# Three point bending test for timber joists

In document An investigation into the strength properties of reclaimed timber joists (Page 89-94)

## 3 METHODOLOGY AND TESTING

### 3.6.6 Three point bending test for timber joists

The three-point bending test serves as a means to determine mechanical properties in flexure; modulus of elasticity, stress-strain response, yield stress and modulus of rupture. The test measures the force required to bend a joist under three point loading conditions. The main advantages of the three-point bending test are; its simplicity, ease of setup and speed of testing.

The test joist is supported at the ends and a transverse load is applied in the middle; hence, loads are applied at three points only. Each specimen is passed through and tested, to a set deflection, on the plank edge, at increments of 150 mm, and to within 800 mm of each end of the joist; the timber joist is turned over and then reversed and readings taken from the opposite edge. Strength can be calculated from the overall measurements over the two plank edges, but for this research a further static bend test was carried out on the weakest area of any visually assessed joist. The static bend test then gave a minimum strength rating for the reclaimed timber joist as a whole.

Dynamic bend test method

1. Breadth and height for the specimen are measured (in mm).

2. The specimen should be placed in the three-point bend test apparatus ensuring that the test piece is correctly oriented (the joist should be lying on its plank edge). The first test area placement is at 800 mm from the joist end.

3. The pressure anvil is lowered into position so that the tip touches the upper edge of the specimen. The micrometer indicator should be set to read zero deflection. 4. The load on the anvil should be set at 2000N. 30 seconds of loading should be

allowed for the deflection to stabilise.

5. The load on the joist and the deflection obtained should be noted.

6. Items 1-5 of this test should be repeated at increments of 150 mm along the length of the joist. The test ends when the increments come to within 800 mm of the opposite end of the joist.

This method will, in graphical form, illustrate a joist deflection diagram similar to that one shown by Figure 3.17.

Figure 3.16. Large timber specimen testing rig set up for dynamic bend test

Figure 3.17. Joist load-extension graph (60 x 170 x 2400mm under 2000N load)

5.3 5.4 5.5 5.6 5.7 5.8 5.9 6 6.1 6.2 E x te n s io n ( mm )

Static bend test method

1. Breadth and height for the specimen are measured (in mm).

2. The specimen should be placed in the three-point bend test apparatus ensuring that the test piece is correctly oriented (the joist should be resting on its narrow edge – see Figure 3.15). The test area placement is at the weakest point on the joist, as indicated by the results from the dynamic bend test.

3. The pressure anvil is lowered into position so that the tip touches the top of the specimen. The micrometer indicator should be set to read zero deflection.

4. The load on the anvil should be increased, by increments (of 1000N) to 10,000N; however, displacement should be kept below 5 mm (this could signal an early

conclusion of the test). 30 seconds per increment in load should be allowed for the deflection to stabilise.

5. The load on the joist and the deflection obtained should be noted and plotted as a load/deflection graph.

Figure 3.18. Large timber specimen testing rig set up for static bend test

By measuring the deflection (δ) as a function of load (m) in the three-point bend test apparatus the Modulus of elasticity of the joist can be calculated. This part of the process investigates the elastic deformation of the timber, so the test piece should not be overloaded. A total force of 10,000 N will usually be sufficient to give an accurate indication of MOE, unless the timber specimen has a particularly large cross sectional area.

The main advantage of a three point flexural test is in the ease with which the specimen is prepared; the test itself does not call for any special setup or equipment other than the rig, load apparatus and deflection indicator.

The deflection at any location along the length of a simply supported joist with a single mid-span point load can be determined by:

Where

Δy = deflection in the vertical direction

x = point distance from supports

L = distance between supports

E = modulus of elasticity

I = moment of inertia

For a rectangular cross section, the moment of inertia is:

Where

b = width of joist

h = height of joist

Thus, the modulus of elasticity can be resolved by rearranging Equation 6.

3.6.7 Small clear tests

In the static small clear bend test the orientation of the growth rings is parallel to the direction of loading and an extensometer is usually attached to provide a load- deflection diagram from which is calculated the modulus of elasticity, as determined by BS 373 (BSI, 1957).

For this research small clear specimen test pieces should be cut from the larger timber joist specimens, and machined to size by being passed through a bench plane to acquire the 20 mm dimension expressed in the standard as accurately as possible. The machined specimen is tested to destruction on a small, purpose built test rig (see -

Δy = Px(3L 2 -4x2) 48EI (6) I = bh3 12 (7) E = Px(3L24x2) 48I Δy (8)

Figure 3.19). The standard has largely fallen out of practice since the advent of automated computerised testing of large joists; however, it has proven useful for this research in the calculation of stiffness values and where, ultimately, a smaller scale reclamation setup is being considered.

Figure 3.19. Example of a non automated ‘small clear’ test apparatus setup

Small clear test method

1. The specimen should be placed in the test apparatus ensuring that it is correctly oriented (taking careful note of the angle of the growth rings; they should be as near vertical as they can be placed).

2. The pressure anvil is lowered into position so that the tip touches the upper edge of the specimen. The load cell indicator should be zeroed.

3. The load on the anvil is gradually increased, maintaining a constant momentum of 0.11 mm/s (this equated to 6.6 mm/minute; six and a half turns of the screw guide in the piece of apparatus used for this research – Figure 3.17)

4. The reading from the load cell should be marked at each full turn of the screw guide, this will yield a load reading every 10 s, and for every 1.1 mm of

deflection (The deflection of the joist at mid length is measured with reference to the outer points of loading)

5. Readings continued until the specimen either fails to support one tenth of the maximum load recorded, or is deflected by more than 60 mm; whichever occurs first.

6. A load deflection displacement diagram should be plotted for each specimen.

Three strength properties are usually determined from this test; Modulus of rupture (MOR), work to maximum load, and Total work. The MOR is a measure of the ultimate bending strength of timber for that size of specimen and that rate of loading. This is actually the equivalent stress in the extreme fibres of the specimen at the point of failure. In three-point bending the MOR is given by:

Where

P is the load in Newtons (at the point of maximum load/rupture) L is the span length in mm,

b is the width of the joist in mm, and

d is the thickness of the joist in mm.

The second strength parameter is work to maximum load, which is a measure of the energy expended in failure and is determined from the area under the load-deflection curve up to the point of maximum load. The third parameter, total work, is the area under the load-deflection curve, and is taken to complete failure.

The intention in carrying out two different methods of strength tests is to find a correlation in properties between small clear specimens and large timber joists.

In document An investigation into the strength properties of reclaimed timber joists (Page 89-94)