Gondola Assignment.docx

Mechanics of Materials Lab LAB ASSIGNMENT

Muhammad Arslan 2017-ME-158 Department of Mechanical Engineering Section - D

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Contents 1- Introduction: ..................................................................................................................................................................... 3 2- Theory: ................................................................................................................................................................................ 3 2.1 History:................................................................................................................................................................................. 3 2.2 Cable Transport: ............................................................................................................................................................... 3 2.3 Cable Propelled Transit: ................................................................................................................................................ 3 2.3.1 Top Supported: ....................................................................................................................................................................... 3 2.3.2 Bottom Supported:................................................................................................................................................................ 4

2.4 2.5 2.6 2.7

Advantages of Cable Transport: ................................................................................................................................. 4 Disadvantages of Cable Transport: ........................................................................................................................... 4 Cable car: ............................................................................................................................................................................. 5 Types of Cable car: ........................................................................................................................................................... 5 2.7.1 Aerial Lift: ................................................................................................................................................................................. 6 2.7.2 Railway System: ..................................................................................................................................................................... 6

2.8 Construction: ..................................................................................................................................................................... 6 2.8.1 Mono-cable technology: ...................................................................................................................................................... 6 2.8.2 Bi-cable or tri-cable technology: ..................................................................................................................................... 7 2.8.3 Grips:........................................................................................................................................................................................... 7

2.9 Mechanism: ....................................................................................................................................................................... 8 2.10 Stress: ................................................................................................................................................................................. 8 2.11 Strain: ................................................................................................................................................................................. 9 2.12 Hooke’s Law: ................................................................................................................................................................... 9 2.13 Effect of Temperature: ..............................................................................................................................................10 2.13.1 2.13.2 2.13.3 2.13.4

Thermal Stress: ................................................................................................................................................................10 Thermal Strain: ................................................................................................................................................................10 Effect of increase in temperature:............................................................................................................................11 Effect of decrease in temperature:...........................................................................................................................11

3- Problem: .......................................................................................................................................................................... 12 3.1 Method of Analysis: .......................................................................................................................................................12 3.1.1 Condition of Equilibrium:...................................................................................................................................................12

3.2 3.3 3.4 3.5 3.6

Free Body Diagram:.......................................................................................................................................................13 Calculations: .....................................................................................................................................................................13 Statics at point B and C: ...............................................................................................................................................14 Stress in the cable: .........................................................................................................................................................14 Strains in the cable: .......................................................................................................................................................15

4- Simulation Using Solidworks: ................................................................................................................................. 15 4.1 Stress and Strain at point A:.......................................................................................................................................15 4.3 Stress and Strain at point C: .......................................................................................................................................17

5- List of Accidents: .......................................................................................................................................................... 18 6- Comments: ...................................................................................................................................................................... 18 7- References: ..................................................................................................................................................................... 18

Gondola Lift Find out stress and strain produced in the wire connected between two poles, carrying cable car with specified number of passengers in it.

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1- Introduction: Cable transportation is used for quick access to mountains equipped to ski slopes and connects the massive of mountains for tourist attraction. It also represents a means of travel and entertainment, having an important role in the development of mountain tourism, but also for winter tourism. Experiments remain present in the life of a cable transport installation and after its introduction into production, to check the stability of manufacturing technology, maintain quality and reliability, confirmed during certification. Any changes to a product in mass production involve a review and approval based on appropriate tests. [1]

2- Theory: 2.1 History: The first design of an aerial lift was by Croatian polymath Fausto Veranzio and the first operational aerial tram was built in 1644 by Adam Wiebe in Gdańsk. It was moved by horses and used to move soil over the river to build defences. It is called the first known cable lift in European history and precedes the invention of steel cables. It is not known how long this lift was used. In any case, it would be another 230 years before Germany would get the second cable lift, this newer version equipped with iron wire cable. Other miningsystems were developed in the 1860s by Hodgson, and Andrew Smith Hallidie. Hallidie went on to perfect a line of mining and people tramways after 1867 in California and Nevada. The first gondola built in the United States for a ski resort was located at the Wildcat Mountain Ski Area. It was a two-person gondola built in 1957 and serviced skiers until 1999. The lift was later demolished in 2004. The lift and its cabins were manufactured by a former Italian lift company: Carlevaro-Savio. One of the longest gondola rides in the world, Gondelbahn Grindelwald-Männlichen, is in the Bernese Oberlandin Switzerland and connects Grindelwald with Männlichen. [2]

