What is a compatibility condition?
Compatibility conditions are mathematical conditions that determine whether a particular deformation will leave a body in a compatible state. In the context of infinitesimal strain theory, these conditions are equivalent to stating that the displacements in a body can be obtained by integrating the strains.
What is Saint Venant theory?
Saint-Venant’s Principle simply states that the stress measured at any point on an axially loaded cross section is uniform given that the measured location is far enough away from the point of load application or any discontinuity in the member’s cross section.
What is compatibility equation in SOM?
The compatibility equation (1.88) for the nonsymmetric deformation of shallow caps were given in Chapter I. This equation reveals the connection between the membrane stress function F(r, ϕ) and the changes of the Gaussian curvature in the initial and deformed state Γ − Γ ¯ .
How many compatibility equations should be written?
| Q. | How many compatibility equations should be written if we have n no. of redundant reactions? |
|---|---|
| C. | n + 1 |
| D. | n + 2 |
| Answer» b. n | |
| Explanation: xplanation: no. of redundant reactions and compatibility equations are equal. |
What do the conditions of compatibility ensure mathematically and physically?
Physical Meaning of the Compatibility Condition 1 illustrates possible deformations and rigid body motions for three line elements in a material. Compatibility ensures that they stay together after the deformation.
Was Saint-Venant a saint?
His mother was Marie-Thérèse Josèphe Laborie (born Saint-Domingue, 1769). His father was Jean Barré de Saint-Venant, (1737–1810), a colonial officer of the Isle of Saint-Domingue (later Haiti)….
| Adhémar Jean Claude Barré de Saint-Venant | |
|---|---|
| Died | 6 January 1886 (aged 88) Saint-Ouen, Loir-et-Cher, France |
What is the Saint-Venant equation?
In the sequel, m(x,t) denotes the mass by unit length of the channel and it is defined as m(x,t) = ρA(x,t). The variables are supposed to be continuous and differentiable, so that their par- tial derivatives with respect to x and t always exist and are continuous.
How many compatibility equations 1 point should be written if we have n No of redundant reactions?
How many slope deflection equations are possible if 4 supports are there?
6 equations
How many sde (slope deflection equations) are possible if 4 supports are there? Explanation: Each part will give 2 unique equations, so there will be a total of 6 equations.
Why compatibility equation is required?
Compatibility conditions are those equations that are essential for solving indeterminate structures, considering the displacement equilibrium of the structure. Compatibility means at a joint in structure there cannot be more than one displacement i.e. horizontal, vertical, or rotational.
What is shallow water flow?
Shallow water flows, or the flow of water and entrained sand from sub-seafloor strata up by the drill bit or surface casing, are a recently encountered phenomenon found in the Gulf of Mexico, West of the Shetlands, the Norwegian Sea, Southern Caspian Sea, and North Sea. The flows are typically found in deepwater.