Question $9$: The simply$-$supported glulam beam shown in figure $Q9$ is subjected to a characteristic,

permanent load, $P_{G,k},$ at mid$-$span $(P_{G,k}=300kN).$

The properties of the beam are:

The beam is located in Service Class $1.$

$b=200mm,$

Strength class: $Gl24c,$ hence $E_{msen}=11,000\frac{N}{m}{m}^2,G_{\text{m}\text{a}\text{g}\text{a}}=650\frac{N}{m}{m}^2,f_{ksk}=3\mathrm{.}5\frac{N}{m}{m}^2.$

Plasterboard ceiling to underside, hence deflection limit L$/250.$

There is no load$-$sharing, as this is a single beam.

Figure $9$ side elevation of beam, dimensions in $mm$

Determine the instantaneous bending deflection of the beam under the permanent load,

this calculation do not include shear deflections$).$

Answer: Uinst $G=8\mathrm{.}32mm$

Question $10$: Recalculate the instantaneous deflection of the beam in Question $9$ under the permanent

load, $u_{\text{i}\text{n}\text{s}\text{t}\text{G}},$ but this time include the shear deflections. The equation to calculate the shear deflection

of a simply supported beam subject to a point$-$load at midspan is provided below.

$u_{\text{s}\text{h}\text{e}\text{a}\text{r}}=\frac{1\mathrm{.}2Pl}{4G_{\text{m}\text{e}\text{a}\text{n}}A}$

Where:

p is the point load

l is the spn of the beam

Gmean is the shear modulus

A is the cross$-$section area of the beam

answer: uinst, G$=12\mathrm{.}65$mm