Question $1(20$ marks$)$

A simply supported timber beam with a span of L$=4$m is used to support a uniformly

distributed load $($Figure Q$1($a$)).$ The beam consists of a square section with the width

of $150$ mm $($Figure Q$1($b$)).$ The timber material has the Young's modulus of E$\_($w$)=11$

GPa $,$ and the allowable bending stresses are $[\backslash$sigma $\_($t$)]=8$MPa for tension and $[\backslash$sigma $\_($c$)]=12$MPa

for compression.

$($a$)$ Determine the maximum uniformly distributed load q$\_($max$)$ that this timber beam

can carry.

$(6$ marks$)$

$($b$)$ It is proposed to strengthen the beam by bolting one steel plate to the timber

beam. The thickness of the steel plates is t$=10$mm$.$ The Young's modulus of

steel is E$\_($s$)=200$GPa and the allowable bending stress of steel is $[\backslash$sigma $\_($s$)]=140$MPa

for both tension and compression. The strengthening scheme as shown in Figure

Q$1($c$)$ is proposed to strengthen the beam. Determine the maximum load

capacity q$\_($max$)$ after strengthening.

$(14$ marks$)$

$($a$)$

$($b$)$

$($c$)$

Figure Q$1$