Hello,
The main basic study which is important for the design of the structures is the "Strength of materials". Theory of Simple Bending is the theory which must be understood to be an effective structural engineer.
This theory studies the bending of the structural elements and gives us the nature and the magnitude of the induced stresses in the structure due to the applied bending moment.
There are some assumptions:
(1) The material is elastic and homogeneous.
(2) The material obeys Hook's law
(3) Plane sections remain plane after bending.
These are some of the most important assumption now, let's go to the theory part.
According to this theory when a structural element let's take a beam, is applied with the bending moment, it bends into the circular shape. Every section will have the stress variation from the top to the bottom of the section.
The stresses varies linearly along the depth of the section and so does the strain. When sagging moment is applied to the beam the stresses are compressive on the top of the neutral axis and are tensile on the bottom of the neutral axis.
bending stresses are zero at the neutral axis. The variation of the stresses is linear along the depth, maximum at the extreme layers and zero at the center, and of opposite nature on the two sides of the neutral axis.
When the sections is analyzed for the magnitude of the stresses and its variation along the depth, theory gives us a very important formula, known as the "Flexure Formula".
M/I = f/y = E/R
Where, M = Bending moment at the section
I = Moment of inertia of the section about an axis perpendicular to the applied loads.
f = flexural stress/bending stress at a distance 'y' from the neutral axis.
E= Thomas Young's modulus of Elasticity.
R= Radius of the curved beam/ elastic curve of deflection.
Thank you for reading!
The main basic study which is important for the design of the structures is the "Strength of materials". Theory of Simple Bending is the theory which must be understood to be an effective structural engineer.
This theory studies the bending of the structural elements and gives us the nature and the magnitude of the induced stresses in the structure due to the applied bending moment.
There are some assumptions:
(1) The material is elastic and homogeneous.
(2) The material obeys Hook's law
(3) Plane sections remain plane after bending.
These are some of the most important assumption now, let's go to the theory part.
According to this theory when a structural element let's take a beam, is applied with the bending moment, it bends into the circular shape. Every section will have the stress variation from the top to the bottom of the section.
The stresses varies linearly along the depth of the section and so does the strain. When sagging moment is applied to the beam the stresses are compressive on the top of the neutral axis and are tensile on the bottom of the neutral axis.
bending stresses are zero at the neutral axis. The variation of the stresses is linear along the depth, maximum at the extreme layers and zero at the center, and of opposite nature on the two sides of the neutral axis.
When the sections is analyzed for the magnitude of the stresses and its variation along the depth, theory gives us a very important formula, known as the "Flexure Formula".
M/I = f/y = E/R
Where, M = Bending moment at the section
I = Moment of inertia of the section about an axis perpendicular to the applied loads.
f = flexural stress/bending stress at a distance 'y' from the neutral axis.
E= Thomas Young's modulus of Elasticity.
R= Radius of the curved beam/ elastic curve of deflection.
Thank you for reading!
No comments:
Post a Comment