Practice Question: Force on Anchor at a Cantilever Beam Support

NCEES Civil PE Specification Structural Mechanics: Beams

Problem

The elevation pictured shows a cantilever support planned for installation outside of an industrial building. The support is composed of a steel beam welded to an endplate with top and bottom anchorage into a masonry wall. Given the ultimate load w_{u} and dimensions shown, determine the tension on the top anchor.

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Solution

Answer: C) 4.7 kip

Calculate moment at wall:
$$ M_u= \frac{w_u \ast\ l^2}{2}= \frac{250\ plf \ast (5\ ft)^2}{2} $$
$$ M_u=3125\ lb-ft $$

Calculate force at anchor based on moment:
$$ P_{anchor}=\frac{M_u}{d} $$
where moment arm d is:
$$ d=8\ in=0.67\ ft $$
$$ P_{anchor}=\frac{3125\ lb-ft}{0.67\ ft} $$

$$ P_{anchor}\approx4665\ lb\ \approx4.7\ kip $$

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