MATHalino | Engineering Math Review

Problem 5
Eliminate A and B from x = A sin (ωt + B). ω being a parameter not to be eliminated.

Read more about Problem 05 | Elimination of Arbitrary Constants
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This is just a quick post and I hope you will find this useful.

One time, I browse for something at the Morayta branch of National Book Store and I heard a group of students asking to the sales lady if they have a polar graph paper. From the look of her face, the sales lady seemed know nothing about a polar paper and she courteously told the students that they don't have what they are looking.

Read more about Polar Coordinate Printable Paper (Free Download)
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Problem 856
For the beam shown in Fig. P-856, determine the moments over the supports. Also draw the shear diagram and compute the maximum positive bending moment.

Read more about Problem 856 | Continuous Beams with Fixed Ends
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Problem 855
If the distributed load in Prob. 854 is replaced by a concentrated load P at midspan, determine the moments over the supports.

Answers:
$M_1 = \dfrac{PL}{8} \cdot \dfrac{1}{\alpha + 2} = M_4$

$M_2 = -\dfrac{PL}{8} \cdot \dfrac{2}{\alpha + 2} = M_3$

Read more about Problem 855 | Continuous Beams with Fixed Ends
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Problem 854
Solve for the moment over the supports in the beam loaded as shown in Fig. P-854.

Answers:
$M_1 = \dfrac{w_o L^2}{12} \cdot \dfrac{1}{\alpha + 2} = M_4$

$M_2 = -\dfrac{w_o L^2}{12} \cdot \dfrac{2}{\alpha + 2} = M_3$

Read more about Problem 854 | Continuous Beams with Fixed Ends
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Problem 853
For the continuous beam shown in Fig. P-853, determine the moment over the supports. Also draw the shear diagram and compute the maximum positive bending moment. (Hint: Take advantage of symmetry.)