Contents
What does strain compatibility mean?
The essence of strain compatibility is that plane sections remain plane and the steel strain is the same as the concrete strain at all locations. These assumptions require that the reinforcing steel be bonded to the concrete so that the strains in the steel and adjacent concrete are always equal.
What is strain compatibility equation?
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 ¯ .
Why do we use strain compatibility equations?
This compatibility condition is an equation which must be satisfied by the strains at all material particles. When all material particles in a component deform, translate and rotate, they need to meet up again very much like the pieces of a jigsaw puzzle must fit together.
What is FEA compatibility?
A solution is compatible if the displacement at all points is not a function of the path. If the node displacements are given, all element deformations can be calculated from the basic equations of geometry. In a displacement based finite element analysis, node displacement compatibility is satisfied.
What is structural compatibility?
Compatibility is related to the shape of a structure. This includes deformations, location of reaction points and the way that a structure is allowed to bend and deform. Depending on the type of structure, there are some things that we know about its compatibility.
What is compatibility method?
Compatibility is the study of the conditions under which such a displacement field can be guaranteed. Compatibility conditions are particular cases of integrability conditions and were first derived for linear elasticity by Barré de Saint-Venant in 1864 and proved rigorously by Beltrami in 1886.
How are compatibility conditions related to strain theory?
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 the strain compatibility of steel bars?
Strain compatibility question. The stress in the bars is what it is. If the bars haven’t yielded, then the stress is equal to E*epsilon (epsilon being the strain ); if it has yielded (for 60 ksi steel this is at about a strain of .002), then the stress in the bars is the yield stress (typically 60 ksi) regardless of strain.
What is the slope of the stress-strain diagram called?
The slope of the straight-line portion of the stress-strain diagram is called the Modulus of Elasticityor Young’s Modulus. E = σ/ε (normal stress – strain) G = τ/γ (shear stress – strain)
In the two-dimensional case, there are three strain-displacement relations but only two displacement components. This implies that the strains are not independent but are related in some way. The relations between the strains are called compatibility conditions.