Question

Notes about

1- Kind of stresses in structure

2- Straining actions produce normal stresses

3- General equation of normal stress distribution

4- Equation of normal stress distribution in case of principal axes

5- Neutral axe

6- Special loading cases

Answer 1

Types of stresses in a structure

There are 6 types of stresses in a structure that cause failures.Each of these different stresses is caused by a unique situation, and it's the way the object is loaded that dictates what type of stress the object experiences. The two main ways forces can be applied to an object are axially or longitudinally. When an object is axially loaded, the forces are applied in line with the major axis of the object. With longitudinally-loaded structures, forces are applied so they are perpendicular to the major axis.

The six major types of stress are:

1. Compression
2. Tension
3. Shear
4. Bending
5. Torsion
6. Fatigue

Compression stress

• Compression stress is the result of axially-loaded forces pointing towards the center of an object.

There are two major issues with compression stress:

•Compression forces can cause an object to shorten, or they can cause an object to buckle.

•When an object buckles, it bends in such a way that it can no longer hold the load.

Tension stress

•Tension stress is caused when axially loaded forces are pulling away from an object's center, and perpendicular to the object's surface.

•Tension stress can cause lengthening of an object.

Eg: Under tensile stress the bar suffers stretching or elongation.

Shear stress

•Shear stress is caused when the forces applied to an object are parallel to the object's cross-section.

•This stress can cause the object to deform and, in some cases, pull apart.

Bending stress

•Bending stress is the normal stress that is induced at a point in a body subjected to loads that cause it to bend.

•When a load is applied perpendicular to the length of a beam (with two supports on each end),bending moments are induced in the beam.

Torsion

•Shear stress produced when we apply the twisting moments to the end of the shaft about its axis is known as torsional stress.

•In sections perpendicular to the torque axis, the resultant shear stress in the section is perpendicular to the radius.

Fatigue stress

•Fatigue occurs when a structure is subjected to cyclic loading.

•If the stress amplitude exceeds a threshold value, microscopic cracks will initiate at locations with high stresses.

2)Straining action produce normal stresses

•A normal stress is a stress that occurs when a member is loaded by an axial force.

•The value of the normal force for any prismatic section is simply the force divided by the cross sectional area.

Normal stress = P/A

P= Axial force

A = Cross-sectional area

•A normal stress will occur when a member is placed in tension or compression.

•Examples of members experiencing pure normal forces would include columns, collar ties, etc.

•Straining occurs when there is an elongation or shortening due to normal stress.

3)General equations of normal stress distribution

Rotating the stress state of a stress element can give stresses for any angle.

•The basic stress equation is:

Normal stress = P/A

P = Axial force

A = cross sectional area

4)Equation for normal stress distribution in case of principal axes

Where,

Sigma(x) and sigma(y) are the normal stresses along x and y direction and the third term denote the shear stress.

The first equation represent maximum principal stress and the second equation represent minimum principal stress.

5)Neutral axis

•The neutral axis is an axis in the cross section of a beam (a member resisting bending) or shaft along which there are no longitudinal stresses or strains.

•If the section is symmetric, isotropic and is not curved before a bend occurs, then the neutral axis is at the geometric centroid.

•All fibers on one side of the neutral axis are in a state of tension, while those on the opposite side are in compression.

•Using the force and Moment equilibrium, you can find the location of neutral axis

•The natural axis is the axis where there is no stress.

6)Special loading cases

•There are a number of different types of load than can act upon a structure, the nature of which will vary according to the design, use, location and materials being used.

Loads are generally classified as either dead loads (DL) or live loads (LL):

• Dead loads refer to the structure's self weight and generally remain constant during the structure's life.
• Live loads, such as traffic loads may vary. They are imposed loads which are usually temporary, changeable and dynamic.

•Environmental loads:

Environmental loads may act on a structure as a result of topographic and weather conditions.

Some examples of environmental loads are :

•Wind loads

Wind loads can be applied by the movement of air relative to a structure.It may not be a significant concern for small, massive, low-level buildings, but it gains importance with height, the use of lighter materials and the use of shapes that my affect the flow of air, typically roof forms.

•Earthquake load

Significant horizontal loads can be imposed on a structure during an earthquake. Buildings in areas of seismic activity need to be carefully analysed and designed to ensure they do not fail if an earthquake should occur.

•Thermal loads

Materials expandor contract with temperature change and this can exert significant loads on a structure.

Example:Expansion joints can be provided at points on long sections of structures such as walls and floors so that elements of the structure are physically separated and can expand without causing structural damage.

•Snow loads

Load that is imposed by the accumulation of snow.