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This calculator enables analysis on abutment design relative to the superstructure and soil conditions. Components covered by this calculator include:
  1. Earth pressure
  2. Temperature effects
  3. Friction effects
  4. Live load surcharge
  5. Seismic load

Abutments

In short, abutments are a bridge substructure at the ends of a span to resist lateral loads exerted by the superstructure they are supporting. They provide vertical support to the structure and retain the horizontal earth pressure of the embankment. Not to be confused with piers, the intermediate supports which are mainly designed to resist vertical loads.
The following calculations are based on the general design shown in the diagram below and will require prior information on the superstructure and are in accordance with:


Conceptual Abutment Section


Load Calculations

Inputs

Abutment Dimensions



Abutment Depth
:8.4m​


Stem

Stem Hunch

Cap

Backwall

Approach Slab Hunch

Bearing



Superstructure



Span
:20.0m​



Cross Girder Span
:4.0m​



Loads



Wheeled loading
:872.5kN​



Pedestrian loading
:88.9kN​


UDL (kN/m)



Slab
:53.4​



Main Girder
:38.1​



Cross Girder
:32.1​



Railing Post
:2.0​



Footpath
:16.5​



Surfacing
:10.56​


Output

Note

Sign conventions for the following outputs:
  1. Positive moment - clockwise direction
  2. Negative moment - anticlockwise direction
  3. Positive distance - to the right of the reference point
  4. Negative distance - to the left of the reference point

Loads From Self Weight


1323​
-0.3​
-396.9​
441​
0.35​
154.35​
6.56​
-0.83​
-5.47​
151.2​
-0.4​
-60.48​
119.7​
0.85​
101.75​
13.13​
-1.13​
-14.77​
6.56​
-1.08​
-7.11​
2061.15​
-228.63​

Dead Load from Superstructure


1068​
534​
762​
381​
128.4​
64.2​
40​
20​
330​
165​
1164.2​
211.2​
105.6​

Total Loads


1164.2​
-0.35​
-407.47​
105.6​
-0.35​
-36.96​
961.4​
-0.35​
-336.49​

Earth Pressure

Inputs



Angle of Soil Internal Friction
:32.0​



Angle of wall earth face to vertical
:0.0​



Slope of earth fill
:0.0​



Unit weight of backfill, kN/m^3
:20​


Output



Angle of friction between the earth and earth fill
:21.333333333333332deg​



Coefficient of active earth pressure(K_a)
:0.27502231956254497​



Earth pressure
:52.25424071688355kN/m2​



Total Force
:2084.9442046036547kN​


1942.083​
3.99​
7748.912​
758.489​
0.75​
568.866​
1942.083​
3.135​
6088.431​

Explanation

Temperature

Inputs



C
:30​



α
:0.000012​



Shrinkage strain
:2.0E-4​



Pedestal height
:0.15m​



Bearing



Shear rating of elastomer bearing, kn/m/m2
:1000​



No. of bearings
:3.0​



Height
:0.05m​



Width
:0.4m​



Breadth
:0.4m​


Output



Thermal elongation
:0.0072m​



Shrinkage elongation
:0.004m​



Total strain
:0.0056​




Bearing area
:0.16m2​




Force
:19.712kN​



Total temperature force
:59.136kN​



Moment
:461.2608kN m​


Explanation

Friction

Calculation

Inputs



Bearing friction coefficient
:0.05​


Output



Total vertical reaction
:2231.2kN​



Horizontal load
:111.56kN​



Moment due to friction
:870.168kN m​


Explanation

Live Load Surcharge

Calculation

Inputs



Equivalent height of soil for vehicular loading
:1.2m​


Output



Pressure
:6.60053566950108kN/m2​



Force
:526.7227464261864kN​



Moment (1)
:2501.9330455243835kN m​


Explanation

Seismic Load

Inputs



Zone factor
:V​


Output



Ah
:0.18​



Av
:0.12000000000000006​




Ca
:0.43568085689417246​



Total Dynamic Force
:393.20197334699026kg/m​


Explanation

As the name suggests, seismic loading involves the impact of earthquake-generated seismic waves on a structure. With the abutment in direct contact with the backfill, seismic loading exerts force laterally.
The coefficient of dynamic, active earth pressure is given by:

Ca=(1±Av)cos⁡2(θ−λ−α)cos⁡(λ)cos⁡2(α)cos⁡(δ+α+λ)⋅(11+sin⁡(θ+δ)sin⁡(θ−β−λ)cos⁡(α−β)cos⁡(δ+α+λ))2C_a = \frac{(1\pm A_v) \cos^2(\theta - \lambda - \alpha)}{\cos(\lambda) \cos^2(\alpha) \cos(\delta + \alpha + \lambda)} \cdot \left(\frac{1}{1 + \frac{\sin(\theta + \delta) \sin(\theta - \beta - \lambda)}{\cos(\alpha - \beta) \cos(\delta + \alpha + \lambda)}}\right)^2
Where:
  1. Av = vertical seismic coefficient

λ=tan⁡−1(Ah1±Av)\lambda = \tan^{-1}\left(\frac{A_h}{1\pm A_v}\right)
For conservative design approach, both scenarios are tested and the greatest value for C_a is selected.
The total dynamic force per abutment wall length due to seismic loading is determined by:

Pawdyn=12⋅γ⋅h2⋅CaP_{aw}dyn = \frac{1}{2} \cdot \gamma\cdot h^2 \cdot C_a