Impasse on Edge


Engineers often run into challenges that seem like an impasse. Observe Peggy and Alex as they work through a sensitive problem.

“No, you can’t lay them flat on top of each other because the coating will get damaged,” Alex insisted.

“But you can’t stand them on end because they’ll buckle,” Peggy countered. “Look.” Peggy grabbed a sheet of white paper from the conference room printer, an eight and a half by eleven inch sheet, pinched two corners along the short edge, stood it vertically on the conference table, and let go of it. It of course immediately buckled and fell on the table sliding on air toward Alex. Peggy held her hands to her sides, palms up and looked intently at Alex.

Alex responded, “I can’t believe you would trivialize the physics like that. I’m very aware that you can’t make a thin flat sheet stand on edge.”

“But with your requirements,” Peggy said, “we’ll be forced to transport the sheets one at a time, and that’s ridiculous.”

Alex, a bald, six foot tall senior materials engineer wearing his Friday baseball cap, and Peggy, a brunette, almost six foot tall lead chief mechanical engineer seemed at an impasse, struggling to design a special pallet to transport thin valuable proprietary sheets from the chemical processing plant to the assembly building.

“There must be a compromise,” Alex repeated, then looked around the room. “Grab the paper tray out of the printer.”

“What for?”

“Just grab the tray. It’s my turn to try something.”

The two inch deep tray was about half full. He laid the tray flat on the table then slowly lifted one end of the tray while the far end remained on the table. He raised it slowly until the stack of paper was near vertical. At about 80 degrees from the horizontal, the outer most sheet buckled and slipped from the tray. Before the next sheet fell, Alex quickly lowered the tray.

“What are you trying to prove,” Peggy asked.

“I’m just experimenting.” Alex thought deeply while he played with the tray. It’s not physical contact that causes one sheet to damage the other, it’s the weight of the stack that is the problem. This is very sensitive film on an ultra-thin substrate.”

Peggy gave a puzzled look.

“Trust me. The coating is very fragile. If we could have the stack near vertical without causing buckling, then perhaps the pressure between sheets might be small enough to avoid damage.”

“As I recall from civil engineering classes,” Peggy said, “column buckling critical load (Pc) is a function of material (E) and geometric properties (I), and weight, thickness, width, and length (L)?” These are the factors we would consider if this were a structural column problem. But this is a thin sheet problem. Do you think the same factors apply?”

Pc = ((π^2EL)/(KL^2))

“Perhaps, but I expect the structural buckling equations have some small deflection assumptions. You’re the mechanical engineer; you should know.”

“Can we try this tray experiment with the actual proprietary sheets instead of paper?” Peggy said.

“No way. Too expensive.”

Alex lifted his cap and scratched his head. “You’ll have to check the literature on thin film buckling equations.”

“I think it might be called thin cylindrical shell theory.”

“Ah, you were paying attention in mechanics of materials class,” Alex said. “Unfortunately, at about 80 degrees I think there will still be too much weight on the sheet at the bottom of the stack. We would need to get near 85 degrees or higher…”

“But we’ve already seen that the sheets fall out at 85.”

The room fell silent for a minute.

“Wait.” Peggy looked at the rigid visor on her colleagues baseball cap. The rounded brim cast a shadow across Alex’s nose. “What if we curved the stack of papers?”

This time Alex looked up, puzzled.

“Like the front of your hat.” Peggy looked around the room. She removed the paper stack from the tray, grabbed two white board dry erase marker pens and laid them inside the tray along the long edges. She then replaced the stack of paper on top of the pens such that the stack now sat in the tray with an arch, concave upward.

Alex took his hat off. “Good thinking Peggy.”

“Now lift it,” Peggy said holding both hands over the tray, palms down. “Slowly.”

Alex carefully raised the end of the tray upward past 80, past 85, and then to vertical. After a few seconds at 90 degrees, the outer sheet finally buckled and fell from the tray.

“That’s it,” Alex said. “I think this can be made to work. We can probably use an arched tray at about 85 to 87 degrees. Each sheet will stand nearly on its own with very little weight being applied to the lower sheets.”

“I’ll get a prototype going right away,” Peggy said.

“Just to be safe, you should also look into thin film buckling theory,” Alex added. “I will analyze the theoretical pressure between the arched sheets.”

Peggy put the tray back into the printer and they both left the room. She forgot to remove the pens.

Mentor Questions

Engineers often run into challenges that seem like an impasse. Further discussion, research, and experimentation opens up new ways of thinking. Did Peggy and Alex see eye to eye at first? Did they buckle under pressure? Both engineers had valid arguments regarding weight, damage, and the stackable nature of the sheets.  By studying the problem they found new solutions. Was it a mistake to draw conclusions using familiar column buckling theory when what they needed was thin film theory? Maybe, but it was enough to move forward to the next level while studying the correct theory. Name several ways in which they found solutions in familiar objects around them.

#engineerclips

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