University of New Mexico

Civil Engineering Department

Civil Engineering Materials Laboratory, CE 305L

BENDING OF WOOD.

General

In bending, it is assumed that wood is linearly elastic for low values of stress, i.e., the stress and strain are proportional to each other and produce an elastic or straight-line plot on the typical stress-strain curve. This may be confirmed by investigating deflection of wood beams under bending action resulting from typical transverse loads and solving the deflection equation for the modulus of elasticity. For example, for a simply supported beam of span L and with a concentrated load P applied at the center of the span, the maximum deflection, which occurs at the center of the span, is determined by the equation

(1)    

in which E is the modulus of elasticity and I is the moment of inertia of the section with respect to its centroidal x-axis. Solving the equation for E yields:

(2)    

By loading a sample beam of the above description and simultaneously recording values of the concentrated load ( P ) and the resulting deflection ( D ). The slope of the resulting linear elastic portion of this load-deflection curve is simply a stiffness value ( k ). Rearranging Equation 2 above, one can represent this stiffness as follows:

(3)   

This stiffness value can be ascertained by experiment as the slope of the load-deflection curve up to the proportional limit. With this stiffness know, the modulus of elasticity can then be determined as follows by rearranging Equation 3 and solving for E , i.e,

(4)   

where L and I are measured properties of the beam. The computed value of E should be approximately equal to the value determined from the investigation of loads parallel to the grain of short wood compression blocks.

Up to the proportional limit, the bending stress of at the outer fibers is determined by the equation:

(5)    

in which s is the bending stress at the outer fibers (either in compression or tension), M is the maximum bending moment, c is the distance from the neutral axis (coincident with the centroidal x-axis of the section) to the extreme outer fibers, and I is the moment of inertia of the section with respect to its centroidal x-axis. Here, the moment of inertia for a rectangular beam is assumed in term of the base width ( b ) and the depth ( d ). The plot of load and deflection provides the proportional limit and ultimate load. Substitution of these loads into Equation 5 will yield the proportional limit stress and the ultimate stress.

As stated earlier, this maximum proportional limit stress may be in either compression or tension, or in the case of a section with x-axis symmetry, the bending stress in compression is assumed to be equal to that in tension.

It may therefore be seen that a bending test (flexural test) of a wood beam can provide information resulting in a reasonably accurate determination of the modulus of elasticity of the material and also the proportional limit and ultimate stress in bending. Yield stresses for wood are difficult to determine accurately as noted earlier, and are therefore infrequently used as an important mechanical property of this material.

Objectives

The nature of wood in flexure (bending) will be evaluated. Flexural mechanical properties of wood will be ascertained.

Equipment

•  Universal Testing Machine (UTM) with applicable bending accessories,

•  Deflectometer (1 inch dial gage),

•  Beam support to simulate a simply supported beam,

•  Mechanical calipers,

•  Tape measure

Specimen

Nominal 2” x 2” x 30” clear wood specimen.

Procedure

Click here to download the bending of wood procedures.

  1. Mark the center and end points for a 26 inch span of the beam.
  2. Place the beam on the beam support and into the testing machine so that a concentrated load may be applied at the center of the span.
  3. Position the dial gage between the load platen and the moveable crosshead of the testing machine.
  4. Select a load range on the testing machine that will provide a minimum of 2000 pounds total load.
  5. Apply the load slowly, obtaining simultaneous readings of load and mid-span deflection in 50 pound load increments.
  6. Continue loading to total failure of the specimen.
  7. Describe the type of failure (see Figure 1).

Required

  1. The load-deflection curve of the beam.
  2. Calculate the following:
  3. Proportional limit stress at outer fiber.
  4. Ultimate stress at outer fiber.
  5. Modulus of elasticity.
  6. Compare the calculated values with established values for clear wood in flexure. Compute experimental errors.

References

  1. ASTM D143, Standard Methods of Testing Small Clear Specimens of Timber , Vol 4.10.
  1. ASTM D2555, Standard Test Methods for Establishing Clear Wood Strength Values , Vol 4.10.

Figure 1. Types of Failures in Static Bending.

Test setup

Bending of wood at fracture. Type (a) simple tension.

Sample Data

Data obtained in CE 305, Fall 2003