MET414_Midterm_Richardson_Brendon
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ECPI University, Virginia Beach *
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Course
414
Subject
Mechanical Engineering
Date
Apr 3, 2024
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docx
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5
Uploaded by AmbassadorWildcatMaster552
Problem One
The circular rod shown is made of the steel alloy AISI 4140 OQT 700. It has a diameter of 2.00 in and an initial length of 72 in. An axial tensile load of 35 000 lb is applied during a certain operation.
Compute:
1.
the equivalent spring constant K,
2.
the deformation X of the rod.
The Young’s modulus of the steel is known to be 30,000,000 psi.
Problem Two
Write the global stiffness matrix of the spring assemblage shown. Assume that all springs remain horizontal, the vertical bars at nodes 2 and 3 are rigid
and allowed to slide horizontally to the left or right.
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Related Questions
PROBLEM: 5 A helical valve spring is to be designed for an operating load range of 90N to 195N. The maximum deflection of the spring for this load range is 7.5 mm. Assuming a spring index of 9, a permissible shear stress of 550 N/mm2 for the material and the modulus of rigidity of 0.85x105 N/mm2. Determine the dimensions of the spring. (i.e. Diameter of the spring wire ,Mean coil diameter, Outer diameter of the spring, number of active turn and free length of the spring). Assume the spring coil is squared and ground.
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Design a helical spring to be used in spring balance with a wire diameter of 6mm and the outside diameter should be limited to 66mm. if the permissible shear stress of the spring material is 325 N/mm? and the Modulus
of rigidity is 85kN/mm?.
a) Compute the deflection of spring per active turn and the axial load on the spring considering the effect of curvature, take Wahl's factor as Kw= 1.1
b) Calculate the value of axial load neglecting the effect of stress factor.
**Note: Please upload your handwritten working/solution to the link provided.
The value of Mean diameter of the spring in mm .
The Spring Index is.
Shear stress factor, neglecting curvature effect .
Deflection per active turn in mm
Axial Load W in N ..
Axial Load W in N. considering effect of curvature .
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A helical compression spring has a scale of 500 lb/in., an outside diameter of 2.75 in, a free length of 8 inches and with squared and ground ends. The load is 1,000 lbs and the working stress on the wire material is 65000 psi. If the Wahl factor of 1.25 is to be used, calculate the following:
A. The standard wire diameter
B. The number of active coil if G = 10 800 000 psi
C. The solid height
D. The stress at solid height
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A helical compression spring is subjected to a maximum force, Fmax of 1250 N. The deflection
of the spring corresponding to the maximum force should be approximately 30 mm. The spring
index is 6. The allowable shear stress is 350 MPa and the modulus of rigidity is 81 370 N/mm².
Design the helical spring by calculating the wire diameter, mean coil diameter, number of active
coils and the total number of coils. State all assumptions and decisions in your design.
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I need the solution to be handwritten.
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1. Design a compression helical spring to carry a load of 500 N with a deflection of 25 mm. The spring
index may be taken as 8. Assume the following values for the spring material:
Permissible shear stress
= 350 MPa
Modulus of rigidity
= 84 kN/mm2
4С - 1
0.615
Wahl's factor
where C-spring index.
4С - 4
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A helical compression spring is wound using 0.12-in-diameter phosphor-bronze B159 wire. The spring index
C = 10 and the total number of coils is N = 14. You may assume that the spring has both ends squared and
ground and is supported between fixed ends. Also, Sgy = 0.45 · Sut-
a. Estimate the spring rate.
b. Estimate the static load corresponding to the yield strength.
c. What should the free length of the spring be to ensure that when it is compressed solid the torsional
stress does not exceed the yield strength?
d. Calculate the critical value of the free length of the spring to avoid buckling.
arrow_forward
No cursive
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Please solve and include units in each step. Your work and solution will be appraciated much. Thank You!
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A spring made from music wire ASTM 228 steel has the following data:Free length=1.75” Outside diameter=0.561”Wire diameter=0.055” Applied load= 14 lbEnds=square and ground both ends hingedNumber of coils=10 G=11.85 x 106psi E= 30 Mpsi
Findspring rate, force at solid length,check for buckling,coil clearance and hole diameter
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Problem 4:
A helical compression spring is to be cycled between 150 lbf and 300 lbf with a 1-in stroke. The number of
cycles is low, so fatigue is not an issue. The coil must fit in a 2.1-in diameter hole with a 0.1-in clearance
all the way around the spring. Use unpeened music wire with squared and ground ends.
