Teng’s Method for Modified Bearing Pressure

Designing any structure involves a lot of assumptions that are based on analysis, experimentation and safety considerations.

we typically assume loads are transferred via centerline of the footing and that the entire base of the foundation remains in full contact with the ground.

But in real-world conditions, columns may experience eccentric vertical loads from machinery, lateral forces/moments due to wind or seismic forces, tension and unsymmetrical geometry.

Eccentricity can be caused due to off-center application of loading or from centric loading with bending moments.

All this leads to non-uniform soil pressure below the footing, which is difficult to calculate, especially in case of Loss of Contact.

(Refer Loss of Contact in Concrete Foundation Design)

Teng's method helps us modify the bearing pressure to realistically account for

Eccentricity
Loss of Contact
Non-Linear Soil Response

while still using simple mechanics.

Assumptions of Teng's Method

Teng's Method is based on the following practical assumptions:

1. Soil contact pressure beneath the footing is assumed to vary linearly, resulting in a planar pressure distribution over the contact area.

2. A footing subjected to bending moments and eccentric vertical loads may be treated as an equivalent footing carrying a vertical load acting at an imaginary eccentricity, where the eccentricity,

$e=\frac{M}{P}$

and M is the resultant moment due to bending and load eccentricity, and P is the total vertical load.

3. The footing is assumed to be geometrically symmetrical about the axis (or axes) of eccentric loading.

(Only the portion of the footing symmetric about the applied load may be considered for analysis, while the remaining portion may be ignored.)

Notations
P = Total Vertical Load on the footing
A = Total Cross-sectional Area of the footing
M = Moment acting on the footing
I = Moment of Inertia of the footing
e = eccentricity of the footing
x, y = Distance of maximum compression/tension fiber from the center
L, W = Dimensions of rectangular footings
r = Radius of circular footing
K = Modification factor as per Teng
Z = Ratio of partially compressed edges

Procedure

1. For Rectangular Footings

For rectangular footings having combined axial load in Z Direction, and biaxial bending in both X and Y directions, given that footing is symmetrical is,

Bearing Pressure = $\frac{P}{A}\pm\frac{M_x\,y}{I_x}\pm\frac{M_y\,x}{I_y}$

If we considered the same footing now with only the axial load acting at some eccentricity in X and Y directions, the Bending Pressure can be written as,

Bearing Pressure = $\frac{P}{A}\pm\frac{P\,e_x\,y}{I_x}\pm\frac{P\,e_y\,x}{I_y}$

On simplifying the moment of inertia for rectangular footing

$I=\frac{B L^{3}}{12}$

we get,

Bearing Pressure = $\frac{P}{A}\left(1\pm\frac{6 e_x}{L}\pm\frac{6 e_y}{W}\right)$

Case1: No Loss of Contact

If no loss of contact occurs due to eccentricity of the loading, we can get the maximum bearing pressure without any modification using the above Bearing pressure equations.

Bearing Pressure = $\frac{P}{A}\left(1+\frac{6 e_x}{L}+\frac{6 e_y}{W}\right)$

Case2: Triangular Loss of Contact (Single Corner point in tension)

If one of the corner points have Loss of Contact, we can get the maximum bearing pressure using modification factor (K) obtained using graph given in Fig. 6-14 (d)

Bearing Pressure = $K\,\frac{P}{A}$

Shaded portion shows the area of no contact

Case3: Trapezoidal Loss of Contact (Two Corner point in tension)

If two of the corner points have Loss of Contact, we can get the maximum bearing pressure using modification factor (K) obtained using graph given in Fig. 6-14 (d) along with empirical equations formulated in 'Foundation Design" by Wayne. C. Teng. We can use maximum of them as bearing pressure.

