📐 Effective Bearing Calculator – Crane Mat

⚠️ DISCLAIMER: Based on the article "Bearing Efektif Crane Mat" by Muh. Burhanuddin. This calculator must be applied by a qualified professional engineer. The author is not responsible for direct application without appropriate professional supervision.

📐 Design Formulas Reference

1. Allowable Bearing Pressure

q_a = q_ult / FS

2. Mat Self-Weight

W = d × B × L × ρ × g / 1000 [kN]

3. Nominal Bending Moment Capacity

M_n = F_b × B × d² / 6 [kN·m]

4. L_eff from Bending (Quadratic)

q_a·B·L_eff² + (q_a·B·C − W)·L_eff + (q_a·B·C + C·W − 8M_n) = 0

5. Nominal Shear Capacity

V_n = 1.5 × F_v × B × d [kN]

6. L_eff from Shear (Quadratic)

q_a·B·L_eff² + (V_n − q_a·B·C − q_a·B·d − W)·L_eff + (W·C + W·d²) = 0

7. Moment of Inertia

I = B × d³ / 12 [m⁴]

8. L_eff from Deflection

L_c = ∛(0.06·E·I / (0.9·q_a·B)) → L_eff = L_c + C

9. Final L_eff

L_eff,final = min(L_eff,bend, L_eff,shear, L_eff,defl, L_mat)

10. Verification – Bearing Pressure

q = P / (L_eff × B)  [kPa]

            q_t = (P + W) / (L_eff × B) ≤ q_a

11. Verification – Bending Stress

L_c = (L_eff − C) / 2

            M = q·B·L_c² / 2

            f_b = 6M / (B·d²) ≤ F_b

12. Verification – Shear Stress

V = q·B·(L_c − d)

            f_v = 1.5·V / (B·d) ≤ F_v

📥 Design Input Data

Mat Material * Selecting a material auto-fills density, Fb, Fv, and E with typical values

Geometry

Crane Load (P) * kN

Mat Thickness (d) * meter (m)

Mat Width (B) * meter (m)

Mat Length (L) * meter (m)

Outrigger Pad Width (C) * meter (m)

Soil Parameters & Factor of Safety

Ultimate Bearing Capacity (q_ult) * kPa

Factor of Safety (FS) q_a = q_ult / FS

Material Properties

Density (ρ) kg/m³ → W = d × B × L × ρ × 9.81 / 1000 [kN]

Allowable Bending Stress (F_b) MPa → M_n = F_b × B × d² / 6

Allowable Shear Stress (F_v) MPa → V_n = 1.5 × F_v × B × d

Modulus of Elasticity (E) MPa → used in deflection criterion

📊 Calculation Results

Material

–

L_eff,final

–

q_a (Allow. Bearing)

–

q_t / q_a

–

Overall Status

–

💪 From Bending Strength

L_eff (bending):

Quadratic: q_aB·L² + (q_aBC−W)·L + (q_aBC+CW−8M_n) = 0

0 m

Nominal Moment (M_n):

M_n = F_b·B·d²/6

0 kN·m

Equation solved: -

✂️ From Shear Strength

L_eff (shear):

Quadratic shear equation → see formula #6

0 m

Nominal Shear (V_n):

V_n = 1.5 × F_v × B × d

0 kN

Note: -

📏 From Deflection Criterion

L_eff (deflection):

L_eff = L_c + C

0 m

Cantilever (L_c):

L_c = ∛(0.06·E·I / (0.9·q_a·B))

0 m

Moment of Inertia (I):

I = B·d³/12

0 m⁴

✅ Final Effective Length

L_eff,final (governing):

min(L_bend, L_shear, L_defl, L_mat)

0 m

Cantilever (L_c):

L_c = (L_eff − C) / 2

0 m

Governing criterion: –

Mat self-weight (W):

W = d·B·L·ρ·g/1000

0 kN

Allowable pressure (q_a):

q_a = q_ult / FS

0 kPa

🔍 Design Verification

🌍 1. Bearing Pressure Check –

Bearing pressure (q)

q = P / (L_eff · B)

0 kPa

Total bearing pressure (q_t)

q_t = (P + W) / (L_eff · B)

0 kPa

Allowable bearing (q_a)

q_a = q_ult / FS

0 kPa

Utilization q_t / q_a

q_t ≤ q_a → ratio ≤ 1.00

📐 2. Bending Moment Check –

Cantilever length (L_c)

L_c = (L_eff − C) / 2

0 m

Bending moment (M)

M = q · B · L_c² / 2

0 kN·m

Actual bending stress (f_b)

f_b = 6M / (B · d²)

0 MPa

Allowable bending (F_b)

from material properties

0 MPa

Utilization f_b / F_b

f_b ≤ F_b → ratio ≤ 1.00

✂️ 3. Shear Force Check –

Shear force (V)

V = q · B · (L_c − d)

0 kN

Actual shear stress (f_v)

f_v = 1.5 · V / (B · d)

0 MPa

Allowable shear (F_v)

from material properties

0 MPa

Utilization f_v / F_v

f_v ≤ F_v → ratio ≤ 1.00