(a) Determine a suitable wire diameter, using a spring index of C = 7.
(b) Determine a suitable mean coil diameter.
(c) Determine the necessary spring constant.
(d) Determine a suitable total number of coils.
(e) Determine the necessary free length so that if the spring were compressed to its solid length,
there would be no yielding
arrow_forward
A helical spring made of oil hardened and tempered steel
compression springs, made of circular wire, is subjected to
an axial force, which varies from (2.5 KN) to (3.5 KN). Over
this range of force, the deflection of the spring should be
approximately (5 mm). The spring index can be taken as (5).
The spring has square and ground ends. If ultimate tensile
strength of (1050 N/mm2) and modulus of rigidity of (81370
N/mm2). The permissible shear stress for the spring wire
should be taken as (50 %) of the ultimate tensile
strength.Design the spring and calculate the following: 1.
Wire diameter; 2. Mean coil diameter; 3. Number of active
coils; 4. Total number of coils; 5. Solid length of the spring; 6.
Free length of the spring: 7. pitch of coils (p); 8. Required
spring rate; 9. Actual spring rate; and 10. Draw a neat sketch
.of the spring showing various dimensions
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Q3/ Design a helical compression spring made from stainless steel for the
following operating conditions: Spring load when the valve is open = 600
N, Spring load when the valve is closed = 250 N, Maximum inside diameter
of spring = 25 mm, Length of the spring when the valve is open = 40 mm,
Length of the spring when the valve is closed = 50 mm, take into account
the Wahl stress factor.
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2. A helical valve spring is to be designed for an operating load range of approximately 90 to 135 N. The
deflection of the spring for the load range is 7.5 mm. Assume a spring index of 10. Permissible shear
stress for the material of the spring = 480 MPa and its modulus of rigidity 80 kN/mm2. Design the
spring.
4С - 1
0.615
, C being the spring index.
Take Wahl's factor
%3D
4С - 4
[Ans. d = 2.74 mm ; D = 27.4 mm ; n = 6]
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A helical spring composed of 20 turns of 20mm diameter wire on a mean radius of 80mm when the spring is supporting a load of 2kN. (G=83,000 GPa)
Compute for the following respectively :
1) stress factor
2) shear stress (MPa)
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please show all steps
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O1:
Valve diameter = 60 mm
A safety valve is loaded by a tension type close coiled helical spring having the following data:
Minimum pressure on valve = 0.7 Mpa
Maximum pressure at blow off = 0.78 Mpa
Valve lift = 3 mm
Spring index = 6
Modulus of rigidity = 81370 N/ mm2
Permissible shear stress = 600 N/ mm?
Design the spring.
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Design a helical compression spring to be used in a cam and follower mechanism made of oil tempered carbon steel, is subjected to a load which varies from 416 N to 970 N. The spring index is 6.2 and the design factor of safety is 1.25. If the yield stress in shear is 770 MPa and endurance stress in shear is 350 MPa,find:
1. Size of the spring wire,
2. Diameters of the spring,
3. Number of turns of the spring, and
4. Free length of the spring.
The compression of the spring at the maximum load is 30 mm. The modulus of rigidity for the spring material may be taken as 80 kN/mm2.
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A spring with squared and ground ends is used for a load and deflection of 1.2 kN and 20 mm, respectively, with a spring index of 4. The wire diameter is 6 mm and the modulus of rigidity is 84 GPa. Which of the following is the active number of turns of the spring?
