Problem 1004 | Increase in moment capacity due to aluminum plate reinforcement Jhun Vert Sun, 04/26/2020 - 12:34 am

Problem 1004
Repeat Problem 1002 assuming that the reinforcement consists of aluminum plates for which the allowable stress is 80 MPa. Use n = 5.
 

1002-given-section.gif

 

Problem 1002 | Increase in moment capacity due to steel plate reinforcement Jhun Vert Sun, 04/26/2020 - 12:27 am

Problem 1002
A timber beam is reinforced with steel plates rigidly attached at the top and bottom as shown in Fig. P-1002. By what amount is moment increased by the reinforcement if n = 15 and the allowable stresses in the wood and steel are 8 MPa and 120 MPa, respectively?
 

1002-given-section.gif

 

Beams of Different Materials Jhun Vert Sun, 04/26/2020 - 12:22 am

From assumption no. (3) in the previous page: The strains of any two adjacent materials at their junction point are equal.
$\epsilon_s = \epsilon_w$

$\dfrac{f_{bs}}{E_s} = \dfrac{f_{bw}}{E_w}$

$\dfrac{f_{bs}}{f_{bw}} = \dfrac{E_s}{E_w}$
 

Chapter 10 - Reinforced Beams Jhun Vert Mon, 04/20/2020 - 11:57 am

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