2.2 Cable Transport: Cable transport is a broad class of transport modes that have cables. They transport passengers and goods, often in vehicles called cable cars. The cable may be driven or passive, and items may be moved by pulling, sliding, sailing, or by drives within the object being moved on cableways. The use of pulleys and balancing of loads moving up and down are common elements of cable transport. They are used in mountainous areas where cable haulage can overcome large differences in elevation. [3]

2.3 Cable Propelled Transit: Cable-Propelled Transit (CPT) is a transit technology that moves people in motor-less, engine-less vehicles that are propelled by a steel cable. There are two Cable Propelled Transit types: top supported and bottom supported. [4]

2.3.1 Top Supported: Top supported systems, also known as aerial cable systems, are supported from above via a cable (which may or may not be the same cable that propels the cabins — this varies by technology.) Aerial cable technologies include: i. Mono-cable detachable gondola ii. Bi-cable detachable gondola iii. Tri-cable detachable gondola iv. Aerial Tram v. Pulsed Gondola [4]

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2.3.2 Bottom

Figure 1 Top Supported [5]

Supported:

Bottom supported systems are supported by tracks or rails underneath, yet are still propelled by a cable. Bottom supported cable technologies include: i. Heritage Cable Car ii. Funicular iii. Hybrid Funicular iv. Cable Liner v. Mini Metro [4]

2.4 Advantages of

Figure 2 Bottom Supported [6]

Cable Transport:

Aerial Cable Transport have the following advantages compared with other transport modes: i. Independent transport relief and suitable for hilly areas ii. Powered by electricity iii. No CO2 emissions, if renewable energy is used for electricity iv. Significantly-reduced noise emissions v. No need of surfaces for transport [7]

2.5 Disadvantages of Cable Transport: Despite their good characteristics, aerial cable cars also have certain limitations: i. Limited Speed and capacity ii. Suitable only for distances up to 7 km and offers wind resistance iii. Extensive maintenance and controls iv. Difficult to rescue people from aerial cable cars 4

v. vi.

Expensive infrastructure No heating or air conditioning in cabins [7]

2.6 Cable car: A cable car is any of a variety of cable transportation systems relying on cables to pull vehicles along or lower them at a steady rate. The terminology also refers to the vehicles on these systems. The cable car vehicles are motor less and engineless and they are pulled by a cable that is rotated by a motor off-board. [8]

2.7 Types of Cable car: Following are the two types of cable car:

2.7.1 Aerial Lift: Aerial lift is further divided into two types: [9] 2.7.1.1 Aerial Tramway: An aerial tramway, sky tram, cable car, ropeway or aerial tram is a type of aerial lift which uses one or two stationary ropes for support while a third moving rope provides propulsion. With this form of lift, the grip of an aerial tramway cabin is fixed onto the propulsion rope and cannot be decoupled from it during operations. [9]

Figure 3 Aerial Tramway [10] 2.7.1.2 Gondola: Gondola lift is a means of cable transport and type of aerial lift which is supported and propelled by cables from above. It consists of a loop of steel cable that is strung between two stations, sometimes over intermediate supporting towers. The cable is driven by a bull wheel in a terminal, which is typically connected to an engine or electric motor. They are often considered continuous systems since they feature a haul rope which continuously moves and circulates around two terminal stations. [9]

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Figure 4 Gondola [11]

2.7.2 Railway System: A cable car is a type of cable railway used for mass transit where rail cars are hauled by a continuously moving cable running at a constant speed. Individual cars stop and start by releasing and gripping this cable as required. Varieties in which the vehicle rests on rails or a road:  A system to haul trains along streets, for example the San Francisco cable car system  A funicular is an isolated, passenger-carrying railway where the cars are permanently attached to a common cable.  A cable railway uses a cable or rope to haul trains. [9]

Figure 5 Railway System [12]

