Final answer:
To design a timber beam cross section, one must know the maximum bending moment, which was not provided. Given an allowable normal stress of 13 MPa, the design ensures that the stresses do not exceed this limit, and the dimensions of the beam would depend on specific load and span conditions.
Step-by-step explanation:
Designing a Timber Beam Cross Section
To design the cross section of a beam with a given loading condition and material properties, first, we need to determine the maximum bending moment acting on the beam. Once the maximum bending moment (M) is established, we use the flexural formula:
M = (σ x I) / c
where σ is the allowable normal stress, I is the moment of inertia, and c is the distance from the neutral axis to the outer fiber of the beam. However, in this case, details about the loading condition are not provided, so we cannot perform the full design process.
Given the allowable normal stress (σ) is 13 MPa for the timber, and assuming this is the maximum stress allowed, we would ensure that our design keeps the normal stresses within this limit. The actual cross-sectional dimensions will depend on the loading scenario, such as whether it's a single point load or a distributed load, and the span length of the beam.
Engineers must also consider other factors such as deflection limits, safety factors, and serviceability criteria when designing structures.