element models, masonry is treated as an orthotropic material to reflect differing stiffness in principal directions.[2]
Nonlinear effects are addressed specifically for different masonry types. Reinforced masonry permits cracked section analysis under bending, assuming no tensile capacity in unreinforced sections but allowing redistribution via reinforcement, with linear elastic or plastic theory applicable.[2] For unreinforced masonry, a no-tension material model may be used in certain cases, particularly for assessing stress distributions under vertical or lateral loads, though linear elastic theory remains the default.[2]
Load combinations for analysis derive from EN 1990, incorporating permanent actions (G), variable actions (Q), and accidental actions (A) in fundamental, quasi-permanent, and exceptional combinations for ULS and SLS.[2] Effects of imperfections, such as initial crookedness (e.g., 1/450 of effective height for walls), and second-order effects are included either explicitly or via design expressions.[2]
Masonry's material properties in analysis emphasize its orthotropic nature, with the modulus of elasticity given by E=K⋅fkE = K \cdot f_kE=K⋅fk, where fkf_kfk is the characteristic compressive strength and KKK is a factor dependent on the masonry unit type (e.g., K=1000K = 1000K=1000 for clay units).[2] Long-term effects, like creep, adjust the modulus to Elong-term=E/(1+ϕ∞)E_{\text{long-term}} = E / (1 + \phi_\infty)Elong-term=E/(1+ϕ∞), where ϕ∞\phi_\inftyϕ∞ is the final creep coefficient.[2] These properties, including shear strength fvkf_{vk}fvk, inform the model's stress-strain response without tensile capacity for unreinforced masonry.[2]
Design for Ultimate Limit States
In Eurocode 6 Part 1-1, the design for ultimate limit states (ULS) verifies that masonry structures can resist actions leading to collapse or structural failure, using partial factor methods where design resistances (e.g., NRdN_{Rd}NRd, MRdM_{Rd}MRd, VRdV_{Rd}VRd) must exceed corresponding design actions (e.g., NEdN_{Ed}NEd, MEdM_{Ed}MEd, VEdV_{Ed}VEd).[2] This involves checking compression, bending with axial forces, shear, and stability, incorporating material partial factors γM\gamma_MγM (typically 1.5–3.0 for masonry depending on unit and mortar type).[2] Structural analysis from prior sections provides the internal forces, assuming plane sections remain plane and zero tensile strength perpendicular to bed joints for unreinforced masonry.[2]
For compression in unreinforced masonry walls under mainly vertical loading, the design axial resistance per unit length is given by NRd=ϕtlfkdN_{Rd} = \phi t l f_{kd}NRd=ϕtlfkd, where ϕ\phiϕ is the reduction factor for slenderness and eccentricity, ttt is the wall thickness, lll is the length, and fkd=fk/γMf_{kd} = f_k / \gamma_Mfkd=fk/γM is the design compressive strength (with fkf_kfk derived from unit and mortar strengths per Section 3.6.1, e.g., fk=Kfb0.7fm0.3f_k = K f_b^{0.7} f_m^{0.3}fk=Kfb0.7fm0.3 for general-purpose mortar).[2] The factor ϕ\phiϕ accounts for buckling and offsets, calculated at mid-height and edges using eccentricities including imperfections (e.g., initial ei=0.05te_i = 0.05 tei=0.05t) and creep effects if slenderness λ=hef/t>15\lambda = h_{ef}/t > 15λ=hef/t>15; ϕ≥0.4\phi \geq 0.4ϕ≥0.4.[2] For concentrated loads, an enhancement β≤1.5\beta \leq 1.5β≤1.5 applies to the bearing area.[2]
Bending and combined axial loading use interaction approaches, often represented by N-M diagrams, to ensure no tension under service-like conditions where eccentricity e<t/6e < t/6e<t/6.[2] For unreinforced walls, the design moment resistance per unit length is MRd=fxkdZM_{Rd} = f_{xkd} ZMRd=fxkdZ, with flexural strength fxkd=fxk/γMf_{xkd} = f_{xk}/\gamma_Mfxkd=fxk/γM (parallel or perpendicular to joints, typically 0.10–0.20 N/mm²) and section modulus Z=t2/6Z = t^2 / 6Z=t2/6; vertical compression enhances apparent strength fxk,app=fxk+σd≤fxk+0.2fkdf_{xk,app} = f_{xk} + \sigma_d \leq f_{xk} + 0.2 f_{kd}fxk,app=fxk+σd≤fxk+0.2fkd.[2] In reinforced cases, equilibrium determines the neutral axis, with MRd=Asfyd(d−0.4x)M_{Rd} = A_s f_{yd} (d - 0.4x)MRd=Asfyd(d−0.4x) limited to 0.4fkdbd20.4 f_{kd} b d^20.4fkdbd2 (or 0.3 for certain units), where AsA_sAs is reinforcement area, fyd=fyk/1.15f_{yd} = f_{yk}/1.15fyd=fyk/1.15, ddd is effective depth, and xxx is neutral axis depth assuming a parabolic-rectangular stress block (εcu=0.0035\varepsilon_{cu} = 0.0035εcu=0.0035).[2] Eccentricity limits prevent tension, and flanged sections use effective widths up to rib spacing or height/3.[2]
