Direct and Bending stresses

Direct and Bending stresses

Strength of Materials - AST 201 (2+1)

IntroductionWhenever a body is subjected to an axial tension or compression, a direct stress comes into play at every section of body. We also know that whenever a body is subjected to a bending moment a bending moment a bending stress comes into play . A little consideration will show that since both these stresses act normal to a cross section, therefore the two stresses may be algebraically added into a single resultant stress.

Stress• Every material is elastic in nature. That is why,

whenever some external system of forces acts on a body, it undergoes some deformation. As the body undergoes deformation, its molecules set up some resistance to deformation. This resistance per unit area to deformation is known as stress.

• σ = P/A• Where, P - load or force acting on the body, and A - Cross-sectional area of the body.• In S.I system, the unit of stress is Pascal (Pa) which

is equal to 1 N/m2

Combined Stress• We have studied a number of separate situations

(tension, compression, direct, bending, torsion, pressure in cylinders and spheres.)

• In order to find the combined effect we have to look at an element of material at particular locations, where both effects determine the stresses. We calculate the stresses as though they occurred separately, and then combine them to find the overall effect expressed as Principle stresses.

Torsion and Bending

Tension and Compression

Structures LabApplying Loads

Combined bending and direct of a stocky strut:

• Consider a short column of rectangular cross section. The column carries an axial compressive load P, together with bending moment M, at some section, applied about the centroidal axis Cx

The area of the column is A, and Ix is the second moment of the area about Cx . If P acts alone, the average longitudinal stress over the section is (–P/A)

The stress being compressive. If the couple M acts alone, and if the material remains elastic, the longitudinal stress in any fiber a distance from Cx is (-My/Iy)

Clearly the greatest compressive stress occurs in the upper extreme fibers, and has the value,

Eccentric Loading: A load, whose line of action does not coincide with the axis of a column or a strut, is known as an eccentric load.

Ex: A bucket full of water, carried by a person in his hand, then in addition to his carrying bucket, he has also to lean or bend on the other side of the bucket, so as to counteract any possibility of his falling towards the bucket. Thus we say that he is subjected to

•Direct load, due to the weight of bucket • Moment due to eccentricity of the load.

Beam Mode•

Limit of Eccentricity• When an eccentric load is acting on a column, it

produces direct stress as well as bending stress. On one side of the neutral axis there is maximum stress and on the other side of the neutral axis there is a minimum stress.

• A little consideration will show that so long as the bending stress remains less than direct stress, the resultant stress is compressive. If the bending stress is equal to the direct stress, then there will be a tensile stress on one side.

….continue

• Though cement concrete can take up a small tensile stress, yet it is desirable that no tensile stress should come into play

e ≤ Z/A

• It means that for tensile condition, the eccentricity should be less than (Z/A) or equal to (Z/A). Now we shall discuss the limit for eccentricity in the following cases,

LimitsLimit of eccentricity for a rectangular section• No tension condition, e ≤ d/6Limit of eccentricity of a hollow rectangular section• No tension condition,

Limit of eccentricity of a circular section, e ≤ d/8Limit of eccentricity for hollow circular section e ≤

E - References:

• www.cenfile.com• www.ebookee.com/Mechanics-and-strengh-of-ma

terials_67103.html• www.typesofstresses.com

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Submitted By,S.VigneshBTG-12-0-37