Time to read: 9 min
一位新的工程师，当某事发生时，我已经习惯了隔间生活的“兴奋”。一个月前，我们将流量计的一部分加固，我们的一位客户开始抱怨破裂。楼上的灰熊正在捍卫这一变化，而我的工程合作伙伴则努力解释为什么未成年人的调整会导致破裂。
这就是我进来的地方。刚毕业的刚刚毕业，我刚刚花了四年的时间来磨练我的工程分析技能。几分钟后，在白板上，我们有了论点的基础：剪切力图将管子简化为悬臂梁，清楚地证明了为什么在底部造成更多强度会导致损坏。
We made the change and were back to shipping product within the week. I felt like a hero.
I wasn’t.
这种干燥的小轶事不会在工程职业上吸引任何肾上腺素瘾君子，但这对我来说是对工程学的基本基础的提醒。在该领域十年后，您有时会忘记刚熟悉的毕业生刚刚学到的东西：我们不需要设计就不会知道它会。从自由的身体图（新生物理，有人吗？）到更复杂的静态力分析，甚至FMEAon a supercomputer, engineers have been working for years to give us tools to understand the world around us and, more importantly, to predict real-world outcomes, so we can improve our designs before going to prototype.
Basics of Engineering Analysis: Newton and the Free Body Diagram
While specific types of analysis are needed for unique situations (防水住房设计，，，，塑料的快照设计， 或者tolerance stackup，，，，to mention a few), most engineering analysis examines how forces interact between parts of a design. Though studied as freshman, no tool rivals the free body diagram (FBD) for understanding forces on a design element in mechanical or structural designs. Or even a toboggan race down the stairs.
什么？雪橇在楼梯上比赛？我很高兴你问。假设让我们假设一家大公司的年轻工程师对隔间感到无聊，并决定从包装纸板上创建烟草，以了解谁可以在建筑物中心的楼梯上获得最佳的时光。
(Of course, please keep in mind this didn’t happen. And I will swear that to Eileen in HR all day long—there’s no video. On a completely unrelated note, I’d like to give a shout-out to my friend Frank in security.) If we wanted to know how fast these young engineers would be moving, how could we figure out the net acceleration?
Here’s where the FBD comes into its own. With an FBD, we look at all the forces acting on a body (element) and the direction of those forces to create a net force and net moment, and then predict what will happen.
由于纸板足够僵硬，可以接触多个楼梯，因此我们可以将其简化为经典的坡道和块FBD，在那里我们将工程师和纸板视为块和楼梯作为坡道。什么力量是什么，他们在拉什么方向？
重力力（G TIMES质量）在工程师上垂直向下拉。为了使用我们，我们需要将其分解为正常力（垂直于楼梯，m*g*cosθ）和平行力（从楼梯驶向楼梯，m*g*sinθ）。
楼梯支撑（推）在纸板上，并沿垂直于楼梯角度的方向进行工程师。由于工程师既不掉过楼梯，也没有从它们上飞走，因此我们知道这种正常力量在宽幅（M*G*cosθ）的垂直力（正常）力量上等于。
摩擦（事实证明，它不够，以防止工程师从楼梯对面的板玻璃窗口奔跑）将平行于楼梯的楼梯推到楼梯（摩擦= F）k*m*g*cos θ)
尽管很难在重力和地毯之间找到真正的摩擦系数，但是当我们抬头common friction coefficients，我们将系数代替雪地上的蜡木k=0.15. We can also assume a stair rise-run angle of 30° (θ).
When we sum the force vectors, we get a single sum of a force pointing directly down the stairs equal to:
F结果= m*g*sinθ - 0.15*m*g*cosθ=（190磅）*sin 30° - 0.15*（190 lbs-f）*cos 30°= 70磅
(about ⅓ the speed of total freefall)
and find that this engineer is going down the stairs really, really fast, which is both intuitively true and also true from experience (had it actually happened, which of course it didn’t).
你说太简单了吗？这是一个更复杂的分析的基础，我们可以通过组合自由车身图来分析机器中的力来研究元素之间的相互作用，从而使我们达到了新的水平：静态。
Statics: Expanding the FBD
Free body diagrams are great, but when do we have the simplicity of a one-piece machine? Almost never—but we can often reduce machines to a series of elements in mechanical equilibrium, where all the forces cancel each other out, and we end up with an understanding of entire systems using static analysis.
示例1 - 装载起重机
For example, let’s assume that on another long day, the young engineers in this company decided to use the crane in the loading dock area to take a ride and check out the view over the valley. (Again, hypothetically. Geez, Eileen; relax.)
我们想知道起重机上的液压缸是否能够抬起两名工程师和一箱啤酒（这成为我们的体重，W）。这可能很复杂，但是我们通过查看一个类似的问题来简化它：没有运动时，气缸会体验多少力量？
这就是静态允许我们解决这个问题的地方。因为没有运动，所以我们知道周围没有旋转，这意味着A周围的力为零，因此我们得到了非常重要的：
∑m一种= 0
Looking at each force causing a moment (remembering that a moment is the force at a point, multiplied by the distance from that point, multiplied by the sine of the angle between the force and the lever arm), and we end up with:
fcd * lac *sinθ - w *（lac + lcb） * sin = 0
一种little algebra yields:
Fcd * Lac * sin θ = W * (Lac + Lcb) * sin ɑ => Fcd = W * (Lac + Lcb) * sin ɑ / Lac * sin θ
We can plug in some numbers, using:
w = 350磅，= 70°，θ= 10°，lac = 5 ft，lcb = 15 ft
and:
Fcd = (350 lbsf) * (5 ft+15 ft) * (sin 70°) / (5 ft)*(sin 10°) = (350 lbsf)*(20 ft)*(0.94)/(5 ft)*(0.17) = 7576 lbsf of force on the cylinder.
知道液压缸的评分为5吨，我们假设年轻的工程师度过了一个美好的夜晚，并在日落时留下了美好的回忆。
Example 2 – The Beam Connection
当然，工程师不仅要关心机器的任何部分：我们负责将所有这些都绑在一起的气缸，电缆，附件和光束。而且，由于我们通常可以将机械元件简化为具有各种附件的光束，因此特别值得一看。
对于上面的示例，我们知道（当什么都没有移动的时候）有关点A的矩为零，但是我们也知道整个机器中的垂直和水平力必须为零，因此我们可以计算附件处的反应点A：
Ay - fcd * sin（90-θ-©） - w = 0 =>
=>Ay = Fcd * sin(90- θ- ɑ ) + W = 7576 lbs * 0.17 + 350 lbs = 1666 lbs
and:
ax - fcd * cos（90-θ-ɑ）= 0 => ax = fcd * cos（90-θ->）= 7576 lbs * 0.985 = 7461 lbs
更仔细地看，这里正在发生一些有趣的事情。点A被称为pinned end，，，，which means in mechanical equilibrium, it has a reaction force in both the x and y direction, but has no moment reaction (in other words, moment is zero). Knowing about this unique property helps us analyze different beams.
Beam Supports
In considering beams, several types of support need consideration and are used in creating mental models for beam elements. Fixed supports (think cantilever beams, like diving boards) have both x and y reaction forces, and a moment reaction, too. A pin support has x (horizontal) and y (vertical) reaction forces, but no moment (it’s like a hinge), while a roller support is like a wheel, where the load is supported vertically, but is free to move horizontally—t has a y reaction force, but neither an x reaction force nor a moment.
一种beam can have nearly any combination of these supports, but more importantly, we can often simplify machines into several beams with different types of supports.
For the crane, we simplify the arm as a horizontal beam with a pinned support at one end (point A), a roller support at point C, and a load at point B. So, in the crane example, we know what’s happening at the ends of the beam. But what’s happening in the beam itself?
光束中的剪切力分析：直观底漆
For failure risk analysis, we move beyond simple statics and look at forces inside the beam itself. Though FEA and other high-tech methods are great for final analysis, an approximation from moment and shear diagrams using beam analysis will suffice early in the design—and train your engineering intuition.
Looking at our simplified crane beam again, we know there is zero moment at point A, and that we’ll have a reaction force at point C, as well as the load at point B. We can also see that the moment at B will be zero. For shear and moment diagrams, we typically ignore any axial force along the beam, and so we have perpendicular forces at B, C, and A of:
b = - w * sin = - （350磅） * sin 70°= - 329磅
[negative – the force is pointing down]
c = - b *（lac + lcb） / lcb = - （ - w * sin * 20 ft / 5 ft）= 1316磅
[ because ∑MA = 0 ]
and:
一种= – B – C = – 987 lbsf
[no movement, so the sum of the y forces is zero]
如果我们想知道光束会经历多少弯曲力或试图裂缝的力量，我们需要设置矩和剪切图。首先，我们的下部力为987磅，从A到C，然后我们的反作用力向上1316磅，导致的向上力为329磅，末端的力下降到零。。由此产生的剪切图看起来像这样：
Without point moment loads, the moment along the beam will be continuous: the shear force multiplied by the distance, starting at zero (because ∑M一种= 0). The moment will reach its greatest magnitude at C, then gradually reach zero again at B:
Intuition check: Where is the beam most likely to bend? At the hydraulic attachment. Intuition is trained and reinforced by sketching these diagrams. (By the way, not to worry: The crane beam held fine with no bending and none in HR the wiser.)
Infinite variations of loads and beam attachments exist, but a很少的基本梁将训练您的直觉，深入了解您的机械设计。超越剪切和力矩，我们如何预测这些力何时会造成损坏？我建议您在本系列有关刚度和力量的系列文章中保持关注（您可以在下面注册）并查看我的文章How to Design for Stiffness Using Material Properties。
您还可以在网上找到一些很棒的免费课程。对于这样的分析方法，我建议您研究麻省理工学院结构力学（梁分析，挠度和应力）或更深入的反馈控制系统的分析和设计（时间和频率分析，控制回路的类型以及机械稳定性分析）。实际上，有比任何一个人都能学到的更多的分析工具，更不用说使用了。
在老板看到之前预测破裂
While I’ll always remember Doc O’s lecture at the end of sophomore year on how most of these tools were for training intuition more than for daily use, after ten years in the field, I can’t help but to also be grateful he spent the time drilling these engineering analysis equations into our heads. Maybe I don’t use them every day, but it’s a rare design project that doesn’t prompt me to at least quickly sketch a free body diagram or use force analysis to see what’s happening in the heart of the design.
工程分析在兄弟救了我几千ken prototypes—and the embarrassment of explaining those broken pieces to clients. Want more tools like these? Sign up below for great tips sent right to your inbox. And if you’re finished with your analysis, you can check out our prototype加工and印刷options to see if you were right!