2.8 Construction: Technologies differ depending on the number of cables and their function.

2.8.1 Mono-cable technology: Mono cable technology is a term is used when a single cable is used to pull and support the cars. As apparent in the name, Mono-cable Detachable Gondolas uses a detachable grip. This means cabins can detach from the cable when in the station allowing for intermediary stations and turning. A Mono-cable Detachable Gondolas utilizes a single cable which provides both support and propulsion. Mono-cable Detachable Gondolas systems are generally supported by cylindrical towers, although custom towers or lattice structures are also possible. Mono-cable systems are generally supported by cylindrical towers, although custom towers or lattice structures are also possible. [13]

Figure 6 Mono-cable Gondola [14]

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2.8.2 Bi-cable or tri-cable technology: Bi-cable or tri-cable technology terms are used when one cable is used to pull the cars whilst one or two others support their weight. The Bi-cable Detachable Gondolas uses a detachable grip. This means cabins can detach from the cable when in the station. A Bi-cable Detachable Gondolas has two cables, one which provides support and a second which provides the system’s propulsion. Bi-cable Detachable Gondolas systems are generally supported by cylindrical towers. Cost is slightly higher than a Mono-cable Detachable Gondolas system. The Bi-cable technology still has a slight speed advantage over the Mono-cable technology. [15]

2.8.3 Grips: There are two types of grips used in the Figure 7 Bi-cable Gondola [16] construction of the gondola. 2.8.3.1 Non-Detachable Grips: A fixed grip is one that permanently connects a cable propelled transit vehicle to the cable. Because of this direct connection, stopping or slowing a fixed grip vehicle involves stopping or slowing the entire system. Aerial trams and pulsed gondolas both utilize fixed grip technologies. For an aerial tram, cabins are located at opposing ends of the cable so that vehicles dock at the end stations at the same time. Generally fixed grip systems can achieve greater speeds but have other limitations such as longer wait times and reduced capacities, as compared to detachable grip systems. [17]

2.8.3.2 Detachable Grips: Figure 8 Non-Detachable Grip [18] A detachable grip is one that can separate itself from the cable. The detachability allows a cabin to slow or stop within a station, without disrupting the flow of the entire system. Upon approaching a stop, a mechanism located at the station opens the grip and the vehicle is slowed by another mechanism. Passengers get on and off, the vehicle is re-accelerated to line speed, and while 7

departing the grip is re-engaged. This process is incredibly fluid, seamless and is virtually invisible to riders. Since the design of the grip allows it to only open under a constant, targeted, external and speciallydesigned force, a cabin with a detachable grip would never simply fall of the cable. [17]

Figure 9 Non-Detachable Grip [19]

2.9 Mechanism: An aerial tramway consists of one or two fixed cables called track cables, one loop of cable called a haulage rope, and two passenger cabins. The fixed cables provide support for the cabins while the haulage rope, by means of a grip, is solidly connected to the truck. An electric motor drives the haulage rope which provides propulsion. Aerial tramways are constructed as reversible systems; vehicles shuttling back and forth between two end terminals and propelled by a cable loop which stops and reverses direction when the cabins arrive at the end stations. The fixed ropes at the two sides and the haulage rope in the middle used for propulsion. Usually the cableway station at the end is enough to hold the weight of the cable cars, but sometimes the strain is too much that they have to transfer that strain to bollards. These bollards have rock anchors penetrating deep into the mountain to provide additional support. All the machinery including the electric motor which provides propulsion is housed in the lower station. Sometimes, Mono cable detachable gondola technology is used. This means that only one rope is used for both support and propulsion. This is used for short distances and for limited number of people. [20]

2.10 Stress: The term stress (s) is used to express the loading in terms of force applied to a certain cross-sectional area of an object. From the perspective of loading, stress is the applied force or system of forces that tends to deform a body. From the perspective of what is happening within a material, stress is the internal distribution of forces within a body that balance and react to the loads applied to it. The stress distribution may or may not be uniform, depending on the nature of the loading condition.

