Finding Max Deflection of Beam with Bending Curve Eqn

Thread starter teng125
Start date Jul 24, 2006
Tags

Deflection Maximum

In summary, the "Finding Max Deflection of Beam with Bending Curve Eqn" problem is a common question in engineering and physics that involves determining the maximum deflection of a beam under a given load using the bending curve equation. This equation, also known as the Euler-Bernoulli beam equation, describes the relationship between bending moment, shear force, and deflection of a beam. The steps to solve this problem include determining the bending moment and shear force equations, finding the deflection equation, applying boundary conditions, and differentiating to find the maximum deflection point. Common assumptions made when solving this problem include a straight beam with a constant cross-section, uniform and isotropic material, small deflections, and static loads. Real-world

Jul 24, 2006

teng125

if i have a bending curve eqn of w'(x) = (q/6)<x-l>^3 - ql/4 <x-0>^3 - 3ql/4 <x-l>^2 + (9ql^3)/24

suppose to find the deflection of maximum of the beam, we have to set w'(0)=0 .Am i right??

then if it is right,how can i find the value for x on which the max bending occur because i don't know how to factorize the heaviside function such as <x-l>^3

anybody pls help
thanx

Physics news on Phys.org

Jul 25, 2006

teng125

pls help...

FAQ: Finding Max Deflection of Beam with Bending Curve Eqn

What is the "Finding Max Deflection of Beam with Bending Curve Eqn" problem?

The "Finding Max Deflection of Beam with Bending Curve Eqn" problem is a common question in engineering and physics, where the goal is to determine the maximum deflection of a beam under a given load using the bending curve equation. This calculation is important in designing and analyzing structures to ensure they can withstand the expected loads.

What is the bending curve equation?

The bending curve equation, also known as the Euler-Bernoulli beam equation, is a mathematical formula that describes the relationship between the bending moment, shear force, and deflection of a beam. It is based on the assumptions that the beam is straight, the material is homogeneous and isotropic, and the deflection is small compared to the beam's length.

What are the steps to solve the "Finding Max Deflection of Beam with Bending Curve Eqn" problem?

The steps to solve this problem are:

Determine the bending moment and shear force equations for the beam.
Find the equation for the beam's deflection by integrating the bending moment equation twice.
Apply any boundary conditions to the deflection equation.
Differentiate the deflection equation to find the maximum deflection point.
Substitute the maximum deflection point into the deflection equation to find the maximum deflection value.

What are some common assumptions made in solving this problem?

Some common assumptions made in solving the "Finding Max Deflection of Beam with Bending Curve Eqn" problem include:

The beam is straight and has a constant cross-section.
The material of the beam is uniform and isotropic.
The deflection of the beam is small compared to its length.
The load on the beam is static and does not change over time.

What are some real-world applications of this problem?

The "Finding Max Deflection of Beam with Bending Curve Eqn" problem has numerous real-world applications, including:

Designing and analyzing structures such as bridges, buildings, and aircraft.
Calculating the maximum deflection of a diving board or a beam in a gymnastics routine.
Assessing the structural integrity of existing structures.
Determining the strength and durability of materials used in construction.