Buckling calculations for the legs, foot extender and crane shoulder corrected

recently went over some of my old calculations for the legs and realised i had used the wrong Euler formula for the crane shoulder legs and foot extender. Here are my corrected calculations.

P.S these calculations do not imply that any changes should be made to the crane, material or design wise. I simply wanted to correct my mistakes.

approximate prices for crane materials

Aluminium alloys
According to London Market Exchange figures on http://www.metalprices.com/ the averegae price of an alluminium alloy is 1 us dollar/ pound. Using this info and my estimates on the mass of the legs iv calculated that the approximte cost of the legs.

mass of both legs = 27.4 kg = 60.28 lb

cost = $60-$61 = £40

Carbon steel
The LME doesn't give a specific price for carbon steel (at least i couldn't find one) however its most recent price on steels in general was £350 per tonne. however http://www.meps.co.uk/ has a specific prices for carbon steels that are used to build beams but the prices are 4 months old. As meps gives a specified price i will use this to calculate the price of the boom.

mass of ub178 boom = 94.77 kg
cost of carbon steel = $691 per tonne
cost of boom = $65.5 = £42.55

The prices used are bulk purchase prices, individually the boom and the legs may cost more. Also these prices dont take into consideration the cost of manufacturing the boom and the legs.

Calculations for pins using the smallest and largest pins

Using the info mark published on hex bolts i decided to calculate the shear stress that would be experienced M12/ smallest bolt (largest stress) and the M36/ biggest bolt (smallest stress). I also calculated the stress on the leg pins by using the dimensions in mark's cad drawings. I found that the largest stress obtained was 92mpa when using the M12 bolts, which is not a problem as carbon steel generally has a shear stregnth of 42000psi = 289.5mpa.

( source: http://www.tpub.com/content/construction/14250/css/14250_14.htm)

Full calculations for legs (corrected)

references : http://www.matweb.com
http://www.roymech.co.uk/Useful_Tables/Tribology/co_of_frict.htm
ps. i have already estimated the masses of the legs (see older blog)

calculations for IPE 160 beam and legs

To find the stresses on each leg, I had to go over the calculations for the IPE160 beam using the dimensions sandy published. This also gave me a chance to check sandy's answers (they are all correct). The calculations show that the maximum amount of stress experienced by any part of the legs is 4.818mpa. The lowest compressive yield strength for an aluminium alloy that I have come across is 105mpa, therefore this comfirms that the vast majority aluminium alloys would be able to be used on the legs.Now its just a question of finding the most cost effective one.

My calculations for current boom (corrected)

in my final page i forgot to intergrate the step function. however the value of the deflection is unaffected due to the fact that i copied these calculations from my original rough notes, and in those i did intergrate the step function correctly.

List of alloys that can be used for legs / boom is too thick!!! - Jarrett D

LEGS
we have estimated that the maximum amount of stress any part of the legs are exposed to is around 8mpa. Although our calculations need to be refined it is unlikely that this value will not be greatly affected. Therefore i have put together a list of aluminium alloys that can be used.

alloy....................... ...compression yield stregnth (mpa)
Aluminum 2014-O .................................................185
Aluminum 2014-T4; 2014-T451 ............................425