Bearing Pressure (as per graph) = $K\,\frac{P}{A}$

Bearing Pressure (as per equations) = $\frac{6P}{X\,Y_{\max}\,(1+Z+Z^2)}$

where,

Z = $\frac{Y_{\min}}{Y_{\max}}$

Y = Length of Edge of footing that is partially not in contact (minimum and maximum on opposite edges)

X = Length of Edge of footing that is fully not in contact

Shaded portion shows the area of no contact

Case4: Triangular Area in contact (Three Corner point in tension)

If three of the corner points have Loss of Contact, we can get the maximum bearing pressure using modification factor (K) obtained using graph given in Fig. 6-14 (d) along with empirical equations formulated in 'Foundation Design" by Wayne. C. Teng. We can use maximum of them as bearing pressure.

Bearing Pressure (as per graph) = $K\,\frac{P}{A}$

Bearing Pressure (as per equations) = $\frac{3P}{8\left(\frac{L}{2}-e_x\right)\left(\frac{W}{2}-e_y\right)}$

Shaded portion shows the area of no contact

2. For Circular Footing

A General formula for circular footings having combined axial load in Z Direction, and bending in lateral direction, given that footing is symmetrical is,

Bearing Pressure = $\frac{P}{A}\pm\frac{M\,y}{I}$

If we considered the same footing now with only the axial load acting at some eccentricity, the Bending Pressure can be written as,

Bearing Pressure = $\frac{P}{A}\pm\frac{P\,e\,y}{I}$

On simplifying the moment of inertia for circular footings

$I=\frac{A r^{2}}{4}$

we get,

Bearing Pressure = $\frac{P}{A}\left(1\pm\frac{4e}{r}\right)$

Case1: For eccentricity less than or equal to one-fourth of radius of footing,

In this case, there will be no loss of contact, and we can get the maximum bearing pressure without any modification using the Bearing pressure equations given below.

Bearing Pressure= $\frac{P}{A}\left(1+\frac{4e}{r}\right)$

Case2: For eccentricity more than one-fourth of radius of footing,

If we have Loss of Contact in circular footings, we can get the maximum bearing pressure using modification factor (K) obtained using table given in Fig. 6-14 (c)

Bearing Pressure = $K\,\frac{P}{A}$

Why Teng's Method is Important?

1. The method provides a more realistic bearing pressure than simply ignoring the loss in area of contact when tension or zero pressure cases arise.
2. This also prevents unconservative design of foundations.
3. This method is primarily useful when we design foundations manually without any FEM Analysis.

Final Thoughts:

Teng’s method modifies bearing pressure by considering only the effective compression zone of soil. Eccentricity that causes partial contact with soil must be accounted for in the design of concrete.

You may also refer to the blog on Bearing in concrete foundations to know more about this.

This is the third blog in the series.

Next, we will discuss:

1. Sliding in Concrete Foundations
2. Overturning in Concrete Foundations

Stay Tuned.

This article is intended for educational understanding of foundation behavior. Designers must refer to relevant codes, standards, and professional judgment for actual design.
Cover Image Designed by Freepik
Reference: Teng, W. C., Foundation Design. Concepts explained here are interpreted and rewritten for educational purposes.

What is Sliding in Concrete Foundation Design

Foundations fail in a number of ways. When we say a foundation fails in sliding , we are not talking about cracking concrete or soil punching. We are talking about something more fundamental: The entire foundation block tries to move sideways as a rigid body. Sliding vs Other Failures Bearing failure → soil beneath fails in compression (local or general shear). Overturning → foundation rotates about an edge due to moment. Sliding → horizontal forces overcome lateral resistance at the base. These are independent failure modes . A footing can be: Safe in bearing ✔ Safe in overturning ✔ But, Unsafe in sliding ✖ Why Sliding Is Often Ignored 1. Engineers focus heavily on vertical loads and soil bearing capacities. 2. Sliding does not “ look dramatic ” in drawings. 3. Friction is assumed to be “ automatically sufficient. ” There isn't heavy settlement if sliding failure occurs and you always have good frictional force that resists sliding which itself increases with vertical lo...

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