Problem 1005 | Maximum concentrated load at the midspan that the reinforced timber beam can carry

Problem 1005
A timber beam 6 in. by 10 in. is reinforced only at the bottom by a steel plate as shown in Fig. P-1005. Determine the concentrated load that can be applied at the center of a simply supported span 18 ft long if n = 20, fs ≤ 18 ksi and fw ≤ 1200 psi. Show that the neutral axis is 7.1 in. below the top and that INA = 1160 in.4.
 

1005-given-timber-and-steel.gif

 

Chapter 10 - 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 the ratio of the moduli of elasticity of stronger material to the weaker material. In the above case, n = Es / Ew.
 

Pages