[amp_mcq option1=”$$\\frac{{{\\text{wa}}}}{{27}}$$” option2=”$$\\frac{{{\\text{w}}{{\\text{a}}^2}}}{{27}}$$” option3=”$$\\frac{{{{\\text{w}}^2}{\\text{a}}}}{{\\sqrt {27} }}$$” option4=”$$\\frac{{{\\text{w}}{{\\text{a}}^2}}}{{9\\sqrt 3 }}$$” correct=”option3″]<\/p>\n
The correct answer is $\\frac{{{\\text{w}}{{\\text{a}}^2}}}{{27}}$.<\/p>\n
The maximum bending moment in a simply supported beam occurs at the point of contraflexure, which is the point where the bending moment is zero. In this case, the point of contraflexure is located at $\\frac{a}{2}$ from the left end of the beam.<\/p>\n
The bending moment at any point along the beam can be calculated using the following equation:<\/p>\n
$$M = \\frac{w}{2} x \\left( \\frac{a}{2} – x \\right)$$<\/p>\n
where $w$ is the load per unit length, $x$ is the distance from the left end of the beam, and $a$ is the length of the beam.<\/p>\n
Substituting $x = \\frac{a}{2}$ into the equation for $M$, we get the following expression for the maximum bending moment:<\/p>\n
$$M_{\\text{max}} = \\frac{w}{2} \\left( \\frac{a}{2} \\right)^2 = \\frac{{{\\text{w}}{{\\text{a}}^2}}}{{27}}$$<\/p>\n
Therefore, the maximum bending moment in a simply supported beam carrying a varying load from zero at one end and $w$ at the other end is $\\frac{{{\\text{w}}{{\\text{a}}^2}}}{{27}}$.<\/p>\n
The other options are incorrect because they do not take into account the fact that the maximum bending moment occurs at the point of contraflexure, which is located at $\\frac{a}{2}$ from the left end of the beam.<\/p>\n","protected":false},"excerpt":{"rendered":"
[amp_mcq option1=”$$\\frac{{{\\text{wa}}}}{{27}}$$” option2=”$$\\frac{{{\\text{w}}{{\\text{a}}^2}}}{{27}}$$” option3=”$$\\frac{{{{\\text{w}}^2}{\\text{a}}}}{{\\sqrt {27} }}$$” option4=”$$\\frac{{{\\text{w}}{{\\text{a}}^2}}}{{9\\sqrt 3 }}$$” 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-5680","post","type-post","status-publish","format-standard","hentry","category-theory-of-structures","no-featured-image-padding"],"yoast_head":"\n