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Consider the following scenario: I am would like to mount a shelf to my wall. To support the shelf, I am using two drywall anchors, which each are rated at 50 lbs. If each anchor is placed on one end of the shelf, does that mean that two mounts could support 100 lbs together?

Here's a more detailed example. If my shelf is 1.10 m long, then each drywall anchor is placed 0.05 m from the end (so the distance between the anchors is 1 m exactly). If the anchors are rated to support 50 lbs each, and the shelf weighs 5 lbs, would I be able to place a 95 lb object in the middle of the shelf? Essentially, I am wondering if I can approximate the 'upward-pointing' support forces of the two dry-wall anchors as one force, to counteract the downward force of 100 lbs (shelf plus object). Does the distance between the anchors affect how much weight can be on the shelf?

I made a crude picture to showcase what I am talking about:

enter image description here

The red dots are the wall anchors, the black beam is the shelf, and the blue box is the object. In the above scenario, will the wall anchors support the load? What if the two drywall anchors were placed directly on to of each other in the exact middle of the beam (I know this is not technically possible, but assume for this instance that this can be done)? Would that change how much the weight the system can support?

Can I approximate the situation like so: enter image description here where the black lines represent the forces of the FBD (sorry, no arrow heads on lines)?

This isn't a homework problem, I am actually mounting a shelf and am wondering how much weight I can put on it.

EDIT: As pointed out and requested by @Whit3rd, the drywall anchor specifically says "hangs up to 50 lbs," as seen here. In addition, the shelf is 1.5 in thick and protrudes 1 ft from the wall.

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closed as off-topic by sammy gerbil, knzhou, user36790, John Rennie, heather Aug 23 '16 at 10:45

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  • $\begingroup$ The details heavily depend on the properties of the shelf material and the anchors. $\endgroup$ – knzhou Aug 23 '16 at 4:02
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    $\begingroup$ As a preliminary answer: yes, you should be able to place about 95 pounds in the center. But you definitely can't place 95 pounds on the edge, since only one anchor will be supporting it. $\endgroup$ – knzhou Aug 23 '16 at 4:03
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There is not enough information. Anchors can fail in tension (pull out of the wall), or in shear (snap in two). The shelf can act as a lever, with a fulcrum at the shelf/wall intersection, and pry the anchor out of the wall with a force up to 95 lbs *shelf_depth/shelf_thickness. Or worse. The '95lbs' is a down gravity force on the long arm of a lever, and it's the short arm that pulls (out from the wall) on the anchor. The shelf/wall fulcrum as well as the weight are applying force on the anchor. enter image description here

So, what does the '50 lb' rating refer to, the anchor shear load or the anchor axial load? And, what forces keep the shelf level?

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  • $\begingroup$ Thanks for the preliminary help. I tried to answer your questions and clear up some confusion with my most recent edit $\endgroup$ – wcarhart Aug 23 '16 at 5:03
  • $\begingroup$ Hanging weight (like, hanging a picture) only depends on the shear limit of the fastener; like a strong nail, it needn't break to fail, the shelf and load can pull it out. So, a practical shelf design usually needs some kind of bracket that keeps it from hingeing downward. The shelf projecting out from the wall is a twist/torque problem for which the anchor is not specified. $\endgroup$ – Whit3rd Aug 23 '16 at 5:17

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