Bending Stress and Shearing Stress in Timber Beam
| Bending Stress $f_b = \dfrac{M}{S} = \dfrac{Mc}{I}$ Horizontal Shear Stress |
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March 2017
Integration issue
After deriving an equation I have ended up with equation where I have a complex denominator and I am not sure how to simplify. I am trying to work out as a function of x. Equation link is below. Thanks in advance.
https://www.flickr.com/photos/baldypaul/32722700004/in/datetaken/
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Equation of the Diameter of Parabola Bisecting Parallel Chords of Given Slope
Problem
A parabola has an equation of y2 = 8x. Find the equation of the diameter of the parabola, which bisect chords parallel to the line x – y = 4.
| A. y = 2 | C. y = 4 |
| B. y = 3 | D. y = 1 |
Timber Design
Basic Formulas
$f_b = \dfrac{Mc}{I}$
Horizontal Shear Stress
$f_v = \dfrac{VQ}{Ib}$
Formula for Spacing of Bolts and Nails
$s = \dfrac{RI}{VQ} = \dfrac{R}{q}$
Notching of Beams Formulas
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Safe Dimensions of the Notch at a Joint of a Timber Truss
Situation
The truss shown in is made from timber Guijo 100 mm × 150 mm. The load on the truss is 20 kN. Neglect friction.
Compression parallel to grain = 11 MPa
Compression perpendicular to grain = 5 MPa
Shear parallel to grain = 1 MPa
1. Determine the minimum value of x in mm.
| A. 180 | C. 160 |
| B. 150 | D. 140 |
2. Determine the minimum value of y in mm.
| A. 34.9 | C. 13.2 |
| B. 26.8 | D. 19.5 |
3. Calculate the axial stress of member AC in MPa.
| A. 1.26 | C. 1.57 |
| B. 1.62 | D. 1.75 |
Maximum Stress of Truss Member Due to Moving Loads
Situation
The bridge truss shown in the figure is to be subjected by uniform load of 10 kN/m and a point load of 30 kN, both are moving across the bottom chord
Calculate the following:
1. The maximum axial load on member JK.
| A. 64.59 kN | C. -64.59 kN |
| B. -63.51 kN | D. 63.51 kN |
2. The maximum axial load on member BC.
| A. 47.63 kN | C. -47.63 kN |
| B. -74.88 kN | D. 74.88 kN |
3. The maximum compression force and maximum tension force on member CG.
| A. -48.11 kN and 16.36 kN |
| B. Compression = 0; Tension = 16.36 kN |
| C. -16.36 kN and 48.11 kN |
| D. Compression = 48.11 kN; Tension = 0 |
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Truss With Tension-Only Diagonals
Situation
Diagonals BG, CF, CH, and DG of the truss shown can resist tension only.
If W = 3 kN and P = 0, find the following:
1. the force in member CF.
| A. 4.76 kN | C. 4.67 kN |
| B. 4.32 kN | D. 4.23 kN |
2. the force in member BF.
| A. 3.2 kN | C. 3.4 kN |
| B. 3.3 kN | D. 3.5 kN |
3. the force in member DH.
| A. 2.8 kN | A. 2.5 kN |
| B. 2.8 kN | D. 2.7 kN |
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3-Panel Truss with Flexible Cables Used as Diagonals
Situation
Flexible cables BE and CD are used to brace the truss shown below.
1. Determine the load W to cause a compression force of 8.9 kN to member BD.
| A. 7.80 kN | C. 26.70 kN |
| B. 35.64 kN | D. 13.35 kN |
2. Which cable is in tension and what is the tensile reaction?
| A. BE = 12.58 kN | C. BE = 6.29 kN |
| B. CD = 6.29 kN | D. CD = 12.58 kN |
3. If W = 20 kN, what will be the tensile reaction of member CE?
| A. 6.67 kN | C. 0 |
| B. 13.33 kN | D. 10 kN |
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Absolute Pressure at 200 mm Below the Surface of Liquid Mercury
Problem
Determine the absolute pressure in a vessel of mercury at a point 200 mm below its surface.
| A. 126 kPa | C. 128 kPa |
| B. 130 kPa | D. 132 kPa |
Fundamental Frequency of Fourier Equation in Cosine Form
Problem
Given the Fourier equation:
$$f(t) = 5 \cos (20\pi t) + 2 \cos (40\pi t + \cos (80\pi t)$$
What is the fundamental frequency?
| A. 10 | C. 40 |
| B. 20 | D. 30 |