March 2017

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
 

2014-may-design-truss-equilateral-triangle-given.gif

 

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

 

Situation
The truss shown in is made from timber Guijo 100 mm × 150 mm. The load on the truss is 20 kN. Neglect friction.

Allowable stresses for Guijo:
Compression parallel to grain = 11 MPa
Compression perpendicular to grain = 5 MPa
Shear parallel to grain = 1 MPa

 

2015-may-design-timber-3member-truss-triangular.gif

 

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

 

Timber Design

Basic Formulas

Bending Stress
$f_b = \dfrac{Mc}{I}$
 

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

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

 

Diameter of Parabola, Diameter of Ellipse, Conjugate Diameters - CE Board Problem

Integration issue

Submitted by vipa2000 on March 21, 2017 - 4:28pm

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/

Bending Stress and Shearing Stress in Timber Beam

Bending Stress
$f_b = \dfrac{M}{S} = \dfrac{Mc}{I}$
 

Horizontal Shear Stress
$f_v = \dfrac{VQ}{Ib}$

 bending-member-corss-section-any-shape.gif
For Rectangular Sections
$f_b = \dfrac{6M}{bd^2}$
 

$f_v = \dfrac{3V}{2bd}$

algebra 1

Submitted by takiyagenji on March 25, 2017 - 10:16pm

what is the best book for algebra

Bolted Connection

Spacing of Bolts / Nails / Screws
 

spacing-of-bolts-nails.gif

 

$s = \dfrac{RI}{VQ}$

$s = \dfrac{R}{q}$
 

Notching on Beams

NSCP 2001
When rectangular shaped girders, beams or joists are notched at points of supports on the tension side, the horizontal shear stress at such point shall not exceed:
 

$F_v = \dfrac{3V}{2bd'}\left( \dfrac{d}{d'} \right)$

Where

$d$ = total depth of beam
$d'$ = actual depth of beam at notch

 

When girder, beams or joists with circular cross section are notched at points of support on the tension side, the actual shear stress at such point shall not exceed:
 

Example 01: Maximum bending stress, shear stress, and deflection

Problem
A timber beam 4 m long is simply supported at both ends. It carries a uniform load of 10 kN/m including its own weight. The wooden section has a width of 200 mm and a depth of 260 mm and is made up of 80% grade Apitong. Use dressed dimension by reducing its dimensions by 10 mm.

Properties of Apitong
Bending and tension parallel to grain = 16.5 MPa
Shear parallel to grain = 1.73 MPa
Modulus of elasticity in bending = 7.31 GPa
  1. What is the maximum flexural stress of the beam?
  2. What is the maximum shearing stress of the beam?
  3. What is the maximum deflection of the beam?

 

2006-may-ce-board-stresses-in-timber-beam.gif

 

Example 02: Required Diameter of Circular Log Used for Footbridge Based on Shear Alone

Problem
A wooden log is to be used as a footbridge to span 3-m gap. The log is required to support a concentrated load of 30 kN at midspan. If the allowable stress in shear is 0.7 MPa, what is the diameter of the log that would be needed. Assume the log is very nearly circular and the bending stresses are adequately met. Neglect the weight of the log.
 

beam-001-circular-log-shear-stress.gif

 

Example 03: Moment Capacity of a Timber Beam Reinforced with Steel and Aluminum Strips

Problem
Steel and aluminum plates are used to reinforced an 80 mm by 150 mm timber beam. The three materials are fastened firmly as shown so that there will be no relative movement between them.
 

beam-002-wood-reinforced-steel-aluminum.gif

 

Given the following material properties:

Allowable Bending Stress, Fb
Steel = 120 MPa
Aluminum = 80 MPa
Wood = 10 MPa		 Modulus of Elasticity, E
Steel = 200 GPa
Aluminum = 70 GPa
Wood = 10 GPa

Find the safe resisting moment of the beam in kN·m.
 

Example 04: Required Depth of Rectangular Timber Beam Based on Allowable Bending, Shear, and Deflection

Problem
A beam 100 mm wide is to be loaded with 3 kN concentrated loads spaced uniformly at 0.40 m on centers throughout the 5 m span. The following data are given:

Allowable bending stress = 24 MPa
Allowable shear stress = 1.24 MPa
Allowable deflection = 1/240 of span
Modulus of elasticity = 18,600 MPa
Weight of wood = 8 kN/m3
  1. Find the depth d considering bending stress only.
  2. Determine the depth d considering shear stress only.
  3. Calculate the depth d considering deflection only.

 

beam-003-required-depth.gif

 

Example 01: Spacing of Screws in Box Beam made from Rectangular Wood

Problem
A concentrated load P is carried at midspan by a simply supported 4-m span beam. The beam is made of 40-mm by 150-mm timber screwed together, as shown. The maximum flexural stress developed is 8.3 MPa and each screw can resist 890 N of shear force.
 

spacing-of-bolts-001-box-beam-cross-section.gif

 

  1.   Determine the spacing of screws at A.
  2.   Determine the spacing of screws at B.

 

Example 02: Maximum Concentrated Load a Box Beam Can Carry

Problem
A beam is built up by nailing together 25 mm thick planks to form a 200 mm × 250 mm box section as shown. The nails are spaced 125 mm apart and each can carry a shearing force of up to 1.3 kN. The beam is simply supported for a span of 3.6 m and to carry a concentrated load P at the third point of the span. The allowable shearing stress of the section is 0.827 MPa.
 

spacing-of-bolts-002-box-beam-cross-section.gif

 

  1. Determine the largest value of P that will not exceed the allowable shearing stress of the beam or the allowable shearing force of the nails.
  2. What is the maximum flexural stress of the beam for the load P computed in Part (1)?

