Multi-Ply Beams

Last updated May 4, 2022
By Ian Story

Multi-Ply Beams

A multi-ply or built-up beam is a beam made up of multiple smaller beams (plies) fastened together to act as a single member. All members must have the same height, but they are allowed to vary in width or material. There are a couple reasons you might want to use a multi-ply beam instead of a single member:

• Retrofits. If you already have an existing beam and need to increase its strength, adding additional plies is a simple and cost-effective way to do this without having to remove the existing beam.
• Reduce Lifting Weight. Assembling the beam from multiple pieces gives the contractor the option to lift the individual pieces into place one by one. This can make sense for particularly long span beams, as well as for jobs that will be done by a small crew (or solo) without ready access to heavy equipment.
• Cost-effectiveness. Generally speaking, dimensional lumber is significantly more cost effective than engineered lumber, from a materials perspective (Framing Material Prices). By building up a beam from multiple pieces of dimensional lumber, you can replace more expensive engineered wood beams. Generally, it only makes sense to go this route if you need a total thickness greater than 5 1/2″ (6x nominal lumber is readily available at the same price per board foot as 2x stock). When considering this option, it is important to make sure the cost of labor and fasteners required to assemble the beam doesn’t exceed the difference in materials cost, or you’ll wipe out any savings and just make the contractor frustrated.
• Minimize Depth. When you have an absolute limit on depth and can’t get the required stiffness with a wood beam, you can add steel plates to stiffen the beam (this is called a Flitch Beam). This can be a decent option when you don’t want to spend the money on a full steel beam, when you are reinforcing an existing wood beam, or when you want an outer wood layer for appearance or for attaching other elements.

Varying Material

When the plies of a multi-ply beam are not all the same material, the first step in the analysis is to “transform” the stronger materials into an equivalent amount of the weaker material. (note: the transformation steps discussed here only apply to bending stress and deflection, but these are typically the critical factors for beam design).

To do this, first recognize that compatibility requires that all of the plies move as a unit (if they didn’t, then some of the plies would be sticking up from the others, which means the load would get concentrated on these pieces and would push them down until they lined up with the others). This applies to both bending deflection and axial strain – none of the plies are allowed to elongate or slip past the others. The axial strain and deflection of a beam are both inversely proportional to a material-specific constant called the Modulus of Elasticity (abbreviated with a capital E). This means that a material with twice the Modulus of Elasticity will move only half as much under a given load.

When picking which material to transform the materials into, you want to pick the material with the lowest strength to stiffness ratio (F_b / E). This is because each material will attract load in proportion to its Modulus of Elasticity, and you want to make sure that each material can handle the additional load it is attracting. A stiff but brittle material (low F_b / E) will draw lots of load to itself but will break before the other materials can fully help out with supporting the load.

Here are the F_b / E ratios for the common ply materials, ranked in order of increasing F_b / E:

Material	Fb / E (10-3 lb/in6)	Fb (psi)	E (106 in4)	n
Douglas Fir	0.588	1,000	1.7	1.00
SPF lumber	0.625	875	1.4	0.82
LVL	1.38	2,750	2.0	1.17
A36 Steel	119	34,491**For steel I am using an equivalent Fb,allow for a rectangular plate. Per AISC a360, the nominal allowed bending stress of rectangular steel bars is 1.6 times the yield stress (36,000 psi for A36 steel), which is then reduced by a safety factor of 1.67 for ASD.	29.0	17.05

You’ll want to pick the highest row in the table as your target material. To keep things simple, I typically transform everything to an equivalent amount of Douglas Fir.

To transform a ply into another material, you keep the depth the same but multiply the thickness by a number to account for the relative stiffness of the two materials. This number is called the Modular Ratio (abbreviated as ‘n’), and is obtained by dividing the original material’s Modulus of Elasticity by the target material’s Modulus of Elasticity. For example, the Modular Ratio between A36 steel and Douglas Fir is 17.06, so a 1/4″ thick steel plate can be transformed into an equivalent block of Douglas Fir that is (17.05)(1/4″) = 4.26″ thick. For convenience, I have included the modular ratios for each of the materials relative to Douglas Fir in the table above.

Once you have transformed all of the materials into one material type (I recommend using Douglas Fir for this), you can add up all the thicknesses of the transformed plies and analyze the beam as though it were a single solid member with thickness equal to that total.

