8ft 13 12 A ladder to the attic folds down into the configuration shown. While the total length of the ladder is 8ft, A person standing on the ladder typically applies their weight to the ladder somewhere in the center 6ft of the ladder's length. The bottom of the ladder rests on the floor, and the top of the ladder is secured by two fasteners. Installation instructions on the ladder clearly state, in ALL CAPS, that nails should be used to secure the ladder, not screws. Find the maximum weight the ladder can support if a) Two quarter-inch nails are used b) Two quarter-inch screws are used. For both cases, use a 10 ksi maximum average shear stress for the fasteners The difference between the two situations is that for a nail, the effective diameter (for an area calculation) is the actual diameter of the nail (% inch). For a screw, the outer diameter is % inch, but the threads cut into that area, and the minimum diameter (called the minor diameter) is only 0.189 inches. This diameter is the effective diameter for a screw, and it should be used for the area calculation. Smaller diameter -> Smaller Area -> Larger stress!
8ft 13 12 A ladder to the attic folds down into the configuration shown. While the total length of the ladder is 8ft, A person standing on the ladder typically applies their weight to the ladder somewhere in the center 6ft of the ladder's length. The bottom of the ladder rests on the floor, and the top of the ladder is secured by two fasteners. Installation instructions on the ladder clearly state, in ALL CAPS, that nails should be used to secure the ladder, not screws. Find the maximum weight the ladder can support if a) Two quarter-inch nails are used b) Two quarter-inch screws are used. For both cases, use a 10 ksi maximum average shear stress for the fasteners The difference between the two situations is that for a nail, the effective diameter (for an area calculation) is the actual diameter of the nail (% inch). For a screw, the outer diameter is % inch, but the threads cut into that area, and the minimum diameter (called the minor diameter) is only 0.189 inches. This diameter is the effective diameter for a screw, and it should be used for the area calculation. Smaller diameter -> Smaller Area -> Larger stress!
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12
A ladder to the attic folds down into the configuration shown. While the total length of the
ladder is 8ft, A person standing on the ladder typically applies their weight to the ladder
somewhere in the center 6ft of the ladder's length.
The bottom of the ladder rests on the floor, and the top of the ladder is secured by two
fasteners. Installation instructions on the ladder clearly state, in ALL CAPS, that nails should be
used to secure the ladder, not screws. Find the maximum weight the ladder can support if
a) Two quarter-inch nails are used
b) Two quarter-inch screws are used.
For both cases, use a 10 ksi maximum average shear stress for the fasteners
The difference between the two situations is that for a nail, the effective diameter (for an area
calculation) is the actual diameter of the nail (% inch). For a screw, the outer diameter is % inch,
but the threads cut into that area, and the minimum diameter (called the minor diameter) is
only 0.189 inches. This diameter is the effective diameter for a screw, and it should be used for
the area calculation. Smaller diameter -> Smaller Area -> Larger stress!
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