[amp_mcq option1=”200 mm” option2=”250 mm” option3=”300 mm” option4=”400 mm” correct=”option3″]<\/p>\n
The correct answer is C. 300 mm.<\/p>\n
The maximum bending stress in a simply supported beam is given by the following equation:<\/p>\n
$\\sigma_{max} = \\frac{M}{S}$<\/p>\n
where:<\/p>\n
$\\sigma_{max}$ is the maximum bending stress,
\n$M$ is the bending moment, and
\n$S$ is the section modulus.<\/p>\n
The bending moment in a simply supported beam with a uniformly distributed load is given by the following equation:<\/p>\n
$M = \\frac{wl^2}{8}$<\/p>\n
where:<\/p>\n
$w$ is the load per unit length,
\n$l$ is the span length, and
\n$M$ is the bending moment.<\/p>\n
The section modulus of a rectangular beam is given by the following equation:<\/p>\n
$S = \\frac{bh^2}{6}$<\/p>\n
where:<\/p>\n
$b$ is the width of the beam,
\n$h$ is the depth of the beam, and
\n$S$ is the section modulus.<\/p>\n
Substituting the equations for $M$ and $S$ into the equation for $\\sigma_{max}$, we get the following equation:<\/p>\n
$\\sigma_{max} = \\frac{w\\frac{l^2}{8}}{bh^2\/6} = \\frac{wl^2}{4bh}$<\/p>\n
We are given that the load per unit length is $w = 75 \\frac{N}{m}$, the span length is $l = 8 \\text{ m}$, the maximum bending stress is $\\sigma_{max} = 75 \\frac{N}{mm^2}$, and the modulus of elasticity is $E = 0.2 \\times 10^6 \\frac{N}{mm^2}$. Substituting these values into the equation for $\\sigma_{max}$, we get the following equation:<\/p>\n
$75 \\frac{N}{mm^2} = \\frac{(75 \\frac{N}{m})(8 \\text{ m})^2}{4bh}$<\/p>\n
Solving for $h$, we get the following equation:<\/p>\n
$h = \\frac{(75 \\frac{N}{m})(8 \\text{ m})^2}{4(75 \\frac{N}{mm^2})(0.2 \\times 10^6 \\frac{N}{mm^2})} = 300 \\text{ mm}$<\/p>\n
Therefore, the depth of the joist is 300 mm.<\/p>\n","protected":false},"excerpt":{"rendered":"
[amp_mcq option1=”200 mm” option2=”250 mm” option3=”300 mm” option4=”400 mm” correct=”option3″]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[639],"tags":[],"class_list":["post-5622","post","type-post","status-publish","format-standard","hentry","category-theory-of-structures","no-featured-image-padding"],"yoast_head":"\n