Aluminum 2014-T6; 2014-T651 ...........................470

Aluminum 2048-T851 Plate .................................420

Aluminum 2618-T61.............................................370

Aluminum 5086-H112 ..........................................270

Aluminum 5086-H116; 5086-H32 .......................290

Aluminum 5086-H34 ..........................................325

Aluminum 5086-O ..............................................160

Aluminum 7039-T61 ..........................................390

Aluminum 7039-T64 ..........................................410

Aluminum 7178-T6; 7178-T651 ........................530

Aluminum 7178-T76; 7178-T7651 ...................460

Aluminum 7475-T7351 ...................................380

Aluminum A206.0-T7 Casting Alloy ..............372

Aluminum 206.0-T7 Casting Alloy ................372

Aluminum 208.0-F, Sand Cast .....................105

Aluminum 242.0-T21, Sand Cast ..................125

Aluminum 242.0-T571, Permanent Mold Cast .235

Aluminum 242.0-T571, Sand Cast ....................235

Aluminum 242.0-T61, Permanent Mold Cast ....305

Aluminum 242.0-T77, Sand Cast .....................165

Aluminum 295.0-T4, Sand Cast ......................115

Aluminum 295.0-T6, Sand Cast .....................170

Aluminum 295.0-T62, Sand Cast ...................235

Aluminum 296.0-T4, Cast ...............................140

Aluminum 296.0-T6, Permanent Mold Cast .180

Aluminum 296.0-T7, Cast ..............................140

Aluminum 319.0-F, Permanent Mold Cast .....130

Aluminum 319.0-F, Sand Cast ........................130

Aluminum 319.0-T6, Sand Cast ......................170

Aluminum 336.0-T551, Permanent Mold Cast 193

Aluminum 336.0-T65, Permanent Mold Cast ...296

Aluminum 354.0-T61, Permanent Mold Cast ....250

Aluminum 355.0-T71, Permanent Mold Cast .....215

Aluminum 355.0-T71, Sand Cast ........................205

Aluminum 355.0-T51, Permanent Mold Cast ....165

Aluminum 355.0-T51, Sand Cast .......................165

Aluminum 355.0-T61, Cast ................................215

Aluminum 355.0-T62, Permanent Mold Cast .....275

Aluminum 355.0-T6, Permanent Mold Cast ........185

Aluminum 355.0-T6, Sand Cast ..........................180

STEEL WIRE
I have calculted that if we use steel wire with a thickness of 1cm to lift the objects, it will be exposed to a maximum tension of 124.9 mpa. Therefore a medium carbon steel should be used to create the wire as it typically has a tensile strength much higher than this.

mass estimation of the legs and boom
using the dimensions given on the cad drawings i calculated a rough estimate of the mass of the crane legs and boom.

legs
given that all of the aforementioned alloys have a density between 2800 - 2650 kg/m^3

mass of the crane foot extender= 3.69-3.50kg
'' '' crane foot = 1.76- 1.67kg
'' ''crane leg = 3.25-3.08kg
'' ''crane shoulder = 5.00 - 4.74kg

Boom
when estimating the boom i came across something very worrying. i will show my calculations so someone can spot a mistake if i have made one.

density of carbon steel = 7800kg/m^3

cross sectional area of boom = (0.05x0.06)+2(0.02x0.07)= 5.8x10^-3 m^2
volume of boom = 5.1 x 5.8x10^-3 = 0.02958 m^3
mass of boom = 7800 x 0.02958 = 230.724 kg

here you can see that the boom is very heavy, therefore i suggest we make it thinner or shorter unless my calculations are wrong.

all facts and figures were obtained from http://www.matweb.com/

Aluminium Alloys - Jarrett D

During our last meeting we decided that an aluminium alloy could be used to create the legs of the crane. So I have done some research and found that there are two main categories of alloys, Wrought and cast. We will be using a cast alloy as it is stronger. However, as there are thousands of variations of cast aluminium alloys, I thought it best to find out the upper and lower strength limits of most cast aluminium alloys rather than to find these values for a specific alloy.

Facts on aluminium alloys
Tensile strength = 320-550 mpa
Yield strength = 250-450 Mpa
Density = 2626-2790 kg/m3
Young’s modulus = 70-74 Gpa

Advantages
· Aluminium alloys have a high strength to weight ratio so using them would make the crane easier to carry.
· Has a low fatigue limits which isn’t a problem as it fits the criteria of our crane perfectly.
· Excellent corrosion resistance

Disadvantages
· Has a lower tensile strength than steel so if a metal pipe (ie. The tripod legs) is to built out of an aluminium alloy. The diameter of the pipe would have to be larger then a pipe made out of steel to be able to deal with the same amount of stress.
· Cost is higher then that of steel.

