Problem $1$: Cable Bridge Structure

$1.$ A wire rope bridge is being designed to span $110$ across a small $30$ deep ravine and

stream. Using graphic statics as in Chapter $2$ of Form and Forces, find the form of a

suspended rope for the bridge. Design for the following criteria:

$$ Shape the suspended cable $($wire rope$)$ for a maximum force of $32,000$ pounds on the

main span

$$ Two $25$ tall $6$ diameter steel masts support the suspended rope at each end

$$ One side of the ravine is $10$ higher than the other

$$ Hanger ropes support a $10$ wide bridge deck. The deck is made of heavy timber

planking spanning to cross members that are in turn supported by the hanger ropes.

$$ The total dead and live load of the bridge is $60$ pounds per square foot.

$$ Use a graphic scale of $1=20$ for the form diagram and $1=6000$ lbs for the force

polygon

$2.$ Using a scale of $1=20,000$ lbs$,$ find the force in the supporting backstay ropes after finding

the forces in the suspended cable, backstay and mast.

$3.$ Given an allowable stress on the wire rope of $60,000$ psi, how large of a diameter is required?

Round your answer up to the nearest $1/8.$

$4.$ Derive two more forms for the suspended wire rope $($cable$)$ using the same closing string as

in part $1,$ but locate the pole an arbitrary distance to the left and to the right of the first pole.

Draw these diagrams on the same load line as the first diagram, but use a different color for

each. Transfer those to the form diagram in the same color as used on the force polygon.

Answer the following questions:

$$ What conclusion can you arrive at regarding the forces in each suspended rope design?

$$ Which is design will have the lowest cable forces?

$$ What is the height above the deck at the lowest point of the cable sag for each design

case?

$$ What are the required sizes of the wire ropes for these forms, using the same allowable

stress values as the first design?

$$ Which design is most visually pleasing?

$5.$ Sketch a suggested detail for supporting the cables at the top of the mast, including labels

for materials and sizes of the primary components. Refer to details in Chapter $2$ of Form and

Forces for inspiration.