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Related Questions
- PROBLEM: 5 A helical valve spring is to be designed for an operating load range of 90N to 195N. The maximum deflection of the spring for this load range is 7.5 mm. Assuming a spring index of 9, a permissible shear stress of 550 N/mm2 for the material and the modulus of rigidity of 0.85x105 N/mm2. Determine the dimensions of the spring. (i.e. Diameter of the spring wire ,Mean coil diameter, Outer diameter of the spring, number of active turn and free length of the spring). Assume the spring coil is squared and ground.arrow_forwardDesign a helical spring to be used in spring balance with a wire diameter of 6mm and the outside diameter should be limited to 66mm. if the permissible shear stress of the spring material is 325 N/mm? and the Modulus of rigidity is 85kN/mm?. a) Compute the deflection of spring per active turn and the axial load on the spring considering the effect of curvature, take Wahl's factor as Kw= 1.1 b) Calculate the value of axial load neglecting the effect of stress factor. **Note: Please upload your handwritten working/solution to the link provided. The value of Mean diameter of the spring in mm . The Spring Index is. Shear stress factor, neglecting curvature effect . Deflection per active turn in mm Axial Load W in N .. Axial Load W in N. considering effect of curvature .arrow_forwardA helical compression spring has a scale of 500 lb/in., an outside diameter of 2.75 in, a free length of 8 inches and with squared and ground ends. The load is 1,000 lbs and the working stress on the wire material is 65000 psi. If the Wahl factor of 1.25 is to be used, calculate the following: A. The standard wire diameter B. The number of active coil if G = 10 800 000 psi C. The solid height D. The stress at solid heightarrow_forward
- A helical compression spring is subjected to a maximum force, Fmax of 1250 N. The deflection of the spring corresponding to the maximum force should be approximately 30 mm. The spring index is 6. The allowable shear stress is 350 MPa and the modulus of rigidity is 81 370 N/mm². Design the helical spring by calculating the wire diameter, mean coil diameter, number of active coils and the total number of coils. State all assumptions and decisions in your design.arrow_forwardI need the solution to be handwritten.arrow_forward1. Design a compression helical spring to carry a load of 500 N with a deflection of 25 mm. The spring index may be taken as 8. Assume the following values for the spring material: Permissible shear stress = 350 MPa Modulus of rigidity = 84 kN/mm2 4С - 1 0.615 Wahl's factor where C-spring index. 4С - 4arrow_forward
- A helical compression spring is wound using 0.12-in-diameter phosphor-bronze B159 wire. The spring index C = 10 and the total number of coils is N = 14. You may assume that the spring has both ends squared and ground and is supported between fixed ends. Also, Sgy = 0.45 · Sut- a. Estimate the spring rate. b. Estimate the static load corresponding to the yield strength. c. What should the free length of the spring be to ensure that when it is compressed solid the torsional stress does not exceed the yield strength? d. Calculate the critical value of the free length of the spring to avoid buckling.arrow_forwardNo cursivearrow_forwardPlease solve and include units in each step. Your work and solution will be appraciated much. Thank You!arrow_forward
- A spring made from music wire ASTM 228 steel has the following data:Free length=1.75” Outside diameter=0.561”Wire diameter=0.055” Applied load= 14 lbEnds=square and ground both ends hingedNumber of coils=10 G=11.85 x 106psi E= 30 Mpsi Findspring rate, force at solid length,check for buckling,coil clearance and hole diameterarrow_forwardProblem 4: A helical compression spring is to be cycled between 150 lbf and 300 lbf with a 1-in stroke. The number of cycles is low, so fatigue is not an issue. The coil must fit in a 2.1-in diameter hole with a 0.1-in clearance all the way around the spring. Use unpeened music wire with squared and ground ends. (a) Determine a suitable wire diameter, using a spring index of C = 7. (b) Determine a suitable mean coil diameter. (c) Determine the necessary spring constant. (d) Determine a suitable total number of coils. (e) Determine the necessary free length so that if the spring were compressed to its solid length, there would be no yieldingarrow_forwardA helical spring made of oil hardened and tempered steel compression springs, made of circular wire, is subjected to an axial force, which varies from (2.5 KN) to (3.5 KN). Over this range of force, the deflection of the spring should be approximately (5 mm). The spring index can be taken as (5). The spring has square and ground ends. If ultimate tensile strength of (1050 N/mm2) and modulus of rigidity of (81370 N/mm2). The permissible shear stress for the spring wire should be taken as (50 %) of the ultimate tensile strength.Design the spring and calculate the following: 1. Wire diameter; 2. Mean coil diameter; 3. Number of active coils; 4. Total number of coils; 5. Solid length of the spring; 6. Free length of the spring: 7. pitch of coils (p); 8. Required spring rate; 9. Actual spring rate; and 10. Draw a neat sketch .of the spring showing various dimensionsarrow_forward
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SEE MORE QUESTIONS
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Recommended textbooks for you
- Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning