Rankine’s Theory of Bearing Capacity, Rankine’s ANALYSIS FOR BEARING CAPACITY
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Rankine's theory of bearing capacity, developed in 1885, examines the plastic equilibrium of two elements related to footing pressures. It describes how the vertical and lateral stresses change between elements beneath and beyond the footing, leading to calculations of ultimate bearing capacity. The document formulates equations to derive the bearing capacity based on loading intensity and soil properties.
Rankine’s Theory of Bearing Capacity, Rankine’s ANALYSIS FOR BEARING CAPACITY
- 1. RANKINE’S THEORY OF BEARING CAPACITY PREPARED BY ER. SANJEEV SINGH SNJV@[email protected]
- 2. RANKINE’S THEORY OF BEARING CAPACITY Rankine 1885 considered the plastic equilibrium of two elements, one immediately beneath the footing and the other just beyond the edge of the footing. For the element I beneath the footing, the vertical stress in the major principal stress and the lateral stress is the minor principal stress. However, for the element II, the lateral stress becomes the major stress, and the vertical stress becomes the minor principal stress.
- 3. When the footing pressure approaches the ultimate bearing capacity (𝑞 𝑢), the element I attains a state of plastic equilibrium. However, the element I can fails only when adjacent element II also fails. For the active case For element I, substituting For element II, Therefore σ3 = 𝑡𝑎𝑛2 (450 − ′ 2 )σ1 σ3=γ𝐷𝑓 σ1= σ3 𝑡𝑎𝑛2(450− ′ 2 ) = γ 𝐷 𝑓 𝑡𝑎𝑛2(450− ′ 2 ) ………….. (b)
- 4. As σ3 of element I is equal to σ1 of element II, from eqs, (a) and(b) The approximate value of the ultimate bearing capacity of the soil. Where q is the intensity of loading at base. 𝑡𝑎𝑛2(450 − ′ 2 )𝑞 𝑢 = γ 𝐷 𝑓 𝑡𝑎𝑛2(450− ′ 2 ) Or 𝑞 𝑢= γ𝐷𝑓× 1 𝑡𝑎𝑛4(450− ′ 2 ) Or 𝑞 𝑢= γ𝐷𝑓 𝑡𝑎𝑛4 (450 + ′ 2 ) Or 𝑞 𝑢= γ𝐷𝑓 1−𝑠𝑖𝑛 ′ 1+𝑠𝑖𝑛 ′ 2 (𝐷 𝑓) min = 𝑞 γ 1−𝑠𝑖𝑛 ′ 1+𝑠𝑖𝑛 ′ 2