You are an engineering consultant hired to verify an elevatordesign. The elevator mass is 500kg and has a maximum occupantcapacity of 800kg. Carbon steel cables with total cross sectionalarea of 64cm2 support the elevator. The maximum speed of theelevator is 2 meters per second. At the maximum speed, each cableextends at least 4 meters and cannot extend more than 22 meters,unstretched. When the car is not moving and the cables are extendedby 22 meters of (unstretched) cable, there is 3 meters of clearancebetween the bottom of the elevator and the concrete floor of theshaft.
Carbon Steel Cable:
Young’s Modulus: 207 GPa
Yield Strength:Ă‚Â Ă‚Â Ă‚Â Ă‚Â Ă‚Â 131 MPa
Ultimate Strength: 290 Mpa
Requirements for the elevator include a factor of safety of 3for cable failure and the occupants must not ever experience morethan 5 times the acceleration of gravity.
Make a sketch of theproblem.
Answer the following questions:
1.If the elevator is moving at maximum speed and the motorsuddenly stops, what is the worst case for cable failure?
2.What is the value of the worst case stress in the cable(MPa)?
3.The design meets the cable failure factor of safetyrequirement. (T/F)
4.If the elevator is moving at maximum speed and the motorsuddenly stops, what is the worst case for occupantacceleration?
5.Describe at least one change to improve the design. Explainhow your suggestion would improve performance relative to therequirements.
