WHAT IS THE PROBLEM?FIND THE DIFFERENTIAL

EQUATION TO SOLVE THE RAFTER.

WE NEED TO FIND THE STRAIN OF THE RAFTER.

FIND THE CONDITIONS OF THE PROBLEM.

WHAT IS THE EQUATION APPLIED TO SOLVE THE PROBLEM?

ITS A LINEAR DIFFERENTIAL EQUATION OF FOURTH ORDER.

RESOLVED BY CASE FOUR (~HCCC).

RESOLUTION Yg~h=Ygh + Yp~h

The mathematical model allows us to describe a real phenomenon by means of a mathematical formulation which consists in identifying a reason to change, its constants and variables.

Will be obtained by means of differential equations the deflection of a rafter depending on support conditions.

Bending of beams is determined by a linear equation of fourth order

CONDITIONS OF THE PROBLEM

homogeneous rafter

uniform cross section

the weight of the rafter despises

ELASTICA CURVE

Is the line connecting the centroids of all cross sections of the rafter, so the shape of the beam is described.

Demonstrated by the theory of bending elasticity that when any distance x, is determined by the next equation.

Is demonstrated by the theory of elasticity than the flexion moment at any distance x, is determined by the following equation:

E: Young's modulus

I: Moment of inertia

K: Elastic curve of the rafter

EI: Flexural rigidity

Replacing k to the equation 2:

Therefore, it is necessary to find Y derive the equation twice to both sides and get:

derive twice

Then equals and replace

Conclusiomes

1. Within real world, such as in engineering there are problems whose solution is approached rafters with resolution of Linear Ordinary Differential Equations

2. Application in designing structures

3. Bending of rafter is determined by a linear differential equation 4th Order. Is obtained by means of differential equations the deflection of a rafter depending on support conditions

4. the distribution of loads or forces that are submitted and how they are supported, the rafters can be deflected or distorted by the action of its own weight by its negligible weight was taken, the influence of loads external or a combination of both. This deflection y (x) is known as deflection and can be determined by a linear differential equation of the fourth order

Recommendations

1. Should assume that a rafter of length L is homogeneous and has a section cross uniform throughout its length

2. The weight of the rafters will be cero

3. Should take the maximum deformation in the diagrams

4. Take care when applying the formulas of deformation in rafter

Literature: Ecuaciones Diferenciales; autor: C. Henry Edwards;

4th edition; Editorial: Prentice Hall; Page 235 238

Analisis de estructuras mtodos clsicos y matriciales; autor: Jack C Mc Cornat and James k Nelson; Editorial group Alfaomega; Page 312-315

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