Example 03: Moment Capacity of a Timber Beam Reinforced with Steel and Aluminum Strips

Problem
Steel and aluminum plates are used to reinforced an 80 mm by 150 mm timber beam. The three materials are fastened firmly as shown so that there will be no relative movement between them.
 

beam-002-wood-reinforced-steel-aluminum.gif

 

Given the following material properties:

Allowable Bending Stress, Fb
Steel = 120 MPa
Aluminum = 80 MPa
Wood = 10 MPa
Modulus of Elasticity, E
Steel = 200 GPa
Aluminum = 70 GPa
Wood = 10 GPa

Find the safe resisting moment of the beam in kN·m.
 

Reinforced Beams

Flexure formula do not apply directly to composite beams because it was based on the assumption that the beam was homogeneous. It is therefore necessary to transform the composite material into equivalent homogeneous section. To do this, consider a steel and wood section to be firmly bolted together so that they can act as one unit. Shown below are the composite wood and steel section and the corresponding equivalent in wood and steel sections.
 

001-equivalent-sections.gif

 

The quantity n is usually taken as the ratio of the moduli of elasticity of stronger material to the weaker material. In the above case, n = Es / Ew.