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# Writing Assignment Answer All Questions On Engineering (Math Problem Sample)

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ANSWER ALL QUESTIONS

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Assignment 1
TASK 1
1 Figure 1 represents a light beam ABCD of length 10m which is simply supported at the points A and C. The beam carries a uniformly distributed load of 30kN/m between A and B and point loads of 100kN and 70kN at points B & D, as shown.
Show that the reactions at A & C are 120kN and 230kN respectively
8Rav +2×70 = 180×5+ 100×2
8Rav = 900+200-140
8Rav =960
Rav is therefore 120 kN
8Rc =180×3 + (100×6) + (70×10)
8Rc = 1840
Rc = 230 Kn

29199273297002919937855300259720316307825892631707623088597155394
SFD(KN) 6-X
11756575319129967696867
33809744551
18902083265700187441316896900 X
176672517191400
2604887433800BMD(KN)
3991702675910039957129159300 (-)
(+)
X/120 = (6-X)/160
X= 18
Max shear
= ½ x 960 x 18
=8.640KN
Task 2
1 Suitable I-beam from table
The suitable beam will be of 200.9 kg/m
2 v1 = 120
v2 = 120-180 = -60
v3 = -60-100 =-160
v4 = -160= 230 = 70
therefore max moment = 120KNM at point A
i = 3 x 160/(2 ) = 240/100
2.4MPa
Which is more than there it will fail.
3. The standard beams such as the I-beams resists shear forces, while the flanges resist most of the bending moment experienced by the beam. Beam theory shows that the I-shaped section is a very efficient form for carrying both bending and shear loads in the plane of the web. On the other hand, the cross-section has a reduced capacity in the transverse direction, and is also inefficient in carrying torsion, for which hollow structural sections are often preferred. Therefore, the design and structure of the I beam makes it uniquely capable of handling a variety of loads.
Task 3
1 A hollow circular shaft has an external diameter of 80mm and an internal diameter of 50mm. The shaft is designed to transmit 450kW of power at 1200rpm.
Taking G = 75GPa, answer the following questions:
* Find the maximum and minimum shear stress acting on the shaft.
I=π32D4-d4
external diameter = 0.08 m
internal diameter = 0.05 m
= π36 (0.084-x0.054) =π363.471×10-5
=3.41×10-6Nxm4
Torque
T = p×62πN = 450×1000×602×π×1200
=3579.55 Nm
Shear maximum = TRJ = 3575.55×0.043.41×10-6
= 4.1954×107 Pa change to mPa
= 4.1954×101 mPa
Minimum shear
=3575.55×0.0253.41×10-6
=26.21 mPa
(b) angle of twist
θ= ἰ LGR =41.95×1.6×10675×109×0.04 =0.022 radians
Converting to degrees = 180π×0.0223 = 1.28°
Angle of twist for minimum
=26.21×106×1.675×109×0.025 = 0.0223 radian
Converting to degrees = 180π× 0.0223
=1.28°
Hence the angles are the same
angle of twist = 1.28°.
(c) Find the diameter of a solid circular shaft that would perform the same operation as above.
* Polar moment
Torque =3575.55
Power =450 KW
RPm =1200
G =75 Gpa
L =1.6 M
J = πD432 hence
3.41×10-6 = π32D4
D =0.07676 m =0.077 m
=77 mm
Task 3
Question two
2) A hollow steel shaft with a diameter ratio of 0.8 and a length of 2.5 m is required to transmit 1250 kW at 200rpm. The maximum shear stress is not to exceed 60 MPa. Determine the following:
1 The diameters of the shaft
Diameter ratio = 0.8
P = 1.25 x 106 watts
Polar moments =
J = pi/32(D4 -d4)
Pi/32 (D4 – 0.8D4)
Pi/32 x 0.5904
= 0.05799D4
Torsional loads
= (p x 60)/2 x pi x N
(1.250 X 106 X 60)/( 2 X 3.142 X 200)
=59659.091 Nm
TJ = ἰΥ =59659.091Nm0.05799D2 = 2×60×106D
=2×60×106×0.05799D459659.09D Nm =116.64D4D
D3 =1116.64
D3 =8.5732×10-3
D =∛8.5732×10-3 = 0.2047 meters
Larger diameter= 204.7 mm
But d= 0.8D4 = (0.8×204.7) mm
The smaller diameter = 163.73 mm
2 The maximum angle of twist
θ=TLJ = 59659.091×2.5GJ
Given that J=0.05799×0.20474
G=75×109
=1.0175×10-4 = 0.01954 radian
Converting to degrees = 0.01954×180π
=1.12°
(c) Hollow shafts are much better to take torsional loads compared to solid shafts. shear stress in a shaft subjected to torsion varies linearly from zero at the center to the maximum at the boundary. Inside a solid shaft, most of the material carries a shear stress whose value is much below the maximum shear stress which is the Interior portion of the shaft. But at the

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• Writing Assignment Answer All Questions On Engineering
Description: Figure 1 represents a light beam ABCD of length 10m which is simply supported at the points A and C. The beam carries a uniformly distributed load of 30kN/m between A and B and point loads of 100kN and 70kN at points B & D, as shown....
6 pages/≈1650 words| 1 Source | Harvard | Literature & Language | Math Problem |
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