Bendgate, so much controversy. What started as a few complaints with pictures about the new iPhone 6+ bending while in people’s pockets has turned into a certified internet frenzy. There are videos of people bending the iPhone 6+ with their hands. Countless blogs and news pieces have been written on the subject. Consumer reports did their own test to see if there was any truth to this complaint. Even Apple quickly weighed in to assure consumers that the iPhone 6 bending is not a serious issue. Yes, I know you are asking yourself what more can be written on the subject, and maybe more importantly how much more can I read about this before my brain cells get bent? Well, I am a licensed structural engineer with an advanced degree in the field. I often design and specify materials and members to resist given forces including bending. I’ve read a lot posts and listened to a number of podcasts that address bendgate. There seem to be lingering technical questions and misunderstandings regarding materials and forces (in particular “bending”). I do not intend to resolve all issues but I hope to answer a few technical questions.
Jim I’m an engineer not a lawyer
As a disclaimer I own many Apple products and could be considered an Apple fan. In my free time I develop a number of iOS apps, including a tool for structural engineers that coincidentally aids in performing bending calculations. I do not own an iPhone 6 or 6 Plus, so my assumptions regarding the dimensions and specifications of the device are based on information found online and not from first hand testing.
Bending, broken or deformed?
When stressed, an object changes shape. This deformation can be classified as elastic or inelastic (plastic). After the stress is removed if the object returns to its original shape then the deformation was elastic. If it does not return to its original shape it has deformed plastically. In both cases it is not “broken” i.e. the material is still together. All materials are different in how much stress they can tolerate before they begin to deform permanently (plastic). For some materials it takes very little stress to cause plastic deformation (think rubber band), and for others it takes little stress to cause plastic deformation (think play dough).
Aluminum, plastic or how I learned to stop worrying and love titanium
A lot has been said about how the iPhone is aluminum and aluminum is “soft” and easier to “bend” than plastic. I don’t want to get into the details of Young’s Modulus, Yield Strength and Ultimate Strength here, but in the tradition of Jim Dalrymple let me respond with one word, wrong. I’m assuming the aluminum used in the iPhone is comparable to the 6061 alloy. If you replaced all the iPhone 6’s aluminum parts with plastic parts, not only would it be easier to bend, it would reach plastic deformation with less stress and it would take less stress to break it. Precisely because aluminum is stronger, the engineer’s that designed the iPhone were able to reduce the amount / thickness of material used. I’d be surprised if any “Plastic” phone as thin as the iPhone only used plastic materials to resist bending.
It’s the shape stupid
On to the crux of the issue, the shape. First I must apologize now if I’ve been too technical in this post. I have done my best to keep it simple but out of necessity in describing the issues at play and stoking my ego, I’m about to drop some “letter” math on you. Not only does the material (steel, plastic, aluminum, etc…) of an object affect its ability to resist bending, the cross section shape of the object does as well. We can say as the phone gets thinner its ability to resist bending without deformation is reduced, but by how much? A cross section of a member has a property called “moment of inertia”, or “MI” as I will call it. The MI of a shape describes the shapes ability to resist rotation (bending). The greater the MI is the more force is required to change the members rotation rate. We can calculate the MI of any cross section shape and compare the results to other cross sections to get an idea of bending resistance. For a simple rectangle the MI can be calculated with:
MI = B*H^3 / 12
Where, B = width H = height (thickness)
We can see that as we decrease the width of a rectangle its ability to resist bending only decreases linearly, but if we decrease the height (thickness) of the rectangle because H is cubed the ability to resist bending is decreased more dramatically. To illustrate a point I’ve compiled a table of various smart phones cross sectional properties. If we assume full thickness of the phone is used but only 5% of the width of the phone is used to resist bending you can get an idea what making your phone thinner will do to its ability to resist bending.
|Phone||Thickness (in)||Width (in)||MI (in^4)||Relative|
|iPhone 6 Plus||0.28||3.06||0.00028||1.29|
|Samsung Galaxy Note 4||0.33||3.09||0.000463||2.14|
|Samsung Galaxy Note 3||0.33||3.12||0.000467||2.16|
|HTC One (M8)||0.37||2.78||0.000587||2.71|
|Moto X (2014)||0.39||2.85||0.000704||3.25|
So we can see thinner phones = inherently less ability to resist bending. As a phone design becomes thinner the engineers will have to come up with additional ways to provide stiffness. That brings me to some pictures and comments I read on imgur here. While I agree with much that was written in that post I have one major disagreement with this picture: The metal insert they talk about is not there to reinforce the phone’s frame. It is there to provide a rigid surface for the volume buttons to push against. To pass bending moment from the frame and into the metal insert you would need 2 sets of screws each side of the metal insert. As it is now the author (alleras4), of the piece is correct that the insert does not reinforce the reduced section of the phone frame at the volume cutouts, but it was never intended to.
How much load is a butt load of load?
So how much bending force should a phone be expected to resist? How much force is generated in hipster jeans under a giant tush? I don’t know the answers to these questions. I do know that as a phone gets longer in length there is the potential to generate more bending moment with the same amount of applied force. The equation used to find the max bending moment (BM) in a simple beam with a single load applied to its center span is:
BM = P * L / 4
Where, P = single point of force L = span between supports
So as the span gets longer (length of phone) the same amount of force will increase the bending moment linearly. This explains why it appears the iPhone 6 Plus is easier to bend even though it is slightly thicker than the iPhone 6.
TL;DR but at least it got its own browser tab for a day
To wrap it up, thinner phones = easier to bend. Based on the required force shown in the original video that kicked off bendgate, and based on Consumer Reports tests,I think it’s safe to say its unlikely you will bend your phone with typical use. I would guess most phones that get bent do so during a dynamic event. Even though I am a structural engineer and not a mechanical engineer I know enough about dynamics to know it doesn’t take much to generate dynamic forces much greater than typical static forces. I was at one point a sad owner of a bent iPhone 5. I have neither tight jeans nor a big rear but all it took was an unfortunate drop from pretty high up to bend it slightly at the volume cut outs (it was in a case). These phones are with us all the time and it’s easy to drop something on them, drop them, toss them, whack them into things and maybe even sit on them quickly from height onto a hard surface. As far as portable electronic devices go, I think these phones are insanely robust. It’s an engineering marvel they could be made so thin, and remain as durable as they are. If you’ve made it this far in the post I unfortunately do not have the authority to give you college engineering class credits, but rest assured the next time Young’s Modulus comes up at a dinner party you won’t get bent.