Notched beam properties

[4thorns]

Hi all,
I have a situation where I have 4x8 joists coming into both sides of a 6x12 pine beam sitting in notches. See pic. The problem is that I'm not sure how to get the section properties in order to do the math to see how far the beam can span.

Looking for:

Section Modulus(S)
Moment of Inertia(I)

I split it into rectangular pieces and summed the properties of each but doesn't summing them assume that they are not acting collectively as one beam? Any help would be appreciated.

Doug

 

[msquared48]

The 6X is the critical beam here for deflection. I would model the 6X as three beams, two having the same I and S, and the third, at the joint, having different I and S values. I would fix the joints between the beams and compute the deflection.

Computing I and S for each beam should be no problem. Once you get the I value for the notched section, just use I/c for the extreme fiber S values - there will be two for the notched member - one for the top and one for the bottom.

Mike McCann
MMC Engineering
Motto: KISS
Motivation: Don't ask

 

[asixth]

First you need to calculate the centroid of the section, which should be 3.62" from the bottom fibre. Then you will need to sum the I values of the two rectangles about the centroid.

I=sum(b1*d1^3+A1*dc1^2,b2*d2^3+A2*dc2^2)

 

[asixth]

I forgot to ask, is this a floor detail?

 

[4thorns]

asixth,

Yes. This is a beam carrying a portion of the second floor in a log home.

 

[4thorns]

Mike,

Could you please explain what you mean by "Fix the joints"

 

[hokie66]

asixth,

I get the centroid is about 4.7" from the bottom, and your moment of inertia formula is missing the /12 terms.

Doug,

This is fundamental to mechanics of materials and thus to structural engineering. Suggest you study the Parallel Axis Theorem and Flexural Formula for Beams in your textbook.

 

[cntw1953]

Assume this beam subjects to primarily gravity load only, then just perform analyses on a beam with varying sectional properties along its length. The results would err on the conservative side if the connection is detailed properly, and is dimensionally stable - the coped beam ends will join in actions (moment & displacement) once the gaps are closed.

 

[asixth]

hokie,

you are correct, perhaps I need to study my mechanics textbooks as well.

 

[IDS]

Spreadsheet to calculate section properties of defined shapes or from coordinates that might be useful:

http://newtonexcelbach.wordpress.com/2008/03/25/section-properties-of-defined-shapes-spreadsheet/

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[woodman88]

4thorns, Please note that any knots, holes and/or over-cutting at the notches can cause very reduced capacity in the lumber and that the design values for 6x lumber vary from the design values of 2x and 3x lumber. Also that the Fb (bending values for lumber are based on a rectangle shape with a difference values for compression and tension. If there are no knots, holes or over-cutting at the notches, I would calculate the tension and compression allowable for the top and bottom quarter of the beam at the notches. Use the lowest value and 0.75 the depth to calculate the allowable moment of the beam to check against the actual moment. As for deflection, I would just use the “I” value for the full depth by the width at the notch, which is close to a 3x12. If you calculate the deflection this full depth section and compare it to load capacity of the two side sections for the same amount of deflection, the additional load capacity is very small. Compare the I for a 3x12 (296in<4) vs two 2x6's (2x21 = 42in<4).

Garth Dreger PE
AZ Phoenix area

 

[mmillerpe]

There is some information on the in TFEC 1-07 "Standard for Design of Timber Frame Structures and Commentary" In short, they recommend that the capacity of the beam at the notch location should is calculated as the effective rectanglar cross section consisting of the depth of the member and the net width of the member at the notch. (Section 2.3.4.3 of TFEC -07) In short the two rectangular area of the member below the notch would be neglected.

TFEC1-07 can be downloaded from the library page at

http://www.timberframeenineeringcouncil.org

 

[rowingengineer]

Doug,
I assume the proposed Notched beam arrangement is common to your local area. However have you given consideration to alternative arrangements?


Arguing with an engineer is like wrestling with a pig in mud. After a while you realize that they like it

 

[PSlem]

The link didn't work for me but this one does.

http://www.tfguild.org/publications/tfec1-07.pdf

 

[woodman88]

The tfec-1-07 section 2.3.4.3 also states that the maximum notch shall be b/4 at one face. For a 6x member that would be 5.5"/4 = 1.375". You have 1.5" notch each face which exceeds this criteria.

Garth Dreger PE
AZ Phoenix area