Investigating Drying Checks in a Glulam Beam

An existing glued-laminated timber (glulam) beam is observed to have a drying check on one side. The question arises as to whether or not the check (separation of wood fibers) has a significant impact on the beam's capacity. Well, let's `check'.

The beam is a 5-1/8 in. x 13.5 in. DF/DF 24F-V4 beam and spans 13.0 ft. It is designed to carry distributed loads of 252 lb/ft Dead load, 600 lb/ft Live load plus the weight of the beam itself, 16 lb/ft, and a concentrated load of 1550 lb DL and 3667 lb LL located 10 ft from one end (3 ft from the other). The check runs along the end 4 ft of the beam (more heavily loaded end) at a distance of 3.0 inches from the bottom of the beam. The depth of the check varies but is 1.5 in. deep at its maximum.

Approach

We will follow the guidance of AITC Technical Note 18. First of all the Technical Note gives us `allowable' check sizes in glued laminated timber. In other words, design values (published capacities) for glulam beams already take into consideration the possibility of some checking. If the checking in the beam in question is within the allowable limits, as long as the beam was originally designed adequate for the in-place conditions, we need check no further. The beam is `good'. If, however, the actual check size is greater than the allowable check size, we will need to do some more calculations.

Checking the Check Size and Allowable Check Size

We see in the Technical Note that check depths up to 15% of the beam width are allowed anywhere in the beam without the need for considering capacity reduction.. So, for our beam, the `allowable' check size (for a check anywhere) is 0.15 x 5.125 in. = 0.77 in. The actual check size is greater than that, so we need to look a bit further.

For some regions of the beam the allowable check size is larger. This takes into consideration that the shear stresses are greatest near the neutral axis of the beam, and decrease toward the top and bottom. Figure 4 of the Note provides the allowable check depth graphically. In equation form,

F_W = 0.15 ... for ... 0 ≤ y/D ≤ 0.25;

F_W = 3.25 (y/D) - 0.66 ... for ... 0.25 < y/D ≤ 0.45; and

F_W = 0.80 ... for ... 0.45 < y/D,

where,

F_W = is allowable (fractional) check depth,

y = the distance from the neutral axis to the check (either up or down), and

D = is the beam depth.

These equations are for rectangular section beams, for which the neutral axis (in bending only) will be at the mid-depth, and as such y/D will not exceed 0.50.

These equations take into account the parabolic distribution of shear stress, though at some relative beam depths very conservatively so.

So, for our situation, the check is 3.0 inches from the bottom. Our beam depth is 13.5 in., so the distance of our check from the neutral axis is,

... y = D/2 - 3.0 in. = 13.5 in./2 - 3.0 in. = 3.75 in.

The fractional distance from the neutral axis is,

... y/D = 3.75 / 13.5 = 0.278.

We use the second equation and obtain,

F_W= 3.25 (y/D) - 0.66 = 3.25 (0.278) - 0.66 = 0.24.

And, we get the same thing from Figure 4; good.

So, that means that for the location of `our' particular check, the allowable check width is,

... 0.24 (5.125 in.) = 1.23 in.

Our check width is 1.5 in., so we need to keep going.

Up until now we have not looked in particular with regard to the actual loading on the beam; we have only taken into consideration how shear stress is known to vary in the beam, and in particular with distance from the neutral axis, and we have taken into consideration known excess capacity, regardless of how the beam is actually loaded, assuming it was correctly `sized' in the first place. And in many cases we will find in this regard that existing checks `check out' (good). But in this particular example, we have exhausted the `easy way out', and now need to do some calculations taking into consideration the actual loading on the beam.

Capacity Reduction for Checks Greater than Allowable

For checks of size greater than allowable the demand on the remaining wood at the location of the check is taken into account using a `shear reduction factor for checking', C_VC. This factor is multiplied into the design value for shear in a way similar to other adjustment factors in wood design. The shear stress under design load, f_v, is calculated at the neutral axis and at the section in question, adjusted for as usual, and then is multiplied by C_VC which takes into account that actually our point in question is off the neutral axis where the applied stress would be less, except for the fact that the available shearing surface is less.

Here is the equation,

... C_VC = (1 - s/W) / (1 - F_W),

where,

... s is the check size (depth), and

W is the beam width.

So, in our case,

C_VC= (1 - 1.5/5.125) / (1 - 0.24) = 0.707 / 0.76 = 0.93.

The shear capacity is reduced 7% (more) at `this location' by `this size' check.

So, per the Allowable Stress Design (ASD) approach, our design check will be ...

... is f_v = (3/2) V/A ≤ F_v' (C_VC )...?

where,

... f_v = (3/2) V/A ... is the applied stress at the neutral axis at the section in question,

F_v' = F_v (C_D, C_M, ... all appropriate adjustment factors) ...

where, in this example, we have `normal' load duration, dry moisture condition, and so on ... all the adjustment factors being unity, and

F_v = 265 psi, from AITC 117-04 (design value for shear for the DF/DF 24F-V4, prismatic shape section, etc.) ...

So,

F_v' = 265 psi (1.00)(1.00) ... etc. = 265 psi.

... F_v' C_VC = 265 psi (0.93) = 246 psi.

And now for f_v ...

By principles of mechanics, the maximum shear on the `heavy' end of the beam (where the check is located) is,

... V = (252 + 600 + 16 plf) (13 ft) / 2 + (1550 + 3667 lb) (10 ft / 13 ft) = 9347 lb.

... f_v = (3/2) (9347 lb) / (5.125 in. x 13.5 in.) = 203 psi.

So,

... is f_v = (3/2) V/A = 203 psi ≤ F_v' C_VC = 246 psi? ... YES!!! GOOD!

So, even though the check size is greater than allowable, the excess capacity in the beam is sufficient under the design loading conditions to accommodate the reduction in capacity due to the check.

Discussion

In this example the beam with the drying check checks out okay. The procedure is a bit counter-intuitive in that the applied stress at design load is calculated at the neutral axis at the section in question (without section loss) and evaluated against a reduced allowable stress to account for the checking. In reality, it's the loss of horizontal shearing surface at the location of the check that has us worried, and we are counting on the (remaining) wood having the full allowable stress (if need be). In the end, however, if we use the straight line approximation for the shear stress distribution that is reflected in Figure 4 of the Technical Note, which also factors in/out the allowance for fractional check widths of 15% or more, in any beam, we would come up with essentially the same thing if we calculated the stress at the horizontal surface in question, decreased by distance from the neutral axis, but increased due to section loss from the check.

In the case of drying checks one question remains: has the beam reached an equilibrium condition in which further checking is not anticipated? Obviously if the answer to this question is not known, then further monitoring of the conditions of any checks would be prudent, and subsequent calculations preformed as needed.

References

"Evaluation of Checking in Glued Laminated Timbers," AITC Technical Note 18, March 2004, American Institute of Timber Construction, 7012 South Revere Parkway, Suite 140, Centennial, CO 80112.

Standard Specifications for Glued Laminated Timber of Softwood Species, AITC 117-2004, American Institute of Timber Construction, 7012 South Revere Parkway, Suite 140, Centennial CO, 80112.