Please explain this sentence Traditionally when calculating

Please explain this sentence: \"Traditionally when calculating the deflection of beams, only the component due to the bending action is considered. This is due to the fact that in other materials, for example steel, the shear modulus is considerably higher as a percentage of the true elastic modulus than is the case in timber. A consequence of this is that when considering the deflection of timber beams the effect of shearing deformation may be significant.\" What does it mean for steel the shear modulus is higher than the elastic modulus and why it is not the case for timber. Thank you if you can demonstrate also by some formula.

Solution

Firstly, let us know the exact definition of elastic modulus and shear modulus. Elastic modulus is defined as the ratio between direct stress to direct strain with in the limit of proportionality. Shear modulus is defined as the ratio between the shear stress to the shear strain with in the limit of proportionality. The modulus of elasticity of steel is about 200 GPa and shear modulus is about 79.3 GPa. The shear modulus of timber is a crucial consideration, because 15 % deformation of the bending timber structures based on shear modulus. Meanwhile, In steel structures there is only 2 % deformation, which based on shear modulus. Timber is a natural structure. It is having the strength less than the steel. Steel is having a particular proportional limit in bending. But timber fails when heavy loads appiled on the structure. It is not having high prportional limit. Elastic modulus for timber is 10 GPa. Actually ealstic modulus is higher than the shear modulus for steel. That can be explained by this formula E=2G(1+v). From the above formula elastic modulus is equal to two times the shear modulus. That\'s why we can consider the comparison between elastic modulus and shear modulus. So we can find many differences between the structures of steel and timber. Consideration of shear modulus for timber is always higher than the steel. Shear modulus of timber is more than elastic modulus compared to steel. Timber may get collapsed with less deformation. So that the consideration of shear modulus will be considered more compared to steel. Steel is having higher proportional limit, then it can be deformed even under the heavy loads. The consideration of shear modulus is less compared to timber i.e about 2 percentage. Finally the structural formation of timber is completely different from steel. Timber is having more factor of safety compared to steel. The toghness and hardness of timber are always lesser than those of steel.