By W M C McKenzie

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E. the position x being considered is to the left of the load associated with the bracket. Boundary Conditions The boundary conditions are known values associated with the slope and/or deflection. e. g. e. e. equation (4) is equal to zero and substituting the calculated value of x into equation (5) as above. g. 0 m from the left-hand end the last two terms in the [ ] brackets need not be used to determine the position of zero slope. This assumption can be checked and if incorrect a subsequent calculation carried out including an additional bracket until the correct answer is found.

Determine the shear stress distribution throughout the depth of the section. 40. 40 The maximum value occurs at the same level as the elastic neutral axis. e. 41. 41 Stress diagram The magnitude of the bending stresses at any vertical cross-section can be determined using the simple theory of bending from which the following equation is derived: Structural Analysis Techniques M E σ = = I R y ∴ σ = My I 37 Equation (2) where: M the applied bending moment at the section being considered, E the value of Young’s modulus of elasticity, R the radius of curvature of the beam, the bending stress, σ y the distance measured from the elastic neutral axis to the level on the cross-section at which the stress is being evaluated, I the second moment of area of the full cross-section about the elastic neutral axis.

Plywood webs and softwood flanges fastened together. During bending, the stresses induced in such sections are shared among all the component parts. The extent to which sharing occurs is dependent on the method of connection at the interfaces. This connection is normally designed such that no slip occurs between the different materials during bending. The resulting structural element is a composite section which is nonhomogeneous. ) A useful technique often used when analysing such composite sections is the transformed section method.