Final answer:
To determine the required width of the beam, calculate the bending moment and maximum bending stress caused by the concentrated load. Use the shear force caused by the concentrated load to find the maximum shear stress. Calculate the required width based on the allowable bending stress and shear stress.
Step-by-step explanation:
To determine the required width of the wood beam based on an allowable bending stress, we need to consider the bending moment caused by the concentrated load and the maximum bending stress the wood can handle. The bending moment M can be calculated using the formula M = (W * L) / 4, where W is the concentrated load and L is the length of the main span. The maximum bending stress σ can be found using σ = (M * c) / I, where c is the distance from the neutral axis to the outermost fiber and I is the moment of inertia of the cross-sectional area of the beam.
To determine the required width based on an allowable shear stress, we need to consider the shear force caused by the concentrated load and the maximum shear stress the wood can handle. The shear force V can be calculated using the formula V = W / 2, where W is the concentrated load. The maximum shear stress τ can be found using τ = (V * h) / A, where h is the height of the beam and A is the cross-sectional area of the beam.
Based on the allowable bending stress and shear stress, the required width of the beam can be determined.