Unreinforced Masonry Compression (Refined) — AS 3700 §7.3.4

Masonry · Unreinforced

Compression — Design by Refined Calculation

AS 3700:2018 §7.3.4 Solid, cored & grouted hollow masonry

Characteristic Compressive Strength f′_m — §3.3.2

Unit type, bedding & mortar class Table 3.1 column

Characteristic unit strength f′_uc Table 3.1 row

Table 3.1 → f′_mb

— MPa

Unit height h_u Table 3.2 numerator

Joint thickness t_j Table 3.2 denominator

f′_m = k_h × f′_mb

— MPa —

Masonry Section

Masonry type

f′_m from Tables 3.1 & 3.2

— MPa

Thickness t_w

Wall length L 1000 mm = per metre results

Height & Support Conditions

Clear height H between horizontal lateral supports

Vertical slenderness coefficient a_v Cl. 7.3.4.3, Figures 7.1A–E

Engaged piers Table 7.2

Effective Eccentricity — §7.3.4.4

e₁ / t_w Larger eccentricity ratio at either end — min. 0.05

e₂ / e₁ Ratio of smaller to larger eccentricity (–1 to +1)

Typical eccentricity values (Cl. 7.3.4.4 simplified assumption):

e₁/t = 0.05	Concentric / axial load only (minimum imperfection)
e₁/t ≈ 0.17	Single floor/roof bearing full width — load at t/3 from face
e₁/t ≈ 0.25	Floor on ledge, load at t/4 from face (deeper bearing)
e₂/e₁ = 0	Other end: axial or pinned base (typical single-storey)
e₂/e₁ = +1	Both ends equal eccentricity — same side (governs by crushing)
e₂/e₁ = −1	Equal eccentricities, opposite sides — full double curvature

Applied Loading

Design compressive force F*_d factored, on length L

Wall thickness < 90 mm — Minimum 90 mm required per Cl. 7.3.1.

Slenderness ratio S_r > 40 — Very slender wall. Verify lateral stability carefully. The refined method has no explicit Sᵣ limit, but very high values indicate a highly flexible member.

Calculation — Design by Refined Calculation

AS 3700:2018 Cl. 7.3.4

0 · Material Strength — §3.3.2

Unit type & bedding	—	Table 3.1
Mortar class	—	Table 3.1
Unit strength f′_uc	— MPa	Input
Tabulated strength f′_mb	— MPa from Table 3.1	Table 3.1
Joint factor k_h	— —	Table 3.2
f′_m = k_h × f′_mb	— MPa —	Cl. 3.3.2

1 · Section Properties

Masonry type	—	Unreinforced
Wall thickness t_w	— mm	Input
Wall length L	— mm	Input
Bedded area fraction f_n	—	Input
Bedded area A_b	— mm²	f_n × L × t_w

2 · Basic Compressive Capacity F_o — §7.3.2

Capacity reduction factor φ	0.75	Table 4.1
Characteristic strength f′_m	— MPa	Tables 3.1 & 3.2
Basic capacity F_o = φ·f′_m·A_b	— kN —	Cl. 7.3.2(1)
Capacity per metre F_o/L	— kN/m	Reference

3 · Slenderness Ratio S_r — §7.3.4.3

Clear height H	— mm	Input
Vertical slenderness coeff. a_v	— —	Cl. 7.3.4.3
Thickness coefficient k_t	—	Table 7.2
Slenderness ratio S_r	— = a_v × H / (k_t × t_w)	Cl. 7.3.4.3(c)

4 · Effective Eccentricity — §7.3.4.4

e₁ / t_w (larger eccentricity)	— —	Input (≥ 0.05)
e₂ / e₁ (eccentricity ratio)	— —	Input

5 · Reduction Factor k — §7.3.4.5

k_a — lateral instability Eq. 7.3.4.5(1)	— = 0.5 × (1 − 2e₁/t) × [(1 + e₂/e₁) + (1 − e₂/e₁) × (1.18 − 0.03·S_r)]	Instability
k_b — local crushing Eq. 7.3.4.5(2)	— = 1 − 2e₁/t_w	Crushing
k = min(k_a, k_b)	—— —	Cl. 7.3.4.5

6 · Design Check — §7.3.4.2

Design force F*_d	— kN	Input
Basic capacity F_o (incl. φ)	— kN	Step 2
Reduction factor k	—	Step 5
Design capacity k · F_o	— kN = k × F_o	Cl. 7.3.4.2
Utilisation F*_d / (k · F_o)	—	≤ 1.0 required

F*_d ≤ k · F_o —

0 %100 %

Table 7.3 — Reduction Factor k · Solid & Cored Masonry

AS 3700:2018 §7.3.4.5 — Equations (1) & (2)

Computed from Cl. 7.3.4.5 formulas. Green shading = local crushing governs. Yellow = lateral instability governs. ← marks current S_r row.

S_r	e₁/t = 0.05			e₁/t = 0.10			e₁/t = 0.20			e₁/t = 0.30			e₁/t = 0.40			e₁/t = 0.50
S_r	e₂/e₁ +1	0	−1	e₂/e₁ +1	0	−1	e₂/e₁ +1	0	−1	e₂/e₁ +1	0	−1	e₂/e₁ +1	0	−1	All

Notes: 1 · Linear interpolation may be used. 2 · Grouted hollow masonry treated as solid (use this table). 3 · For ungrouted hollow masonry use AS 3700 Table 7.4.

Scope: Design by refined calculation per AS 3700:2018 Clause 7.3.4. Applies to unreinforced masonry walls and piers of rectangular cross-section subject to uniaxial eccentric compression. Minimum thickness 90 mm (Cl. 7.3.1). Applicable to solid, cored, and grouted hollow masonry — for ungrouted hollow unit masonry, consult AS 3700 Table 7.4 and Equations 7.3.4.5(3)–(4) for the face-shell crushing formula. The basic compressive capacity F_o = φ·f′_m·A_b includes φ = 0.75 (AS 3700 Table 4.1); design check is F*_d ≤ k·F_o. Slenderness ratio formula Cl. 7.3.4.3(c) used — for walls laterally supported on vertical edges with F*_d ≤ 0.20F_o, the two-way formula in Cl. 7.3.4.3(a) may give a lower (more favourable) S_r. The refined method is generally less conservative than design by simple rules (Cl. 7.3.3) because it accepts explicit eccentricity and reduced a_v values. Not for reinforced masonry — see Cl. 8.