Example: A bar loaded in pure tension will essentially have a uniform tensile stress distribution. However, a bar loaded in bending will have a stress distribution that changes with distance perpendicular to the normal axis. The stress in an axially loaded bar is simply equal to the applied force divided by the bar's crosssectional area. [21]

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Figure 10 Stress [22]

2.11 Strain: Strain is the response of a system to an applied stress. When a material is loaded with a force, it produces a stress, which then causes a material to deform. Engineering strain is defined as the amount of deformation in the direction of the applied force divided by the initial length of the material. This results in a unitless number, although it is often left in the un simplified form, such as inches per inch or meters per meter. For example, the strain in a bar that is being stretched in tension is the amount of elongation or change in length divided by its original length. As in the case of stress, the strain distribution may or may not be uniform in a complex structural element, depending on the nature of the loading condition. [23]

Figure 11 Strain [24]

2.12 Hooke’s Law: It states that within the limit of elasticity, the stress induced (σ) in the solid due to some external force is always in proportion with the strain (ε). In other words, the force causing stress in a solid is directly proportional to the solid's deformation. The determination of elastic modulus E from the tensile experiment results is depicted in the figure.

𝛔∝𝛆 𝛔 = 𝐄𝛆 𝛔 𝐄= 𝛆 It can be seen from the graph that the curve of stress versus strain is linear within the limit of elasticity of the material. It is inferred that for the load below the limit of elasticity, the stress induced is in proportion with the strain in the solid. [25]

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2.13 Effect of

Figure 12 Hooke's Law [26]

Temperature:

Static and dynamic mechanical properties of concrete are affected by temperature effect in practice. Therefore, it is necessary to investigate the corresponding influence law and mechanism. Temperature effects on cube compressive strength, splitting tensile strength, prism compressive strength, modulus of elasticity, and frequency. [27]

2.13.1 Thermal Stress: Thermal stress is stress created by any change in temperature to a material. These stresses can lead to fracture or plastic deformation depending on the other variables of heating, which include material types and constraints. Temperature gradients, thermal expansion or contraction and thermal shocks are things that can lead to thermal stress. This type of stress is highly dependent on the thermal expansion coefficient which varies from material to material. In general, the larger the temperature change, the higher the level of stress that can occur. [28]

Figure 13 Thermal Stress [29]

2.13.2 Thermal Strain: Thermal Strain is the tendency of matter to change in shape, area, and volume in response to a change in temperature. Temperature is a monotonic function of the average molecular kinetic energy of a substance. When a substance is heated, the kinetic energy of its molecules increases. Thus, the molecules begin vibrating more and usually maintain a greater average separation. Materials which contract with increasing temperature are unusual; this effect is limited in size, and only occurs within limited temperature ranges. The relative expansion divided by the change in temperature is called the material's coefficient of thermal expansion and generally varies with temperature. [30]

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Figure 14 Thermal Strain [31]

2.13.3 Effect of increase in temperature: Consider that the initial temperature of the wire is 22℃. Let the temperature of the wire increases by 5℃. We can assume that there is no yield on the poles of the wire. The relation of final length of the wire will be: 𝒍𝒕 = 𝒍𝒐 (𝟏 + 𝜶𝒕) 𝑙𝑜 = Original length of the wire = 316m 𝑙𝑡 = Final length of the wire 𝑡 = Rise in temperature 𝛼 = Co-efficient of thermal expansion = 13 × 10−6 /℃ 𝐸 = 200 × 109 Pa Now, put values in the above equation; 𝑙𝑡 = 316(1 + 13 × 10−6 × 5) 𝑙𝑡 = 316.02054 𝑚 Change in length will be: 𝛿𝑙 = 𝑙𝑡 − 𝑙𝑜 𝛿𝑙 = 0.02054𝑚 Strain in the wire will be: 𝛿𝑙 𝑙 𝑒 = 0.000065 𝑒=

Stress in the wire can calculated using the formula:

𝝈 𝒆 𝜎 = 𝐸𝑒 𝜎 = 13 𝑀𝑝𝑎 𝑬=

2.13.4 Effect of decrease in temperature: Consider that the initial temperature of the wire is 22℃. Let the temperature of the wire increases by 4℃. We can assume that there is no yield on the poles of the wire. The relation of final length of the wire will be: 𝒍𝒕 = 𝒍𝒐 (𝟏 − 𝜶𝒕) 𝑙𝑜 = Original length of the wire = 316m 𝑙𝑡 = Final length of the wire 11

t = Rise in temperature 𝛼 = Co-efficient of thermal expansion = 13 × 10−6 /℃ 𝐸 = 200 × 109 Pa Now, put values in the above equation; 𝑙𝑡 = 316(1 − 13 × 10−6 × 5) 𝑙𝑡 = 315.983568 𝑚 Change in length will be: 𝛿𝑙 = 𝑙𝑜 − 𝑙𝑡 𝛿𝑙 = 0.01643𝑚 Strain in the wire will be: 𝛿𝑙 𝑙 𝑒 = 0.000052 𝑒=

Stress in the wire can calculated using the formula:

𝝈 𝒆 𝜎 = 𝐸𝑒 𝜎 = 10.4 𝑀𝑝𝑎 𝑬=

3- Problem: Two gondolas are hung between two poles A and B. The distance between support towers is 300m. The length of each cable segment under gondolas weighing WB = 7000 N and WC = 10000 N are DAB = 36.614 m, DBC = 218m and DCD = 61.4 m. The diameter of the cable is taken as 4cm. The cable sag at B is ∆B = 12m and that at C is ∆C = 22m. Find the stresses produced and also find the strain in the cables.

3.1 Method of Analysis: A particle is said to be in equilibrium if it remains at rest if originally at rest, or has a constant velocity if originally in motion. Most often, however, the term “equilibrium” or, more specifically, “static equilibrium” is used to describe an object at rest. To maintain equilibrium, it is necessary to satisfy Newton’s first law of motion, which requires the resultant force acting on a particle to be equal to zero. This condition may be stated mathematically as: ∑𝑭 = 𝟎

where F is the vector sum of all the forces acting on the particle. It is also a sufficient condition. This follows from Newton’s second law of motion, which can be written as ∑ 𝑭 = 𝒎𝒂 . Since the force system satisfies, then 𝒎𝒂 = 𝟎, and therefore the particle’s acceleration 𝒂 = 𝟎. Consequently, the particle indeed moves with constant velocity or remains at rest. [32]

3.1.1 Condition of Equilibrium: If a particle is subjected to a system of coplanar forces that lie in the x–y plane, then each force can be resolved into its i and j components. For equilibrium, these forces must sum to produce a zero-force resultant, i.e., ∑𝑭 = 𝟎

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∑ 𝑭𝒙 𝒊̂ + ∑ 𝑭𝒚 𝒋̂ = 𝟎

For this vector equation to be satisfied, the resultant force’s x and y components must both be equal to zero. Hence, ∑ 𝑭𝒙 = 𝟎 ∑ 𝑭𝒚 = 𝟎

These two equations can be solved for at most two unknowns, generally represented as angles and magnitudes of forces shown on the particle’s free-body diagram. When applying each of the two equations of equilibrium, we must account for the sense of direction of any component by using an algebraic sign which corresponds to the arrowhead direction of the component along the x-y axis. [32]

3.2 Free Body Diagram: “A drawing that shows the particle with all the forces that act on it is called a free-body diagram (FBD)”

L=300m m

3.3

Figure 15 Free Body Diagram [33]

Calculations:

The gondola is considered to be moving at a constant velocity. So, we should use the equations of equilibrium in order to solve this problem. But first we have to find the angles i.e. 𝜽𝟏 , 𝜽𝟐 and 𝜽𝟑 . The angle 𝜽𝟑 must be greater than 𝜽𝟏 and 𝜽𝟐 because the sag is greater in this portion due to more weight in this portion. First, we compute initial values of theta angles (Degree). For 𝜽𝟏 , we apply the sine rule;

∆𝑩 𝑫𝑨𝑩 ∆𝐵 𝜃1 = 𝑆𝑖𝑛−1 ( ) 𝐷𝐴𝐵 𝜃1 = 19.132𝑜 𝑺𝒊𝒏𝜽𝟏 =

Also, for 𝜽𝟐 we apply the sine rule;

∆𝑪 − ∆𝑩 𝑫𝑪𝑩 ∆ 𝐶 − ∆𝐵 𝜃2 = 𝑆𝑖𝑛−1 ( ) 𝐷𝐴𝐵 𝜃2 = 2.63𝑜 𝑺𝒊𝒏𝜽𝟐 =

And for 𝜽𝟑 , we apply the sine rule; 13

∆𝑪 𝑫𝑪𝑫 ∆𝐵 𝜃3 = 𝑆𝑖𝑛−1 ( ) 𝐷𝐴𝐵 𝜃3 = 20.998𝑜 𝑺𝒊𝒏𝜽𝟑 =

3.4 Statics at point B and C: Applying the equations of equilibrium at point B in the FBD. Summation of all forces on X-axis and summation of all forces will be equal to zero. ∑ 𝑭𝒙 = 𝟎

−𝑇𝐴𝐵 𝐶𝑜𝑠(𝜃1 ) + 𝑇𝐵𝐶 𝐶𝑜𝑠(𝜃2 ) = 0 ∑ 𝑭𝒚 = 𝟎

𝑇𝐴𝐵 𝑆𝑖𝑛(𝜃1 ) − 𝑇𝐵𝐶 𝑆𝑖𝑛(𝜃2 ) = 𝑊𝐵 Also, applying the equations of equilibrium at point C in the FBD. Summation of all forces on X-axis and summation of all forces will be equal to zero. ∑ 𝑭𝒙 = 𝟎

−𝑇𝐵𝐶 𝐶𝑜𝑠(𝜃2 ) + 𝑇𝐶𝐷 𝐶𝑜𝑠(𝜃3 ) = 0 ∑ 𝑭𝒚 = 𝟎

𝑇𝐵𝐶 𝑆𝑖𝑛(𝜃2 ) + 𝑇𝐶𝐷 𝑆𝑖𝑛(𝜃3 ) = 𝑊𝐶 Solving the above equations simultaneously, we get the values of 𝑇𝐴𝐵 , 𝑇𝐵𝐶 and 𝑇𝐶𝐷 . 𝑻𝑨𝑩 = 24619.2 𝑁 𝑻𝑩𝑪 = 23275.6 𝑁 𝑻𝑪𝑫 = 24927.32 𝑁 We can also check the equilibrium at point B and C by using the following equations. From this, we can verify our results and can also make sure that our system is in equilibrium. 𝑇𝐴𝐵 𝑆𝑖𝑛(𝜃1 ) − 𝑇𝐵𝐶 𝑆𝑖𝑛(𝜃2 ) = 7000 𝑁 𝑇𝐵𝐶 𝑆𝑖𝑛(𝜃2 ) + 𝑇𝐶𝐷 𝑆𝑖𝑛(𝜃3 ) = 10,000 𝑁

3.5 Stress in the cable: To find stresses in the cables, we have to divide the tension in the cables by the cross-sectional area of the wire used. The diameter of the wire used in this case is 4cm. So, the stress can be written as, 𝑇𝐴𝐵 = 19.6MPa 𝐴 𝑇𝐵𝐶 = = 18.52 MPa 𝐴 𝑇𝐶𝐷 = = 19.84 MPa 𝐴

𝜎𝐴𝐵 = 𝜎𝐵𝐶 𝜎𝐶𝐷

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3.6 Strains in the cable: Strain in the wire can be calculated in the wire using the formula of change in length. 𝜹𝒍 =

𝑻×𝑳 𝑨×𝑬

𝛿𝑙𝐴𝐵 = 3.6 𝑚𝑚 𝛿𝑙𝐵𝐶 = 20.2 𝑚𝑚 𝛿𝑙𝐶𝐷 = 6.1𝑚𝑚 So, strain in the cable of our gondola is as follows; 𝜹𝒍 𝒍 = 9.8 × 10−5 𝜺=

𝜺𝐴𝐵

𝜺𝐵𝐶 = 9.2 × 10−5 𝜺𝐶𝐷 = 9.9 × 10−5

4- Simulation Using Solidworks: When we perform the above problem on Solidworks, we get the following results:

4.1 Stress and Strain at point A:

Figure 16 Stress at point A

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Figure 17 Strain at point A

4.2 Stress and Strain at point B:

Figure 18 Stress at point B

Figure 19 Strain at point B

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4.3 Stress and Strain at point C:

Figure 20 Stress at point C

Figure 21 Strain at point C

4.4 Stress and Strain at point D:

Figure 22 Stress at point D

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Figure 23 Strain at point D

5- List of Accidents: 

 







The National Ski Areas Association reports 0.138 fatalities per 100 million miles transported compared to 1.23 for cars. October 22, 1979: One person was killed and 17 other injured when two gondolas fell from the "Swiss Sky Ride" at the Texas State Fair. Winds gusting to 40 miles per hour caused three cars to collide and two fell on midway games below the cable. January 29, 1983: The Singapore Cable Car disaster, which saw seven people killed when two cabins plunged into the sea after the cableway was hit by a Panamanian-registered oil rig being towed. September 5, 2005: Nine people died and ten were injured when a 750 kg concrete block was accidentally dropped by a construction helicopter in Sölden, Austria. Hundreds had to be evacuated from the lift. July 13, 2006: Five people, including a three-year-old girl, were injured after two cable cars collided and one crashed to the ground. The accident took place at the Nevis Range, near Fort William in northwest Scotland. There were no fatalities and the gondola was deemed safe for operation shortly after the accident. February 18, 2007: A gondola car derailed from the cable at Ski Apache in New Mexico and rolled backwards hitting another car. Eight people were involved in the crash but only two suffered minor injuries. March 2, 2008: A man fell out of a gondola in Chamonix and died, perhaps after he and one of his friends leaned on and broke the plexiglass window. [34]

6- Comments: The errors in the readings may be due to the following readings: i. The density of the cable may not be uniform throughout. ii. The temperature is not constant which may result in slight expansion of the cable. iii. The error may be due to frictional effects between wire and the gondola. iv. The cable might be less rigid and strong due to negligence of the manufacturer.

7- References: [1] http://aspeckt.unitbv.ro/jspui/bitstream/123456789/407/1/393%20-%20396%2C%20Hodirnau%201.pdf [2] https://en.wikipedia.org/wiki/Gondola_lift [3] https://en.wikipedia.org/wiki/Cable_transport 18

[4] http://gondolaproject.com/learn-the-basics-what-is-cable-propelled-transit/ [5] https://unofficialnetworks.com/2014/03/10/whos-ski-lift-world/ [6] https://liftblog.com/2016/07/14/leitner-poma-minimetro-debuts-at-miami-international-airport/ [7] https://pdfs.semanticscholar.org/1a2b/56222bad70bae34b669f57c5cef6ed6b999e.pdf [8] https://en.wikipedia.org/wiki/Cable_car [9] https://en.wikipedia.org/wiki/Aerial_lift [10] https://www.jacksonholewy.com/directory/jackson-hole-mountain-resort-aerial-tram/ [11] https://mpora.com/skiing/ski-lifts-explained [12] https://sf.curbed.com/2017/9/20/16338488/cable-cars-facts-sf [13] http://gondolaproject.com/mdg/ [14] https://www.skiarlberg.at/en/regions/flexenbahn [15] http://gondolaproject.com/bdg/ [16] https://www.doppelmayr.com/en/products/3s-gondola-lift/ [17] http://gondolaproject.com/grips/ [18] https://www.leitner-ropeways.com/en/products/fixed-grip-chairlifts-26/ [19] https://www.indiamart.com/proddetail/detachable-grip-ropeway-9237791130.html [20] https://www.tititudorancea.com/z/aerial_tramway_69.htm [21] https://www.nde-ed.org/EducationResources/CommunityCollege/Materials/Mechanical/StressStrain.htm [22] https://www.nde-ed.org/EducationResources/CommunityCollege/Materials/Mechanical/StressStrain.htm [23] https://www.nde-ed.org/EducationResources/CommunityCollege/Materials/Mechanical/StressStrain.htm [24] https://www.nde-ed.org/EducationResources/CommunityCollege/Materials/Mechanical/StressStrain.htm [25] https://www.chegg.com/homework-help/definitions/hookes-law-5 [26] https://www.chegg.com/homework-help/definitions/hookes-law-5 [27] https://www.hindawi.com/journals/amse/2014/191360/ [28] https://en.wikipedia.org/wiki/Thermal_stress [29] https://www.comsol.com/multiphysics/thermal-expansion-and-thermal-stresses [30] https://en.wikipedia.org/wiki/Thermal_expansion [31] http://emweb.unl.edu/NEGAHBAN/Em325/05-Thermal-strain/Thermal%20strain.htm [32] Engineering Mechanics Statics 10th Edition (Tenth Edition) by R.C. Hibbeler [33] Mechanics of Materials (8th Edition) James M. Gere, Barry J. Goodno [34] https://en.wikipedia.org/wiki/Gondola_lift

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