Simplification of the Measurement Method of the Shear Modulus of Wood by Torsion Test

Abstract

In a previous paper, we measured the shear moduli of wood by the torsion of a rectangular bar accurately. In this method, two strain gages were bonded on the LR- and LT-planes to measure the shear strains. Although this method is mathematically-accurate, it is not convenient because of the necessity of two torsional moment-shear strains relationships. Here, we tried to simplify the measuring method by using only one torsional moment-shear strain relationship. In this experiment, specimens with various rectangular cross sections of which aspect ratios (b/a) varied from 1/9 to 9 were twisted around the longitudinal directions. The shear moduli were calculated by the following three different relationships; two torsional moment-shear strains relationships, one torsional moment-shear strain relationship, and the torsional moment-torsinal angle relationship. The moduli obtained by these three procedures were compared with each other. The results were summarized as follows: (1) When the cross section of the specimen was narrow enough (aspect ratio=1/9 or 9 in this experiment), the shear moduli obtained from the three procedures were close enough to each other. However, the axial restraint effect was remarkable for the specimen with narrow cross-section, and hence, the shear moduli were evaluated as large. (2) The shear modulus can be approximated properly by bonding one strain gage on the measured plane even when the specimen has an intermediate aspect ratio of 1/3 to 3. The shear modulus on the LR-plane of wood does not usually exceed the twice of that on the LT-plane. Thus, we think that the shear moduli on the LT- or LR-planes can be measured effectively by bonding one strain gage on the measured plane.既報では，矩形棒の2つの側面中央（板目面およびまさ目面）にひずみゲージを貼付してねじり，2つのねじりモーメントせん断ひずみ関係から数学的に厳密な方法でせん断弾性係数を算出したが，多少煩雑な計算が必要であった。そこで今回は，必要とする面（板目面およびまさ目面のいずれか一面）の中央にのみひずみゲージを貼付してねじり，1つのねじりモーメント－せん断ひずみ関係からせん断弾性係数が求められるのかどうか検討した。試験では断面寸法比（b/a）が1/9から9の矩形棒を繊維方向を中心軸としてねじった。せん断弾性係数は以下に示す3つの関係すなわち（i）2つのねじりモーメント－せん断ひずみ関係，（ii）1つのねじりモーメント－せん断ひずみ関係（iii）ねじりモーメント－ねじり角の関係から計算し，それぞれの値を比較した。結果を以下に示すと，（1）断面寸法比が十分に大きければ（本実験では断面寸法比＝1/9あるいは9），3つの関係から得られたせん断弾性係数は互いに近接した。しかし，断面寸法比が大きくなるとねじり軸方向の拘束効果が避けられず，せん断弾性係数は大きく見積もられる傾向があった。（2）ひずみゲージを必要とする一面にのみ貼付した場合，断面寸法比が大きくなくても（断面寸法比が1/3から3の範囲）比較的正確にせん断弾性係数が算出できた。一般的に，木材のまさ目面のせん断弾性係数は板目面のせん断弾性係数の2倍以上にはならないので，この方法でまさ目および板目のせん断弾性係数を求めることは可能であると考えられた