 

Example 01: Safe Uniform Load for a Beam that was Notched at the Tension Fibers at Supports

Problem
A 75 mm × 150 mm beam carries a uniform load wo over the entire span of 1.2 m. Square notches 25 mm deep are provided at the bottom of the beam at the supports. Calculate the safe value of wo based on shear alone.

Allowable shear parallel to grain = 1.40 MPa
Allowable shear normal to grain = 1.85 MPa
notched-beam-001-uniform-load.gif

 

Example 02: Notched beam with concentrated load

Problem
A 150 mm by 300 mm wooden beam having a simple span of 6 meters carries a concentrated load P at its midspan. It is notched at the supports as shown in the figure. For this problem, all calculations are based on shear alone using the 2010 NSCP specification given below. Allowable shear stress of wood, Fv = 1.0 MPa.
 

notched-beam-002-concentrated-load.gif

 

  1. If P = 30 kN, calculate the maximum allowable depth (millimeters) of notches at the supports.
    1. 88
    2. 62
    3. 238
    4. 212
  2. If the depth of notches is 100 mm, what is the safe value of P (kiloNewton) the beam can carry.
    1. 26.67
    2. 17.78
    3. 8.89
    4. 13.33
  3. If P = 25 kN and the depth of notches is 150 millimeters, what is the shear stress (MegaPascal) near the supports.
    1. 0.83
    2. 6.67
    3. 1.67
    4. 3.33

 

NSCP 2010 Section 616.4: Horizontal Shear in Notched Beams
When rectangular-shaped girder, beams or joists are notched at points of support on the tension side, they shall meet the design requirements of that section in bending and in shear. The horizontal shear stress at such point shall be calculated by:
 

$f_v = \dfrac{3V}{2bd'}\left( \dfrac{d}{d'} \right)^2$

Where:

$d$ = total depth of beam.
$d'$ = actual depth of beam at notch.

 

Problem
Three marksman simultaneously shoot and hit a rapidly spinning spherical target. What is the probability that the three points of impact lie on the same hemisphere?

A.   0 C.   1
B.   1/2 D.   2/3

 

Problem
A catapult is placed 100 ft from the castle wall, which is 35 feet high. The soldier wants the burning bale of hay to clear the top of the wall and land 50 feet inside the castle wall. If the initial velocity of the bale is 70 feet per second, then at what angle should the bale of hay be launched so that it travel 150 feet and pass over the castle wall. Use g = 32 ft/sec2.
 

2016-may-math-catapult.jpg

 

A.   49.8° C.   39.2°
B.   50.8° D.   40.2°

 

Situation
A temporary earth retaining wall consists of wooden plank driven vertically into the ground. The wall is designed to resist 2.4 m height of soil.

Given the following:
Cross-sectional dimensions of the plank = 300 mm wide × 75 mm thick
Allowable bending stress of the plank = 10.4 MPa
Allowable shear stress of the plank = 0.8 MPa
Unit weight of retained soil = 17.3 kN/m3
Active earth pressure coefficient = 1/3

1.   Calculate the maximum flexural stress.

A.   12.7 MPa C.   8.6 MPa
B.   14.2 MPa D.   10.1 MPa

2.   Calculate the maximum shear stress.

A.   1.11 MPa C.   0.99 MPa
B.   0.33 MPa D.   0.77 MPa

3.   Calculate the minimum thickness of the plank to prevent failure.

A.   90 mm C.   110 mm
B.   80 mm D.   100 mm

Problem
Samuel Pepys wrote Isaac Newton to ask which of three events is more likely: that a person get (a) at least 1 six when 6 dice are rolled (b) at least two sixes when 12 dice are rolled, or (c) at least 3 sixes when 18 dice are rolled. What is the answer?

A.   (a) is more likely than (b) and (c)
B.   (b) is more likely than (a) and (c)
C.   (c) is more likely than (a) and (b)
D.   (a), (b), and (c) are equally likely

Civil Engineering Refresher Final Preboard: Probability Involving Dice

Problem 909 | Combined Axial and Bending

Problem 909
The bent steel bar shown in Figure P-909 is 200 mm square. Determine the normal stresses at A and B.
 

909-bent-steel-bar.gif

 

Problem 910 | Combined Axial and Bending

Problem 910
A timber beam AD, 6 in. thick by 10 in. high and loaded as shown in Figure P-910, is pinned at its lower end and supported by a horizontal cable CE. Compute the maximum compressive stress developed in the beam.
 

910-boom.gif

 

Problem
A nutritionist in a hospital is arranging special diets that consist of a combination of three basic foods. It is important that the patients on this diet consume exactly 310 units of calcium, 190 units of iron, and 250 units of vitamin A each day. The amounts of these nutrients in one ounce food are given in the following table.
 

  Units Per Ounce
Calcium Iron Vitamin A
Food A 30 10 10
Food B 10 10 30
Food C 20 20 20

 

How many ounces each food must be used to satisfy the nutrient requirements exactly?

A.   6 ounces of Food A, 5 ounces of Food B and 3 ounces of Food C
B.   3 ounces of Food A, 5 ounces of Food B and 6 ounces of Food C
C.   6 ounces of Food A, 3 ounces of Food B and 5 ounces of Food C
D.   5 ounces of Food A, 3 ounces of Food B and 6 ounces of Food C

 

Pages