Sunday, October 27, 2013

Body Forces ,Contact Forces, Stress Invariants and Octahedral Stresses

  • Body forces: These are the types of forces which act on the whole body at a time. Their magnitude depends upon the mass of the body, so they are generally measured as force per unit mass. These forces do not need any contact with the other body which is applying that force to it, but their magnitude depends on the distance between the two bodies.

The examples are gravitational forces, magnetic forces and electromagnetic forces. Gravitational force depends upon the product of the masses of the two bodies, and is inversely proportional to the square of the distance between two bodies. Force do not depend upon the surface area.

  • Contact Forces: These are the forces which are applicable through the contact between two bodies. So they are measured as force per unit area.Contact forces are classified into two broad categories, normal forces and tangential/shear forces.Normal forces act normal to the plane of the action of the force, and shear forces act tangential to the plane of action of the forces.Normal and shear stress, both are measured as the stress per unit area (N/mm2).

  • Stress In variants:When a stress tensor is transformed from one co-ordinate axis to some another co-ordinate axis, their are some values linked to the tensor matrix which do not change even when the elements of the stress matrix are changed.

These values are known as the stress invariant of a given stress tensor. They are generally expressed as I1, I2, and I3.

  • Octahedral stresses: When we take an octahedral element of a stressed body, each of its eight faces will have some stress co-ordinates with respect to the principal stress axes.

All the normal stresses in the eights faces of the octahedral will make some specific/equal angle with the principal axis/reference axes. These stresses on the octahedral planes are known as the octahedral stresses.

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Wednesday, October 23, 2013

Columns with Lateral loads(Beam Columns)

Columns with the lateral/transverse/horizontal loading are known as the beam columns. These columns can be analysed by using the differential equation of the elastic curve. Consider a pinned ends columns, applied with axial thrust P, and a transverse central point load W at center C.

  • Steps:

  1.  Write down the equation of the bending moment at any point x distant from the end A.
  2.  Write down the differential equation in the form of moment and then write down the solution of it. The solution of the equation gives the deflection at any point on the beam.
  3.  If you differentiate the deflection equation it will give you the slope.
  4. There will two constants of integration in equation in the second step, which you have to find out by the condition that, when x =0, y= 0 and when x=l/2, dy/dx = 0.
  5. Finally when the deflection equation is ready, you can find out the maximum deflection also.
  6. Find out the maximum bending moment and then using maximum bending moment you can find out the maximum stress in the column.
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Tuesday, October 22, 2013

Why Balanced Sections are Avoided in R,C.C. Design?

It is considered hazardous to design a balanced section of R.C.C.  Do you know why?

In balanced sections the amount of steel reinforcement used is in such proportion that the steel and concrete both reaches its maximum stress value at the same external loading at same time. So it is considered a brittle failure without any warning.

If there is no warning before failure it can be hazardous in any way, but if we design a structure as under-reinforced the steel will reach its maximum stress value first but concrete will not, so it will undergo certain deflection before getting failed so, it is a failure which will give you warning before getting failed, so just for the alarming purpose we should design the structures as under-reinforced.

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Wednesday, October 16, 2013

Limit state method of design of RCC

There are three theories related to the design of the RCC
(1) Working stress method
(2) Ultimate Load Method
(3) Limit State Method

In working stress method it is assumed that stress and strain vary linearly in the elastic limit for both concrete and steel but it is not so for the concrete in actual. Strength of the materials are divided by the factors of the safety to design it for lower values.
Ultimate Load method is based on the Whiteny's theory. The concrete is designed for its ultimate strength and the stress strain is non-linear opposed to that in the working stress method. The external loads are divided by the load factors to design them for factored loads.
In limit state method there are four limits which a concrete structure is designed for.
(a) Limit state of collapse
(b) Limit state of Serviceability/deflections
(c) Limit state of cracking
(d) Limit state of vibration.
..To be continued...