Engineering - For beginners, Part 6

[Ryan B]

Engineering - For beginners, Part 6

    Material Properties Influence on Stiffness

Different materials have different properties of stiffness
Engineers call this number the Modulus of Elasticity
Easily remembered as the Multiplier of Elastic stiffness of the material
Often abbreviated as M.o.E. or MoE
Materials with higher MoE are stiffer

Chart below gives you a comparison of cost material.
 
MoE material multiplier           Cost factor of Beam with same properties
Rubber                     1,000                             NA
Wallboard           200,000                             NA
Plywood           1,000,000                             .03
Wood                2,000,000                            .01
Magnesium       6,000,000                             25
Aluminum       10,000,000                              4
Brass               17,000,000                              5
Steel                30,000,000                              1

Due to Mother Nature doing most of the manufacturing work for us, wood has the lower cost factor.

Deflection of a same sized beam made with different materials:
(Shear strength of material is ignored)
Examples:
Steel                 .07" deflection
Aluminum       .12" deflection
Wood             1.05" deflection
Again if we add the cost factor, wood is still the best choice.

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

Ryan B

[glenn kangiser]

Ryan,

Do you have any rule of thumb information on what the allowable safe weight is on wood posts by size or square inch?


Thanks- Glenn

[Ryan B]

4x4 8' 6000 lbs
4x4 <14' 2000 lbs

6x6 8' 24000 lbs
6x6 <22' 5000 lbs

12x12 8' 128000 lbs

#2 D.F.
Both ends in a "nonconstraining" style of connection.
No crown.
Free of heart center.
Unbraced (not attached to any portion of wall) for full length.
Ignorance factor +25% is included in max loads.

Beam design of this type takes the stress factor as limiting element, deflection is ignored.
Shorter lengths vs. weight can be interpolated from given maximums above.
Pier size can often be the controlling variable in the upper limits of column design rather than weight due to the cost and complexity of large piers.
4x4 at 8' is close to a required double trimmer in building design codes.
Often taller posts are specified as GLB or a manufactured style of post.
Braced posts (attached to some type of wall sheeting) loads can be higher.
Not given in design formula is a location correction factor that should be included if they are placed where cars might impact post.


The wood column formula has 13 or so variables. It's usually given in two parts because of its length!

Sawn or G.L.
Shape
Size
End Connections 3 types
Braced length
Size factor
Buckling factor 2 types
Fiber stress perpendicular to grain
Modulus of Elasticity
Variable slenderness ratio

[glenn kangiser]

Thanks a bunch, Ryan.  I really appreciate your postings.  Since you have gone to the work of providing this information I am copying it to its own subject with credit to you so it will be more accessible.  I hope you have no objection.  Thanks again.