Description

Draw the shear and moment diagrams for the beam.

SOLUTION

Referring to the FBD of the left segment of the beam sectioned at an arbitrary distance of 𝑥 from the left support, Fig. 𝑎, and setting 𝑉=0,

+uarr𝛴𝐹𝑦=0;,7.50-12(63𝑥)𝑥=0,𝑥=2.739𝑚

⇃+𝛴𝑀=0;,𝑀+12|63(2.739)|(2.739)(2.7393)-7.50(2.739)=0

𝑀=13.69𝑘𝑁*𝑚

=13.7𝑘𝑁*𝑚

When 𝑥=3𝑚,

darr+𝛴𝑀=0;,𝑀+12|63(3)|(3)(33)-7.50(3)=0,𝑀=13.5𝑘𝑁*𝑚

Write an equation as a function of 𝑥 for the following: 𝑥𝐴𝐵𝑉max=+-7.5𝑘𝑁

𝑀max=13.7𝑘𝑁*𝑚4.5, 𝑑𝑜 the cut section from 𝐴 𝑡𝑜 the 3 𝑟𝑑 cut. Then 𝑑𝑜 the cut section from 𝐵 𝑡𝑜 the 3𝑟𝑑 cut 𝑡𝑜 show how the lengths differ.

Ans.

𝑉max=+-7.5𝑘𝑁

𝑀max=13.7𝑘𝑁*𝑚4.5. Make sure the lengths are 𝑖𝑛 𝑥.

For 4.5, 𝑑𝑜 the cut section from 𝐴 𝑡𝑜 the 3 𝑟𝑑 cut. Then 𝑑𝑜 the cut section from 𝐵 𝑡𝑜 the 3𝑟𝑑 cut 𝑡𝑜 show how the lengths differ.

Ans.

𝑉max=+-7.5𝑘𝑁

𝑀max=13.7𝑘𝑁*𝑚3 and 4.5. Make sure the lengths are 𝑖𝑛 𝑥.

For 4.5, 𝑑𝑜 the cut section from 𝐴 𝑡𝑜 the 3 𝑟𝑑 cut. Then 𝑑𝑜 the cut section from 𝐵 𝑡𝑜 the 3𝑟𝑑 cut 𝑡𝑜 show how the lengths differ.

Ans.

𝑉max=+-7.5𝑘𝑁

𝑀max=13.7𝑘𝑁*𝑚

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