Shear design separates cohesion and interface contributions, with total resistance VRd=VRdc+VRdiV_{Rd} = V_{Rdc} + V_{Rdi}VRd=VRdc+VRdi.[2] For unreinforced masonry, the cohesion-based shear VRdc=0.9fvktd/γMV_{Rdc} = 0.9 f_{vk} t d / \gamma_MVRdc=0.9fvktd/γM (per unit height), where fvk=fvk0+0.4σd≤0.065fbf_{vk} = f_{vk0} + 0.4 \sigma_d \leq 0.065 f_bfvk=fvk0+0.4σd≤0.065fb is the characteristic shear strength enhanced by compression σd\sigma_dσd (e.g., fvk0=0.20f_{vk0} = 0.20fvk0=0.20 N/mm² for M10–M20 mortar), and ddd is the distance to the shear face.[2] Interface shear VRdiV_{Rdi}VRdi applies at junctions, based on reduced fvk0f_{vk0}fvk0. In reinforced masonry, shear reinforcement adds VRd=χAswfyd(0.9dcotα)/s+V_{Rd} = \chi A_{sw} f_{yd} (0.9 d \cot \alpha)/s +VRd=χAswfyd(0.9dcotα)/s+ masonry term, with enhancement χ≤1.5\chi \leq 1.5χ≤1.5 and minimum stirrup area Asw/s=0.13(bw/fyk)fckA_{sw}/s = 0.13 (b_w / f_{yk}) \sqrt{f_{ck}}Asw/s=0.13(bw/fyk)fck.[2]
Design for Serviceability Limit States
The serviceability limit states (SLS) in Eurocode 6 Part 1-1 address aspects of masonry structures that ensure functionality, usability, durability, and appearance under normal service conditions, without applying partial safety factors to material properties (γ_M = 1.0). Verifications focus on reversible effects using combinations of actions defined in EN 1990, including characteristic, frequent, and quasi-permanent combinations, where imposed loads in residential and office buildings can be treated as a single variable action with applicable reduction factors from EN 1991-1. For unreinforced masonry, the SLS for cracking and deflection generally need not be verified separately if the ultimate limit states (ULS) are satisfied, though project-specific limits must be agreed upon with the client to control deformations, cracking, and vibrations that could impair function or cause discomfort.[17]
Deformation limits in masonry design emphasize preventing adverse effects on finishes, partitions, or water-tightness, with calculations accounting for time-dependent effects such as creep and shrinkage. The long-term modulus of elasticity is used for sustained loads, given by E_long term = E / (1 + φ_∞), where E is the short-term secant modulus (typically K_E × f_k with recommended K_E = 1000) and φ_∞ is the final creep coefficient, ranging from 0.5 to 3.0 depending on masonry type (e.g., 0.5–1.5 for clay units, 1.0–3.0 for lightweight aggregate concrete). Annex F provides informative limiting height and length-to-thickness ratios for laterally loaded unreinforced walls to ensure acceptable deflections, such as area limits based on effective thickness t_ef and support conditions; deformations are controlled via these ratios or project-specific requirements. Shrinkage or moisture expansion values range from -1.0 to +1.0 mm/m across masonry types, influencing long-term deformation assessments.[17][9]
Cracking in masonry is controlled to avoid damage affecting appearance or function, particularly from restraint stresses or differential material properties, with detailing per Section 8 required to mitigate such issues. For reinforced masonry members, crack widths are limited to w_k ≤ 0.3 mm under quasi-permanent combinations, calculated as w_k = s_r,max × (ε_sm - ε_cm), where s_r,max is the maximum crack spacing, ε_sm is the mean strain at the steel surface, and ε_cm is the mean concrete strain (adapted from aligned principles in EN 1992-1-1 for compatibility). Vibrations are verified to prevent occupant discomfort, with assessments of dynamic responses under service loads per national annexes or project requirements. These masonry-specific considerations, including anisotropic creep, ensure long-term performance without excessive reversible deformations.[17][2]