Sources:
R.E. Sanders, Technology Innovation in aluminium Products, The Journal of The Minerals, 53(2):21–25, 2001.
Metals reference book(5th edn, Butterworths 1976)

Research on materials for the main frame of the crane - Jarrett D

I have found three materials that have the ideal properties to cope with the stresses and strains of a cranes function. the first of which is :

Carbon steel
Carbon steels are steels which contain only carbon as its main alloying ingredient. The amount of carbon ranges from 0.05% to 2% of the steels total wieght. This is a very important factor as generally the more carbon within the steel, the higher its stregnth (tensile and yield) and hardeness, the lower its ductility and harder it becomes to weld. For this reason we should consider using a medium steel containing around 0.5% to 0.6% carbon as this amount balances ductility with stregnth. some facts on general mediums steels are below:

medium steel facts
density = 7850 kg/m^3
tensile stregnth = 520 Mpa
yield stregnth = 350 Mpa
young's modulus = 208 Gpa

Advantages
Carbon steel can be used on parts of the crane where the stresses aren't particularly high (such as the crank arm or perhaps one of the tripod legs) and could even be used to create some of the rivets. doing this would save alot of money on cost.
Disadvantages
Although carbon steel is fairly strong, as far as steel goes it is relatively weak. its low tensile strength means that creating an entire crane out of the stuff would make the end product very heavy. Also as the steel includes no other alloyiong ingredients so its corrosion resistance isnt the best either, which means it may have to be painted to protect it.

T1 (AKA A514)/ High speed steel
High speed steels are steels that contain other alloying elements apart from carbon. they typically contain between 0.05% to 0.025% carbon along with other elements depending on the properties the material is required to have. Carbon steels that are required to be highly weather resistant will include elements such as nickel, silicon and phosphurus. Carbon steels reqiuered to be strong will include elements such as copper, titanium anad vanadium. However one high speed steel in particular is ABSOLUTLY ESSENTIAL to the construction of cranes, which is known as T1.

properties of T1
density = 7800 kg/M^3
tensile stregnth = 700 - 895 Mpa
yield stregnth = 620 - 690 Mpa
young's modulus = 205 Gpa

Advantages

• T1 has a high tensile stregnth therefore less material would have to be used as aposed to carbon steel, which would save weight. because of this fact T1 should be used on high stress components such as the boom, rivets and steel wire
• very good corrosion resistance when compared with carbon steels
• easliy welded and fairly ductile

Disadvantages

• Generally costs more than carbon steel

Titanium Alloys (grade 5)
Titanium alloys are split into 39 grades the most commonly used grade being grade 5, generally the higher the grade the better the alloy. Typically titanium alloys are used because of there extremely high strength to weight ratio however, they are also very hard which makes them great for creating cogs and gears with.

Grade 5 properties
Density = 4500kg/m^3
Tensile strength = 1000 Mpa
Yield strength = 880 Mpa
Young’s Modulus = 110 Gpa

Advantages

• 
  As the titanium alloys have a low density and high tensile and yield strength using this material would save a lot of weight.
• 
  High hardness which makes it ideal for moving parts where metal on metal friction occurs (pulley).
• 
  Alloys tend to include elements such as silicon, phosphorus etc which make the very corrosion resistant

Disadvantages
· Poor shear strength means this material cannot be used to make the rivets or screws
· Very expensive

sources:
metals references book 5th edn Butterworths, 1976
A.M. Howatson, P.G. Lund and J.D. Todd, "Engineering Tables and Data" p41
http://www.matbase.com/material/ferrous-metals/low-temperature-steel/a514-a/properties
http://asm.matweb.com/search/SpecificMaterial.asp?bassnum=MTP641http://www.efunda.com/materials/alloys/carbon_steels/show_carbon.cfm?ID=AISI_1040&prop=uts&Page_Title=Carbon%20Steel%20AISI%2010xx