Evaluation of a Gouged Glulam Beam

Situation

A 6-3/4 in. x 22.5 in. glulam beam is damaged by a forklift. The damage is a `gouge' that runs along the bottom edge of the beam starting about 7 ft from one end and runs about 3 ft. The gouge is about 5/8 in. deep and 2 in. wide. The beam spans 22 ft and is uniformly loaded with Live and Dead loads. The question arises as to the structural significance of the gouge. Let's run some numbers and see.

Approach

Without more detailed information we will assume that the gouge `dimensions' are the same for the length of the gouge. From the information given it appears that the gouge ends before we hit the critical section of the beam for flexure; however, only a little bit so. In fact, the theoretical decrease in the bending moment due to uniform load as we go either direction from the critical section is so slight, that, at least for now, let us consider the gouge to be at the section of critical (maximum) bending moment (or vice versa). Hence, for the beam to still be good at all, there will have to be some excess capacity in the beam with respect to its design loads.

Ideally, the design information for such a beam would be available. Sources of this information could include the Owner, Architect/Engineer, and/or Building Department. If the information is not available, it would need to be reproduced. In this particular example, the beam was expected to be loaded to to 89% of capacity in flexure under design loads. Our task will be to evaluate the loss in capacity due to the gouge. If the demand on the beam does not exceed the reduced capacity of the gouged beam, we could say the condition is still `good'.

Demand on the Beam

In this particular example it was found that the beam will be loaded to 89% of capacity at the critical section under design loads. Since the gouge is pretty close to the critical section, we have decided to take this (89%) as the minimum acceptable capacity of the damaged section.

If, for example, the gouge was at a location more distant from critical section, we would have more `room' to work with. At the quarter points, for example, the theoretical moment is 3/4ths that at the critical section, so we would have ¾ of 89% or 67% of capacity to work with.

In terms of an allowable flexural capacity of the beam, the beam's original capacity, M_r , is ...

M_r = F_b' S,

where

F_^b' is the allowable bending stress adjusted for duration of load, volume effect, etc., and in this example is 2187 psi,

and,

S is the original Section Modulus, bh² / 6 = 569.5 in.³.

So,

M_r = F_b' S = 2187 psi (569.5 in.3) = 1,246,000 lb-in. = ...

M_r = 103,800 lb-ft.

The demand at the point of interest is ...

M_{r needed @ POI} = 0.89 (103,800 lb-ft) = ...

M_{r needed @ POI} = 92,400 lb-ft.

Reduced Capacity Due to Gouge

In this particular example the gouge is in the bottom or tension zone of the beam. And, in fact, the gouge is in the `tension lam'. The tension lam is a lamination that is particularly intended to carry tension stresses in the beam, and generally of higher quality (strength and stiffness) than the other lams. Damage to this lam is not trivial. Furthermore, due to the increased stiffness of the tension lam(s) (and other laminations in the tension zone), the laminations take more stress than is anticipated by a rectangular section approach to the section. As such, in at least a first-order evaluation, the size of the gouge may be increased by 50% to account for possible wood fiber damage beyond the gouge, and the rectangular section approximation to what is in reality a more precise transformed section analysis dealing with the stiffer tension zone laminations.

Using basic section property mechanics,

The reduced area, A*, of the section is,

A* = A - 1.5 (gouge size),

where,

A = b x h,

where,

A, of course, is the original section area,

b = beam width, and

h = beam depth.

So,

A = 6.75 x 22.5 = 151.9 in.²,

and,

A* = A - 1.5 A _gouge = 151.9 - 1.5 (5/8 x 2) = 151.9 in.² - 1.875 in.² = 150.0 in.².

To determine the capacity of the section, the Moment of Inertia, I* of the gouged section must be determined. This may be obtained by first finding the neutral axis of the gouged section.

Using the Principle of Moments with respect to the un-gouged section neutral axis (centroid),

A*y* = Σ A_i y_i...

150.0 in.² y* = 151.9 (0) + (22.5/2 - ½ of 5/8) (- 1.875) = 10.9375 (-1.875) = - 20.5 in.³,

where the 10.9375 is the distance from the original neutral axis up to the `centroid' of the gouge;

thus,

... y* = -20.5 / 150.0 = 0.137 in.

(The neutral axis moves up 1/8^th of an inch due to the gouge.)

The gouged section Moment of Inertia can be found by first determining the Moment of Inertia of the gouged section with respect to the original neutral axis, and then with respect to the new neutral axis.

... I = (1/12) b h³ = for the original, un-gouged section = (1/12)(6.75)(22.5)³ = 6407 in.⁴.

... I _{gouged w.r.t. orig n.a.} = 6407 - 1.875 (10.9375)² = 6407 - 224 = 6183 in.⁴.

Now for I* ...

... I* = I _{gouged w.r.t. orig n.a.} - A* y*² = 6183 - 150.0 (0.137)² = 6183 - 3 = 6180 in.⁴.

From this the Section Modulus of the gouged section may be determined. Now that the section is not symmetric, the Section Modulus with regard to the bottom fiber is different than that for the top; we'll calculate the one with regard to the bottom ...

S* = I* / c* = 6180 / (11.25 - 0.137) = 6180 / 11.1 = ....

S* = 556 in.³.

The reduced allowable flexural capacity of the beam, M_r* is,

M_r* = F_b' S* = 2187 psi (556 in.³) = 1,216,000 lb-in. = ....

M_r* = 101,300 lb-ft.

Capacity Check with Respect to Demand

Now we're ready to check the beam reduced capacity with respect to the demand on the beam at the point of interest.

Is the demand at the point of interest = M_{r needed @ POI} = 92,400 lb-ft ...

... ≤ the reduced capacity at the point of interest = M_r* = 101,300 lb-ft ... ???

Yes. Good.

In terms of fractions ...

Is the reduction in capacity ... 1 - 101,300/103,800 = ... 2.4 % ... less than the excess capacity 1 - 0.89 = ... 11% ... Good!

Concluding Remarks

Had the reduced capacity been less than what is demanded of the beam, the beam would have to be repaired, reinforced, or replaced, or perhaps more detailed calculations and evaluation of in-place conditions performed. In cases where beams may be exposed to `abuse' from below, a sacrificial lam or lams may be recommended in design. Had the calculations landed right on the `knife-edge', an actual transformed section analysis could be performed. A more detailed on-site evaluation might include considering any strength-reducing characteristics (knots, etc. versus clear wood) in the remaining portion of the damaged lam(s).

While damage to the `tension lam' of a glulam beam can be rather `frightening', in this case the damage results in only a rather small loss in capacity of the beam.

References

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.