Roof Vibrations Column Beam Bending Problem

The basic differential equation describing the curvature of the beam at a point x along its length is where y is the lateral deflection and m is the bending moment at the point x on the beam.

Roof vibrations column beam bending problem.

E is young s modulus and i is the second moment of area section a 2. Ordinary usage l 360 l 240. Normal stresses due to bending can be found for homogeneous materials having a plane of symmetry in the y axis that follow hooke s law. Maximum moment and stress distribution.

See the table below. Parks 2 002 mechanics and materials ii department of mechanical engineering mit february 9 2004. Beams and columns deflection and stress moment of inertia section modulus and technical information of beams and columns. Industrial l 180 l 120 commercial plaster ceiling l 240 l 180 no plaster l 360 l 240 floor beams.

Beam bending stresses and shear stress pure bending in beams with bending moments along the axis of the member only a beam is said to be in pure bending. Using elastic beam theory see further reading in section a. Bending buckling and vibration david m. All building codes and design codes limit deflection for beam types and damage that could happen based on service condition and severity.

However if it cannot then the amount of live load deflection that can be accommodated becomes the new deflection criteria for this beam. It is thus a special case of timoshenko beam theory. Certain vibrations have been found to be objectionable in most occupancy classifications. Beams fixed at both ends continuous and point loads support loads stress and deflections.

Any non structural partition under the beam must be able to accommodate this deflection. Euler bernoulli beam theory also known as engineer s beam theory or classical beam theory is a simplification of the linear theory of elasticity which provides a means of calculating the load carrying and deflection characteristics of beams it covers the case for small deflections of a beam that are subjected to lateral loads only. This results in vibration modes involving several beams moving simultaneously together with an area of floor slab. If that same joist had gypsum ceiling l 240 the allowable deflection is 0 6.

Fixed pinned f 1 u º ª s ei l 15 418 2 1 2 where e is the modulus of elasticity i is the area moment of inertia l is the length u is the mass density. Beams fixed at one end and supported at the other continuous and point loads support loads moments and deflections. For example the allowable deflection of a 12ft span floor joist with plaster l 360 is 0 4 12ft divided by 360. Where δ is the deflection due to the self weight and any other loads that may be considered to be permanent.

Fundamental bending frequencies continued configuration frequency hz fixed fixed same as free free beam except there is no rigid body mode for the fixed fixed beam.