Newmark's influence chart
Encyclopedia
Newmark’s Influence Chart is an illustration
used to determine the vertical pressure at any point below a uniformly loaded flexible area of soil
of any shape. This method, like others, was derived by integration of Boussinesq’s equation for a point load.
s by using the equation (R/z)=√((1-(〖∆σ〗_z/q)^(-2/3)-1), where R = the radial distance away from the point at which the load is applied, z = the vertical depth below the applied load, 〖∆σ〗_z = the stress at the point of interest a depth of z below the surface, and q = the load per unit area applied at the surface. Using the pressure ratios obtained from the equation above, he was able to form the influence chart.
When solving a vertical stress problem using Newmark’s influence chart, the influence value (IV) must be taken into account. It is proportional to the number of elements in the chart and is given by 1/N, N being the total number of elements in the chart. For example, a typical chart consists of 200 elements; therefore, the influence value is 0.005. The procedure for obtaining the vertical pressure at any point below a loaded area is as follows:
The formula used to solve for the increase in pressure at the point being considered is 〖∆σ〗_z = (IV)qM, where IV = influence value, q = pressure on the loaded area, and M = number of elements enclosed by loaded area.
. There are however limitations to these theories that one must realize when they are applied to an actual soil. Generally, soil deposits are not homogeneous, perfectly elastic, and isotropic. This being the case, some variation from the theoretical stress calculations should be expected in the field. One could expect up to a 30% difference between theoretical estimates and field values.
, Paris
(1886). In 1883, he solved the problem of stresses produced at any point in a homogeneous, elastic, isotropic soil medium as the result of a point load applied on the surface of an infinitely large half-space.
Nathan Mortimore Newmark (1910-1981) attended Rutgers University
. He graduated in 1930 with High Honors and Special Honors in civil engineering. Newmark was extremely well known in his field for research in structural engineering and structural dynamics at the University of Illinois at Urbana-Champaign
. His research greatly influenced structural and mechanical design across the world. He is also known for his contributions to the design of earthquake-resistant structures and to the trans-Alaska pipeline. In 1942, Newmark expanded on Boussinesq’s work by constructing what is now very widely known in geotechnical engineering
as Newmark’s influence chart.
Illustration
An illustration is a displayed visualization form presented as a drawing, painting, photograph or other work of art that is created to elucidate or dictate sensual information by providing a visual representation graphically.- Early history :The earliest forms of illustration were prehistoric...
used to determine the vertical pressure at any point below a uniformly loaded flexible area of soil
Soil
Soil is a natural body consisting of layers of mineral constituents of variable thicknesses, which differ from the parent materials in their morphological, physical, chemical, and mineralogical characteristics...
of any shape. This method, like others, was derived by integration of Boussinesq’s equation for a point load.
Background
Newmark obtained values of R/z that corresponded to various pressure ratioRatio
In mathematics, a ratio is a relationship between two numbers of the same kind , usually expressed as "a to b" or a:b, sometimes expressed arithmetically as a dimensionless quotient of the two which explicitly indicates how many times the first number contains the second In mathematics, a ratio is...
s by using the equation (R/z)=√((1-(〖∆σ〗_z/q)^(-2/3)-1), where R = the radial distance away from the point at which the load is applied, z = the vertical depth below the applied load, 〖∆σ〗_z = the stress at the point of interest a depth of z below the surface, and q = the load per unit area applied at the surface. Using the pressure ratios obtained from the equation above, he was able to form the influence chart.
Application
The chart is constructed by drawing concentric circles. The circles are divided by equally spaced radial lines. The radii of the circles are equal to the R/z values corresponding to 〖∆σ〗_z/q = 0, 0.1, 0.2,…,1. There are nine circles shown since when 〖∆σ〗_z/q = 0, R/z = 0 also. The unit length for plotting the circles is AB.When solving a vertical stress problem using Newmark’s influence chart, the influence value (IV) must be taken into account. It is proportional to the number of elements in the chart and is given by 1/N, N being the total number of elements in the chart. For example, a typical chart consists of 200 elements; therefore, the influence value is 0.005. The procedure for obtaining the vertical pressure at any point below a loaded area is as follows:
- Verify the depth z below the uniformly loaded area where the stress increase is to be obtained.
- Plot the plan of the loaded area with a scale of z equal to the unit length of the chart (AB).
- Place the plan on the influence chart in such a manner that the point below which the stress is to be determined in located at the center of the chart.
- Count the number of elements (M) of the chart enclosed by the plan of the loaded area.
The formula used to solve for the increase in pressure at the point being considered is 〖∆σ〗_z = (IV)qM, where IV = influence value, q = pressure on the loaded area, and M = number of elements enclosed by loaded area.
Limitations
The equation and chart needed to apply Newmark’s method is based entirely on the principles of the theory of elasticityElasticity (physics)
In physics, elasticity is the physical property of a material that returns to its original shape after the stress that made it deform or distort is removed. The relative amount of deformation is called the strain....
. There are however limitations to these theories that one must realize when they are applied to an actual soil. Generally, soil deposits are not homogeneous, perfectly elastic, and isotropic. This being the case, some variation from the theoretical stress calculations should be expected in the field. One could expect up to a 30% difference between theoretical estimates and field values.
Important Figures
Joseph Valentin Boussinesq (1842-1929) was a French physicist and mathematician. He was a professor of differential and integral calculus at the Faculty of Sciences of Lille (1872-86), and professor of physics and mechanics at SorbonneSorbonne
The Sorbonne is an edifice of the Latin Quarter, in Paris, France, which has been the historical house of the former University of Paris...
, Paris
Paris
Paris is the capital and largest city in France, situated on the river Seine, in northern France, at the heart of the Île-de-France region...
(1886). In 1883, he solved the problem of stresses produced at any point in a homogeneous, elastic, isotropic soil medium as the result of a point load applied on the surface of an infinitely large half-space.
Nathan Mortimore Newmark (1910-1981) attended Rutgers University
Rutgers University
Rutgers, The State University of New Jersey , is the largest institution for higher education in New Jersey, United States. It was originally chartered as Queen's College in 1766. It is the eighth-oldest college in the United States and one of the nine Colonial colleges founded before the American...
. He graduated in 1930 with High Honors and Special Honors in civil engineering. Newmark was extremely well known in his field for research in structural engineering and structural dynamics at the University of Illinois at Urbana-Champaign
University of Illinois at Urbana-Champaign
The University of Illinois at Urbana–Champaign is a large public research-intensive university in the state of Illinois, United States. It is the flagship campus of the University of Illinois system...
. His research greatly influenced structural and mechanical design across the world. He is also known for his contributions to the design of earthquake-resistant structures and to the trans-Alaska pipeline. In 1942, Newmark expanded on Boussinesq’s work by constructing what is now very widely known in geotechnical engineering
Geotechnical engineering
Geotechnical engineering is the branch of civil engineering concerned with the engineering behavior of earth materials. Geotechnical engineering is important in civil engineering, but is also used by military, mining, petroleum, or any other engineering concerned with construction on or in the ground...
as Newmark’s influence chart.