Example:

Flitch beam with (3) 2×10 DF plies and (2) 3/8″ x 9.25″ A36 steel plates

Transform each of the steel plates into an equivalent thickness of Douglas Fir:

(3/8″)(17.05) = 6.39″ equivalent thickness of Douglas Fir

Add up the total thickness of all of the transformed plies:

(3)(1.5″) + (2)(6.39″) = 17.28″ thick

Analyze the beam as though it were a solid 17.28″ thick by 9.25″ Douglas Fir timber

Fastening

To make sure the individual plies perform as a single beam, you need to fasten them together to resist the intended loads.

For top-loaded beams only nominal fastening is required, since the loads pressing on the top of the beam naturally spread themselves out between each of the plies (required since each ply will be forced to deflect the same amount). In this case I recommend fastening the plies with Flatlok screws @ 16″ o/c, staggered in two rows along the length of the beam.

For side-loaded beams (like occur when using hangers to hang joists at the side of the beam), the load is only directly transferred into the first ply. You will need to use fasteners to distributed the load to the remaining plies so they can share the load. At each point along the length of the beam you need to provide enough fasteners to resist the shear load at that location. For uniformly loaded beams, this means you can space the fasteners evenly along the length of the beam. At point loads you will need to provide extra fasteners to resist the total shear force of the point load.

For wood to wood connections, I recommend using Flatlok screws for this purpose. You can install the screws from either side of the beam: the capacity is higher for the ply closer to the head side of the screw, but to make the specification foolproof I recommend using the capacities for the point side of the screw (the value given here is for the point side). For most beams (meeting the conditions in this tooltip)min. 2.75 inch penetration into other plies; fastener penetrates min. 1.25 inch into last ply; up to 4 plies total (this number includes an increase factor of n/(n-1), where n is the number of plies. The base capacity assumes n=4. For n greater than 4, reduce accordingly) the base capacity of each Flatlok screw is 345 lb. Remember to adjust by all applicable adjustment factors, below:

Basic Capacity (Z): 345 lbs per Flatlok screw

Adjustment Factors

Duration Factor	CD	1.60	(for wind/seismic/impact loads)
		1.15	(for snow loads)
Wet Use Factor	CM	0.70
Reduction for SPF Wood	CSG	0.80
Head Side Loading	CHead	1.84	(if load will only be applied to head side)

For wood to steel connections, you will need to use through bolts. Typically these are 1/2″ diameter. The capacity of each bolt depends on too many factors to list here – see NDS or the fastener calculator for calculations. Presented below are some typical capacities for the most common flitch beam configurations:

Flitch Beam	Capacity per 1/2″ through-bolt (lbs)
(2) 2x DF with (1) steel plate	1,050
(2) 2x DF with (3) steel plates	1,960
(3) 2x DF with (2) steel plates	1,960
(2) 4x DF with (1) steel plate	1,650
(1) 4x DF with (2) steel plates	1,960

For typical loadings, I recommend installing bolts at 16″ o/c, staggered in 2 rows top and bottom. Increase number of bolts as required for very high shear loadings.

End Bolts

Flitch plates present one additional consideration: typically the steel plate is slightly shorter than the wood members, so that the steel does not bear directly on the bearing surface at the end of the beam. You will need to transfer all of the load out of the steel plate and into the wood members at this location (remember to check the wood’s bearing capacity). At each bearing point, provide a number of through bolts as required to accommodate the shear at that point (times the ratio of the total load carried by the steel plies).

Typical Fasteners

For uniform loads with wood beams, use the following table (remember to multiply by any applicable adjustment factors):

	16″ o/c	12″ o/c	9″ o/c
1 row (stagger top and bottom)	250 plf	345 plf	460 plf
2 Rows	500 plf	690 plf	920 plf
3 Rows	750 plf	1,030 plf	1,380 plf

Base Loads

Use Flatlok screws for joining multi-ply beams. The base capacity of each Flatlok screw is 260 pounds (this assumes a worst-case scenario where the load is applied to the point end of the fasteners). Fasteners may be installed from one side (not required to stagger on opposite sides, though this does increase the strength). Note: capacity drops to 240 pounds if just fastening (2) 2x members

Resource: ER-0718

Point Loads

At point loads, provide Timberlok Screws sufficient to carry the entire point load (half each side of the point load). Install required fasteners within 12″ of point load

Note: Simpson technical letters allow an increase in fastener capacity (n/n-1). We will neglect this to be conservative

Recommended minimum fastening: (2) rows of fasteners @ 24″ o/c (this is capable of supporting a uniform load of 260 plf)