Ethical Issues in This Case
1) Should Buchanan give approval to the modified Lakewood design?
Numerical Problems
Numerical Problem #1:
Using the AISC LRFD code specifications applicable to crane rails, determine the design loads to which the rails could be subjected, and determine if the beam is acceptable by AISC standards. The beams were W6x12 made of A588 steel, and you may make worst case assumptions about direction and location of loading.
Numerical Problem #2:
Calculate the required lateral deflection of the wide flange assuming that the operator was traveling as slowly as would be required to just barely cause the wheels to slip off of the lower flange. Walk this speed. Would you consider this design safe to use?
Numerical Problem #3:
Using energy methods, determine a lower bound on how fast the crane must have been moving to just barely cause the wheels to slip off. Would you consider this design safe to use?
Numerical Problem #4:
Calculate the expected lateral deflection of the wide flange assuming that the wheels did indeed slip off of the lower flange, and that the operator was negligently running with the crane, and failed to stop it before crashing into the end stops. Note that no permanent plastic deformation of the crane rails was noted after the accident.
Numerical Problem #5:
Using energy methods, determine an upper bound on how fast the crane might have been moving when the wheels slipped off. Does this change your opinion of the safety of the design? Do you feel that it might have been possible that the operator could have caused his own problems by moving too fast with the crane and running into the stops?
Numerical Problem #6:
Shown in figure 3 is a set of calculations provided by Buchanan which they feel proves the original Lakewood design to be inadequate. What is in error about these calculations? Why might using these calculations in court let Lakewood off the hook as regards their liability?
Numerical Problem #7:
Against Buchanan stated safety procedures, and in direct violation of safety stickers on the crane and listed in the user's manual, the load was transported fully raised, above the operator's head, rather than having been lowered close to the floor immediately after removal from the shelf. Did this operator behavior contribute in any way to the accident and/or to the employee's injuries? Note that the employee was not struck by the falling die, which was on the other side of the crane when it fell.
Numerical (Design) Problem #8:
a) What mechanical measures might you add to the HI-Stak unit to prevent similar future accidents? (i.e., wheels slipping off flanges). Do you feel that the added expense would be worth while? Should Lakewood voluntarily track down and retrofit the hundreds of existing cranes they have sold, realizing that this is the first accident noted since their introduction in 1986?
(b) What electronic interlock controls might you add to the crane operating controls to prevent the circumstances that contributed to the accident?
Put the longitudinal tracks on front of shelves, thereby shortening the lateral girders.
Safety hooks.
larger beams.
reinforce existing beams.
Numerical Problem #9:
How fast could a worker travel with the crane and hit the stops if beam safety hooks are used? Assume that both beams will be pulled into complete plastic deformation for this problem. Would you consider this a safe speed? Would you consider the design safe under these conditions?
Numerical (Design) Problem #10:
Redesign the wide flange such that there will be no overstress under normal loading, assuming that safety devices have been installed to prevent lateral disengagement of the wheels under lateral impact loading.
Interlake's Side of the Story
Against all safety precautions, Mr. Michaels was transporting the load at full height above the floor, thus directly causing this accident. This is in direct violation of the safety regulations of Buchanan, as well as the safety stickers prominently displayed on the crane, and in the user's manual. Further, Mr. Michaels took the required safety classes in use of the equipment, where this requirement was emphasized. Loads are never to be transported high, but rather must be lowered to the floor immediately after retrieval from the storage shelves. We contend that this negligence was the full and complete cause of this accident, for the following reasons:
a) Carrying the load level with the upper support beams would directly transmit tremendous impact loads to those beams, should the operator negligently fail to stop the crane and crash it into the stops. Our tests show that if the loads are transported close to the ground, the crane merely swings up, reducing the impact loading at the top of the crane to very low levels, greatly reducing the possibility that the wheels might disengage.
b) We admit that should someone crash the crane into the stops, they might actually cause the wheels to come out of the tracks on the back side of the crane. However, should this happen with the load low, the load will merely rotate the crane about 5 degrees, until the pallet is directly under the engaged wheels, or until the load touches the concrete floor. In either case, the rotation of the crane is slight, and rather than propelling the operator across the room, he will probably not even be touched by the crane.
However, should the wheels disengage with the load high, the load will rotate the crane 40 to 50 degrees before falling off of the forks. Just like a golf ball, the operator's negligence might cause him to be struck and injured by the rotating crane.
c) Although we have no way of knowing how fast Mr. Michaels ran the crane into the stops, it is apparent to us that it must have been at a significant speed. Statements by Mr. Michaels' co-workers that he has caused several other accidents through carelessness, and "hot-dogging" through the plant confirm this behavior. Further, the fact several hundred cranes identical to this model have been in operation for 8 years throughout the country demonstrates that the design is safe and reliable.
d) We have reviewed the calculations made by Buchanan concerning the minimum velocity necessary to disengage the wheels, and would like to point out that this would indeed be a minimum, and has no bearing on how fast Mr. Michaels was actually running at the time of the accident. We would also like to note that although our calculations at this time do appear to show a slight overload condition for the crane when operated at its rated load of 2000 pounds, the 1460 pound load carried by Mr. Michaels would not overstress the crane, according to AISC specifications.
Buchanan's Side of the Story
Buchanan Calculations Showing Beam To Be Poorly Designed
Calculations for wheel loading:
The maximum loading on the W6x12 beam is realized when the pallet and die are rotated directly over one of the carriage wheels, as shown above.
The die and pallet live load rating is 2000 pounds, and can be up to 29 inches from the center of rotation of the crane. The dead load of the crane itself is 1875 pounds, and is located at the point of rotation of the crane. Using AISC-LRFD design procedures, the factored live load, including a 10% allowance for impact (Section A-4.1 and A-4.2) is
Plive = 2000# * 1.6 * 1.1 = 3520#
The factored dead load = Pdead = 1875# * 1.2 = 2250# (no impact needed)
First, assume that the live die load is applied at the center of rotation. Then the live load on each wheel due to central die load = 3520# / 4 wheels = 880#
Since the die load is actually off center, it causes a moment about line A-A:
Moment about line A-A = 3520# * 29" = 102.080 in lbs, which must be resisted by wheels b and d. Since these wheels are on the hypotenuse of a triangle, they are [(41/2)^2+(37/2)^2]^0.5 = 26.6 inches from the center of the crane.
Summing moments about wheel line A-A, to determine load on wheel "b":
Sum moments about line A-A = 0 = 3520# * 29" - wheel b load * 27.6" - wheel d load * 27.6"
Assuming wheels b and d have the same load due to symmetry, Live load on wheel b = 1850#. The load
Calculations for equivalent beam loading:
P2 is the maximum calculated wheel load, which is 1" off center. PL is the equivalent lateral load which gives the same torsional twist to the beam as did P2, when P2 is moved to a direct shear position. This lateral load causes significant bending about the weak axis of the beam, as shown in the calculations below.
