Figure $1.$ Cables $($yellow lines$)$ supporting the entrance

Figure $2.$ Simplified model of the canopy. roof cover system at Stauffer Library.

Cables support the entrance roof at Stauffer Library as shown in Figure $1.$ A simplified model of the canopy is given in Figure $2$ where the cable has been replaced with a force, $F_B,$ that acts through a point $2\mathrm{.}5m$ above the canopy. The canopy can be at any angle, $.$

The analysis below is to be completed using the simplified model in Figure $2.$ For simplicity assume that the roof is pinned at point A $($see Figure $2).$ Figure $2$ also shows additional dimensions of the roof. The roof is $3m$ in length between points A and $C($labelled as length $"$a$").$ The cable force, $F_B,$ acts at point B$,$ which is located at distance $"c"$ from point $C.$

The roof has a load from the self$-$weight of the structure, $T,$ that acts at point $D,$ which is located at distance $"$b$"$ from point A$.$ Snow can accumulate on the roof to a thickness of $0\mathrm{.}3m,$ resulting in a uniformly distributed load $($UDL$),$ w$,$ applied between points A and $C.$ The snow has a density of $990k\frac{g}{m^3}.$

Note: mass of snow $=$ density of snow $*$ thickness of snow $*$ width of roof section

In your tutorial group complete the following and have the TA mark your work during the tutorial and record your work on onQ. Apply a sign convention that forces acting up and to the right are positive and clockwise moments are positive. Complete your calculations for a $1m$ width section of the roof.

Question $2(1$ point$)$

Note that each question will have different values of the force, $T,$ the density of snow, the thickness of snow, and the distance, c$.$

For T of $3kN,$ density of snow of $980k\frac{g}{m}3,$ thickness of snow of $0\mathrm{.}2m$ and distance $c$ of $0\mathrm{.}2m,$ calculate the vertical component of the force in the cable, $F_B.$

Your Answer:

Answer

Question $3(1$ point$)$

Note that each question will have different values of the force, $T,$ the density of snow, the thickness of snow, and the distance, c$.$

For T of $2kN,$ density of snow of $980k\frac{g}{m}3,$ thickness of snow of $0\mathrm{.}2m,$ and distance $c$ of $0\mathrm{.}4m,$ calculate the vertical reaction at $A.$

Your Answer:

Answer

Question $4(1$ point$)$

Note that each question will have different values of the force, $T,$ the density of snow, and the distance, c$.$

For a force in the cable $F_B$ of $6kN$ and distance $c$ of $0\mathrm{.}2m,$ calculate the horizontal reaction at $A.$

Your Answer: