{"id":26314,"date":"2021-09-16T16:52:19","date_gmt":"2021-09-16T20:52:19","guid":{"rendered":"http:\/\/chcollins.com\/100Billion\/?p=26314"},"modified":"2023-04-01T18:40:25","modified_gmt":"2023-04-01T22:40:25","slug":"the-hang-it-on-two-studs-calculator","status":"publish","type":"post","link":"https:\/\/chcollins.com\/100Billion\/2021\/09\/the-hang-it-on-two-studs-calculator\/","title":{"rendered":"The “Hang It on Two Studs” Calculator"},"content":{"rendered":"

Asked and Answered 3.4<\/em><\/strong><\/h4>\n

Hello, and here we are again.\u00a0 I thought I was done with this series on hanging pictures, but it seems physics never dies — it just gets more complicated.<\/p>\n

Some commenters on my previous articles (Why Frames Tilt Forward<\/em><\/a>, The “Hang It with Two Hooks” Calculator<\/em><\/a>, and The Physics of Hanging Pictures<\/em><\/a>) asked how they could hang items on wall studs, if the studs are off-center from the desired hanging spot.\u00a0 This seemed to be a rather specialized topic, and beyond the scope of my series, so I deferred until now.\u00a0 But a recent commenter rekindled my interest and finally inspired me to take a look.<\/p>\n

Before I proceed, however, I must mention that I’m not the first to address this problem.\u00a0 The number-one result (as of now) I found in searches for “hang item on off-center studs” is this article on instructables.com<\/a> by an author named MolecularD.\u00a0 The author describes the principles involved and offers a set of equations (minus the math) that are meant to show the reader where to place the wall hooks.\u00a0 Unfortunately, some readers commented that they did not get the desired result when they followed the author’s instructions.<\/p>\n

The solution provided in the inscrutables.com article is such a complicated equation that there is no way for me to verify it without essentially solving the problem myself.\u00a0 Which is what I will do now, taking a somewhat simpler, more intuitive approach.<\/p>\n

The four consecutive views in Figure 1 demonstrate the concept:<\/p>\n

FIGURE 1: THE CONCEPT
\n\"Concept<\/a><\/p>\n

View (A) depicts a frame hanging on a wall, centered at our desired position (dotted line), using a wire on a single hook.\u00a0 Because of the symmetry of the system, there is no tendency for the frame to rotate one way or the other.\u00a0 Ignore for now the fact that the wire extends above the top of the frame.<\/p>\n

View (B) shows the studs in the wall behind the frame (we use a stud-finder to spot them).\u00a0 The two studs are different distances from the center of the frame.\u00a0 We drive a nail into the center of each stud, just touching the underside of the wire.\u00a0 This does not cause the frame to rotate.<\/p>\n

In View (C), we attach a piece of wire (blue) to the original wire, from the point where the first nail touches the wire to where the second nail touches the wire, without any slack.\u00a0 The load is now shared between the central hook and the nails in the studs.\u00a0 But this still does not cause the frame to rotate.<\/p>\n

In View (D), we snip away the original wire where it touched the nails, leaving our new wire in place.\u00a0 The nails in the studs now assume all the load, with the higher nail bearing more than the lower.\u00a0 Still the frame does not rotate, so we have found the solution.<\/p>\n

Obviously, I don’t expect readers to repeat these steps to hang their pictures — this was just a demonstration of concept.\u00a0 Instead I will offer a calculator, with instructions for taking measurements, placing the hooks and cutting the wire, to help the reader achieve the final result.<\/p>\n

That is, if you really insist on using studs.\u00a0 Personally, I think it would be easier in most cases to forget about the studs and use the Hang-It-With-Two-Hooks calculator that I presented in my earlier article.\u00a0 You would fasten the hooks to the wall with toggle bolts, which can hold a significant amount<\/a> of weight when paired with the appropriate hooks.\u00a0 (This video<\/a> shows how to install them.)\u00a0 But in the end, it’s your call.<\/p>\n

The Setup
\n<\/em><\/strong><\/span><\/h2>\n

Oh, you’re still here!\u00a0 This must mean that you really, really want to use two studs to hang your item.\u00a0 Okay then, onto the intricate details.\u00a0 Please consult Figure 2<\/a> (below) to get a sense of the important lengths and measures:<\/p>\n

FIGURE 2: USING TWO STUDS TO HANG A PICTURE
\n\"Diagram<\/a><\/p>\n

Start by measuring the height H<\/span><\/strong> and the weight of the item you want to hang.\u00a0 Then mark the spot 0n the wall corresponding to the top-center of the item.\u00a0 All other measurements will refer to this point.<\/p>\n

Next, use your stud-finder to measure XA<\/sub><\/strong>, the distance from top-center to the center of the closest stud, and XB<\/sub><\/strong>, the distance from top-center to the center of the next-closest stud.<\/p>\n

Now inspect your hanging hardware.\u00a0 You want to (ideally) hide all your hardware behind the item you are hanging, which means the higher hook (A) should not show.\u00a0 Therefore, you should choose a value for ZA<\/sub><\/strong>, the distance from the top of the frame to the bottom of Hook A, that is slightly greater than the length of the hook.<\/p>\n

While you are it, measure the length (D<\/span><\/strong>) of the D-rings attached to the item.\u00a0 If you plan to attach the wire directly to the item, then this length is zero.<\/p>\n

Your next measurement is WD<\/sub><\/strong>, the distance between the D-ring attachment points.\u00a0 If you have not yet attached the D-rings to your item, then mark the spots where you think they should be attached, and measure the distance between those marks.<\/p>\n

Note that I have not asked you to specify Y<\/span><\/strong>, the distance from the top of the frame to the D-ring attachment point, or ZB<\/sub><\/strong>, the distance from the top of the frame to the bottom of Hook B, or S<\/span><\/strong>, the length of wire to cut.\u00a0 These values will be returned by the calculator.<\/p>\n

There is one last thing you may have noticed on the diagram: to make the item hang true, you need to install a guide hook below Hook A to equalize the slack in the wire — and the forward tilt — on the left and right sides.\u00a0 More on this later.<\/p>\n

The Calculator<\/span>
\n<\/em><\/strong><\/h2>\n

My geometric\/algebraic solution may be found in this attachment<\/a>.\u00a0 Additional comments\u00a0 and assumptions about the problem are provided in the appendix at the end of this post, for those who are interested.\u00a0 But I’m sure most of you want to get right to the calculator, so here we go.<\/p>\n

First enter the height and weight of the frame, then enter the position of the studs closest to the top center.\u00a0 The calculator will identify which hook (left or right) is A<\/span> and which is B<\/span>. Now enter the remaining four values.\u00a0\u00a0 The default wire angle of 30 degrees should be fine in most cases.<\/p>\n

Results update when a new value is entered and are reported to the nearest eighth-inch.\u00a0 The calculator advises how to position the guide hook on the A<\/span> side, and how to attach the wire to the frame.\u00a0 The length of wire S<\/span><\/strong> includes 6 extra inches — 3 inches per side — for tying the wire ends to the D-rings.<\/p>\n