Question 5 of 5: Wood in Compression and Steel Test Methods

Question 5: Wood in Compression and Steel Test Methods (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Part (a) — Wood in compression parallel to the grain (11 marks)

Given. A clear wood prism of actual cross-section 1 in × 1 in and length 4 in, grain parallel to the length, loaded in compression parallel to the grain to failure. The recorded load-deformation pairs are:

Find. The stress-strain plot, the modulus of elasticity from its straight portion, and the failure (peak) stress.

Approach. Divide every load by the 1 in² cross-section to get stress and every displacement by the 4 in length to get strain, plot the pairs, identify the straight run between the seating region and the onset of crushing, take its slope as the modulus, and read the peak stress directly.

1. Part (a), step 1 — convert load and deformation to stress and strain. With $A=1\times1=1\ \text{in}^{2}$ and $L=4\ \text{in}$, $$\sigma=\frac{P}{A},\qquad \varepsilon=\frac{\Delta L}{L}$$ so the stress in psi is numerically equal to the load in pounds, and each displacement is divided by 4. The 5338 lb reading, for instance, becomes $\sigma=5338\ \text{psi}$ at $\varepsilon=0.324/4=0.0810$.
2. Part (a), step 2 — identify the straight portion. The first four readings (7, 10 and 87 lb over displacements up to 0.164 in) carry almost no load while the platens seat and the end grain crushes locally; this is the toe of the record and must not be included in the modulus. Taking consecutive secants from the 530 lb reading onwards gives slopes of $$167\,900,\quad 165\,600,\quad 115\,800,\quad 102\,000,\quad 122\,000\ \text{psi}$$ The first two agree to within 1.4 %, so the straight line runs from the 530 lb point to the 2864 lb point and the material begins to soften after that.
3. Part (a), step 3 — modulus of elasticity. Taking the slope over that straight run, $$E=\frac{\sigma_{2}-\sigma_{1}}{\varepsilon_{2}-\varepsilon_{1}} =\frac{2864-530}{0.0590-0.0450}=\frac{2334}{0.0140}$$ $$\boxed{E\approx1.67\times10^{5}\ \text{psi}}$$ Extrapolating that line back to zero stress locates the corrected origin at $\varepsilon_{0}=0.0450-530/166\,714=0.0418$, which is the amount of apparent strain that was pure seating.
4. Part (a), step 4 — failure stress. The load rises to a maximum and then falls away as the fibres buckle and a crushing plane forms, so the failure stress is the peak: $$\sigma_{f}=\frac{P_{\max}}{A}=\frac{5338}{1}$$ $$\boxed{\sigma_{f}=5338\ \text{psi}\approx36.8\ \text{MPa}}$$ The corrected strain at that point is $0.0810-0.0418=0.039$, and the load then decays to 4331 lb, a drop of 18.9 %, which is the gradual post-peak behaviour typical of wood crushed parallel to the grain rather than a brittle collapse.

Part (b) — Significance and use of the three steel tests (9 marks)

i. Tension test (ASTM A370/E8, CSA G40.20). A machined coupon is pulled to fracture while load and extension are recorded, yielding the yield strength, the tensile strength, the modulus of elasticity, the percent elongation over a 50 mm or 2 in gauge length and the reduction of area. Its significance is that it supplies almost every number a designer actually uses: F_y and F_u enter CSA S16 resistance equations directly, E governs deflection and buckling, and the elongation is the primary index of ductility, which is what allows plastic design, moment redistribution and seismic energy dissipation. Its use is in mill certification of every heat of structural steel and reinforcing bar, in grade verification of material arriving on site, and in failure investigations. The yield-to-tensile ratio and the length of the yield plateau are read from the same curve and are specified for seismic applications.

ii. Charpy V-notch impact test (ASTM A370/E23, CSA G40.20 category T). A 10 mm square bar with a 2 mm deep V-notch is broken by a swinging pendulum at a specified temperature and the energy absorbed is reported in joules. Its significance is that it measures notch toughness — the ability to absorb energy in the presence of a stress raiser at a high strain rate and a low temperature, which is exactly the combination the tension test cannot reveal. Steel passes through a ductile-to-brittle transition as temperature falls, and the Charpy test locates that transition, so its use is in specifying material for structures exposed to Canadian winter service temperatures, for welded and therefore notch-rich details, for bridges and for fracture-critical members. A common requirement is 27 J at a stated temperature; the classic cautionary examples are the Liberty ships and the Hasselt bridge, both brittle fractures in steel that would have passed a tension test.

iii. Bend test (ASTM A370, CSA G30.18 for reinforcement). A specimen or a full-size reinforcing bar is bent cold through a specified angle, usually 90 or 180 degrees, around a mandrel of specified diameter, and the outside of the bend is examined for cracking. Its significance is that it is a direct, qualitative test of ductility and of soundness in the form the material will actually be worked: it exposes surface defects, laminations, inclusions, excessive hardness and embrittlement from over-alloying or improper heat treatment. Its use is in acceptance of reinforcing steel, which must survive field bending around standard pin sizes without cracking, in qualification of welding procedures and welders through the guided-bend test on a welded coupon, and in acceptance of plate that will be cold-formed. It is a pass-or-fail test and requires no instrumentation, which is why it survives as a site and fabrication-shop check.