$(20$ points$)$ A wooden joist $($AB$)$ spans $6m$ and supports a uniformly$-$distributed load of $3k\frac{N}{m}($includes

allowance for self$-$weight$)$ and a point load of $7kN.$ Assume that the joist support conditions are a

pin at A and a roller at $B($i$.$e$.,$ simply$-$supported$).$

The joist $($AB$)$ is to be designed as a built$-$up member consisting of several boards $($each board is

$38mm$ wide $292mm$ deep$)$ placed side$-$by$-$side as shown below.

$($a$)$ Draw a free$-$body diagram, and construct the shear force and bending moment diagrams for joist $AB$

using the relationships between applied load, shear force and bending moment. Clearly label the

diagrams to indicate the magnitude of $V$ and $M$ at discontinuities, maximums, etc. Indicate which

portions of the plots are parabolic, cubic or higher degree functions $($where applicable$).$

$($b$)$ Determine the required number of boards to be placed side$-$by$-$side to make the built$-$up section based

on the design criteria given below. The boards are to be oriented vertically, as shown in the figure,

such that the built$-$up section is $292mm$ deep. Use the attached beam tables for deflection

calculations. Assume $E_{\text{w}\text{o}\text{o}\text{d}}=12,400$MPa.

Elevation View