Engineering – For beginners, part 2

[RAB]

Engineering – For beginners, part 2
Key Elements for Deflection and Shear Limits
    
Deflection limits are specified as the ratio – full load deflection/Span length. Common design ratios are 1/180 - 1/360 - 1/480 or .0055 - .0028 - .0021
Examples:  
A house ridge beam 180" long should not sag more than 1" under load (180 x .0055 = 1").
Residential floor joists should not deflect more than 1" in 360" under full load conditions.
Wind deflection ratio for skyscrapers = 1/200 – 1' of movement per 200' of height is acceptable.

Shear limits are specified as a multiple or percentage - Strength of Material/ Shear Force
Examples:
Aircraft  + 1% :Weight restrictions control design
Residential beams  + 10%  :Deflection usually presents itself first, proven designs, and cost issues will control multiple value
Bridges  3x to 5x :Higher than homes due to transportation interruption and serviceability issues
Cranes for lifting of nuclear fuel rods  13x  :Safety consequences greater than cost factors
        
              **General Rules about setting Deflection and Shear Limits**
Untried materials and or uncertain conditions: a higher stress factor is used.
For reliable materials and better-known designs: a lower stress factor is used.
In designs were lower stress factors are used, deflection and or vibration may control design.
 
Strength percentage=Shear Limit percentage=Service Factor=Safety Factor=Ignorance Factor=Uncertainty Factor

As a reminder
     --Deflection most often precedes Shear Force for limits of beam design in 99% of all beams in a typical residence.

    --Due to the speed of failure and lack of visual clues - Shear Force should always be calculated.

Interested readers – this is a multipart series
Engineers please excuse the simplification that this forum dictates.

Ryan B

[glenn-k]

Thanks Ryan, I'm interested- please continue posting.
I'm kind of a rule of thumber myself and like to pick up on whatever extra information I can.

[jraabe]

Great series Ryan! Part one is very clear and concise. Part two I'm not as clear about.

I guess I thought the safety factor of 10 used in residential work was a multiple of the ultimate fiber stress rather than a percentage increase.

Are you saying we are using only a 10% cushion of ultimate fiber stress when we design beams? Is there not an additional safety factor built into the assigned fiber stresses? Or, perhaps, are we taking some average tested failure value and using that directly? If so, then a 10% cushion over an average assigned failure value seems far too risky to be common practice. (Whereas a 10x safety factor where you take an average tested failure value and use 1/10 of that as the assigned  stress value would be quite conservative.)

[RAB]

Good questions:
My next posts will cover fiber stress and deflection amounts.
I am not exactly sure on averaging of fiber stress numbers but I suspect it's the higher portion of the bell curve. Next posts will also cover change in fiber stress based on grade and species of wood.
Other load factors are considered, such as no floor ever sees 100% loading unless there is a fraternity prank that uses plastic sheeting and a fire hose... umm at an unnamed university.
Yep thats only 10% past failure – but see example below.

Example: A gluelam beam at Agony Acres Ski Area storage shed:
24x24 roof – 1- 5.125 x 15 beam down center of roof – beam load area is 288 sqft
Lbs. Sqft          Deflection              Shear #
10            .39                    4.45
25                  .97                    1.78
35            1.36                  1.27
45            1.75                  .99


Notice that the deflection is quite noticeable at 35 lbs while shear is still 25% over predicted failure. Also the chart implies why most GLBs are crowned.  

For residential construction the finish that we apply is more susceptible to failure at a much smaller deflection (plaster, sheetrock, headers over windows). This constraint is the first variable that should be designed for. Due to nature of the material in residential design, deflection and shear are not equal curves as we vary the load.

Deflection most often precedes Shear Force for limits of beam design in residential construction but don't forget the shear as it could bite you in the rear.

Ryan B
Still working on that column thingy