Last Updated on June 7, 2024 by Maged kamel
Deflection of steel beams part 1.
This is the content of the lecture. What are the deflection parameters?
What are the disadvantages of the deflection of steel beams?
This is a quote from Prof. Mccormac’s book, chapter 10. One of the disadvantages of deflection is that it may damage other materials and create plaster cracks. Therefore, the deflection is usually limited to a maximum value since it
The deflection may damage other materials attached to or supported by the beam in question. The second point is that structures are often damaged by excessive deflections, which give them a bad appearance.
The third point is loss of confidence due to the appearance of deflection for a building. The last point is that it may be necessary for several different beams supporting the same loads to deflect equal amounts for appearance purposes to be the same amount of deflection.
What are the parameters of the deflection of steel beams?
The live load deflections are approximately equal to L/360 of the span length. However, the reader should note that the limitation of the deflection of steel beams falls in the serviceability area.
Therefore, deflections are determined for the service loads, so we cannot use the Ultimate loads, such as the 1.2D+1.60L combination of loads, to estimate the deflection.
What tools enable us to determine deflection? We use the moment area method, converting the area of moments into loads from which we estimate the shear forces, which gives us the value of the slope.
From the bending produced from Moment loads, we can evaluate the deflection values and use the conjugate beam method, which converts the end cantilever portion into fixed support and the hinged end into hinged supports.
The third method is virtual work. The deflection value = 5WL^4/384*EI for a simply supported beam under uniform load.
IBC provision for deflection.
The IBC, the building international building code, in which the beam deflection values are grouped into three categories, was Quoted from Prof. Fredrick Roland’s book Steel Design for Civil P.E.
The first item is for the roof members: Live load L& snow load S or wind load W, and the third category is the dead load plus live load D+L for each category, roof members if supporting plaster ceilings, and the deflection value.
Deflection is permitted for live load L to equal L/360, where L is the span. For snow Load s or wind load W, the deflection equals L/360; for D+L, the deflection is L/240.
For Roof members supporting non-plaster ceilings, the deflection values increased and became L=L/240 for live load, while for snow Load or wind load W=L/240 for D+L, the deflection is L/180.
For floor members, we do not have snow loads.
The allowable deflection is permissible under Live Loads L =span/360, while for D+L loads, the deflection will be considered as ( span/240).
This is the provision of the Aisc specification for Deflection based on serviceability.
What is factor C1 used in the deflection equation by AISC?
In the new section in the AISC, a new coefficient was given as a C1 factor to account for the errors due to the different factors; the deflection is delta =M*L^2/(C1*Ix), so instead of using a deflection value of (5/384)w*L4/EI, we consider instead, M as (W*L^2/8), L as span length in inches, w in kips/ft and E as 29000ksi, we can get the c1 value.
The next image explains how we get the value of c1 for the deflection of a supported beam under uniform loading. Covert the term ML^2 units to kips inch^3 by multiplying the values by 12^3. C1 for the case of a simple beam under a uniform load will be equal to 48*29000/12^3*5=161.11.
We will continue the subject in the next two posts. A solved problem will be presented.
As an external resource for the deflection. Chapter 8 – Bending Members.
This link for the next post solved problem 5-1-part 1-2.