$6\mathrm{.}3$ and $6\mathrm{.}4$ Crews are preparing to perform maintenance on

the roof of a covered walkway. The maintenance contractor

wants to stack supplies on the outer edges of the roof, but

the owner is concerned about overloading the structure.

Our team leader would like us to explore two op$-$

tions for stacking the supplies. The contractor would like

to stack the supplies on the outer edges of the roof be$-$

cause it is easier to put them there; this option would result

in a distributed load of $350$ plf from the supports to the

outer edges. The other option is to distribute the same total

weight of supplies between the supports of the beam; this

option would result in a distributed load of $150$ plf between

the supports. Influence lines will help us in the evaluation.

To promote drainage, the roof drops $1$ foot over its en$-$

tire length. Because the live load does not act normal to the

support beam, it will be easier to construct the influence

lines using the Table$-$of$-$Points Method.

$6\mathrm{.}3$ One of our concerns is the possibility that the loading

will cause uplift at support $D$ that exceeds the connection

design strength.

a$.$ Guess where to put the distributed load to generate the

largest uplift at support $D.$

b$.$ Develop the influence line for the vertical reaction at $D.$

c$.$ Determine the largest uplift that can be generated at

support $D$ by a distributed live load of $350$ plf$.$ This live

load can be placed on either or both ends of the beam.

d$.$ Determine the largest uplift that can be generated at

support $D$ by a distributed live load of $150$ plf$.$ This live

load can only be placed between the supports, $B$ to $D.$

e$.$ Determine the vertical reaction generated at support $D$

by the self$-$weight of $15$ plf $.$

f$.$ Which live load situation generates the largest uplift at

support $D?$ When combined with the self$-$weight effect,

is there still uplift? If so$,$ the team will need to verify that

the connection is sufficiently strong.

g$.$ Comment on why your guess in part $($a$)$ was or was not

the same as what you discovered in part $($f$).$

$6\mathrm{.}4$ Another of our concerns is exceeding the bending ca$-$

pacity of the beam. The critical location will be midspan, $C.$

Because of the material choice and the way the roof is

constructed, the capacity of the beam is the same for both

positive and negative moments.

a$.$ Guess whether the largest midspan moment generated

by the roofing materials will be positive or negative.

b$.$ Develop the influence line for the moment at midspan

of the support beam, point $C.$

c$.$ Determine the midspan moment generated by a distrib$-$

uted live load on both outer ends of $350$ plf$.$

d$.$ Determine the midspan moment generated by a distrib$-$

uted live load between the supports of $150$ plf$.$

e$.$ Which situation generates the largest midspan moment?

We should encourage the maintenance contractor to place

supplies at the location that generates the smallest moment.

f$.$ Comment on why your guess in part $($a$)$ was or was not

the same as what you discovered in part $($e$).$