Instructions on Footing Simulation

This footing simulation program is based on the finite element solution of a beam on elastic foundation. A footing supported on ground (Figure 1) is simulated by a beam-spring system as shown in Figure 2. A linearly elastic spring model as shown in Figure 3 is used in this program.

Figure 1

Figure 2

Geometry of Footing

Footing geometry is described by its total length, width and height. The total length refers to the long side of the footing (along which we will numerically divide the footing into). SI units are used in this program.

Number of Segments

For numerical analysis, specify the number of segments you wish to divide the footing into. This number must be a positive number. Currently the maximum number of segments is 30. Nodes are numbered from left to right, starting with 1, then 2, ..., and ending with the number of segments plus 1. For example, Node No. 10 refers to the center of the footing if you have a total number of 18 segments. You may want to draw a sketch to help you number nodes for the footing.

Figure 3

Modulus of Elasticity and Unit Weight

Specify the values of the Young's Modulus and the unit weight of the footing material (e.g., reinforced concrete).

Modulus of Subgrade Reaction Ks and Spring Model

The modulus of subgrade reaction is defined by the following empirical relation:

K_s= k₀ + b*zⁿ where k₀ is modulus of subgrade at ground surface in kN/m³, z is depth in m, b is depth factor and n is exponent.

For footing, b=0 and K_s= k₀. For Pile, b may be zero (e.g., Over-consolidated clay) or may not be zero (e.g., sand).

There are 3 spring models available at this time as shown below. The stiffness of each spring is calculated by the program based on K_s and footing geometry (e.g., length of segment and footing width).

Footing

Figure 4 linear elastic spring

Figure 5 Elasto-plastic spring without tension (good for footing)

Figure 6 symmetrical elasto-plastic spring (good for pile)

Concentrated Forces, Moments and Node Numbers

Specify values of forces and moments and corresponding node numbers at which these forces or the moments act. You can specify up to 2 point forces and 2 moments.

Nodes are numbered from left to right, starting with 1, then 2, ..., and ending with the number of segments plus 1. For example, Node No. 10 refers to the center of the footing if you have a total number of 18 segments. You may want to draw a sketch to help you number nodes for the footing.

Notes for output file

Negative sign in deflections and soil pressures means soil is in tension. In the presence of a large moment, some soil springs may be in tension, which is unrealistic.