Helical Springs When close-coiled helical spring, composed of a wire of round rod of diameter d wound into a helix of mean radius R with n number of turns, is subjected to an axial load P produces the following stresses and elongation:
The maximum shearing stress is the sum of the direct shearing stress τ1 = P! and the torsional shearing stress τ" = Tr#, with T = PR$
This formula neglects the cur%ature of the spring$ This is used for light spring where the ratio d&R is small$ 'or hea%( springs and considering the cur%ature of the spring, !$)$ Wahl formula a more precise, it is gi%en b(:
where m is called the spring index and *&m - 1+*&m - &+ is the Wahl 'actor$ The elongation of the bar is
otice that the deformation δ is directl( proportional to the applied load P$ The ratio of P to δ is called the spring constant and is e.ual to
Springs in Series 'or two or more springs with spring laid in series, the resulting spring constant is gi%en b(
where 1, ",$$$ are the spring constants for different springs$ Springs in Parallel 'or two or more springs in parallel, the resulting spring constant is
Problem 343 /etermine the maximum shearing stress and elongation in a helical steel spring composed of "0 turns of "0-mmdiameter wire on a mean radius of 0 mm when the spring is supporting a load of 1$2 $ 3se 4.$ *5-10+ and 6 = 75 6Pa$ Problem 343
HideClick here to show or hide the solution → Equation (3-10) Where: ! 1"# k$ ! 1#00 $% & ! '0 d ! 0 % n ! 0 turns ! &*d ! ('0)*0 ! '
answer
answer
Problem 344 /etermine the maximum shearing stress and elongation in a bron8e helical spring composed of "0 turns of 1$0-in$diameter wire on a mean radius of & in$ when the spring is supporting a load of 200 lb$ 3se 4.$ *5-10+ and 6 = 9 109 psi$ Solution 344
HideClick here to show or hide the solution → Equation (3-10) Where ! #00 l+% & ! , in d ! 1 in% n ! 0 turns ! &*d ! (,)*1 !
answer
answer
Problem 344 /etermine the maximum shearing stress and elongation in a bron8e helical spring composed of "0 turns of 1$0-in$diameter wire on a mean radius of & in$ when the spring is supporting a load of 200 lb$ 3se 4.$ *5-10+ and 6 = 9 109 psi$ Solution 344
HideClick here to show or hide the solution → Equation (3-10) Where ! #00 l+% & ! , in d ! 1 in% n ! 0 turns ! &*d ! (,)*1 !
answer
answer
Problem 345 ! helical spring is fabricated b( wrapping wire 5& in$ in diameter around a forming c(linder 7 in$ in diameter$ ;ompute the number of turns re.uired to permit an elongation of & in$ without exceeding a shearing stress of 17 si$ 3se 4.$ *5-+ and 6 = 1" 10 9 psi$ Solution 345
HideClick here to show or hide the solution → Equation (3-')
answer
Problem 346 ;ompute the maximum shearing stress de%eloped in a phosphor bron8e spring ha%ing mean diameter of "00 mm and consisting of "& turns of "0 0-mm diameter wire when the spring is stretched 100 mm$ 3se 4.$ *5-10+ and 6 = &" 6Pa$ Solution 346
HideClick here to show or hide the solution
Where δ ! 100 % & ! 100 d ! 0 % n ! , turns . ! , 000 /a
→ Equation (3-10) Where ! &*d ! (100)*0 ! 10
answer
Problem 347 Two steel springs arranged in series as shown in 'ig$ P-5&< supports a load P$ The upper spring has 1" turns of "2mm-diameter wire on a mean radius of 100 mm$ The lower spring consists of 10 turns of "0-mm diameter wire on a mean radius of <2 mm$ f the maximum shearing stress in either spring must not exceed "0 0 )Pa, compute the maximum %alue of P and the total elongation of the assembl($ 3se 4.$ *5-10+ and 6 = 75 6Pa$ ;ompute the e.ui%alent spring constant b( di%iding the load b( the total elongation$
Solution 347
HideClick here to show or hide the solution → Equation (3-10) or 2rin (1)
or 2rin ()
4se answer
5otal elonation:
answer
Equi6alent s2rin constant7 k equi6alent:
answer
Problem 348 ! rigid bar, pinned at >, is supported b( two identical springs as shown in 'ig$ P-5&7$ 4ach spring consists of "0 turns of 5&-in-diameter wire ha%ing a mean di ameter of 9 in$ /etermine the maximum load W that ma( be supported if the shearing stress in the springs is limited to "0 si$ 3se 4.$ *5-+$
Solution 348
HideClick here to show or hide the solution → Equation (3-')
or this 2ro+le7 the critical s2rin is the one su+8ected to tension" 4se ! #1'"9# l+"
answer
Problem 349 ! rigid bar, hinged at one end, is supported b( two identical springs as shown in 'ig$ P-5&$ 4ach spring consists of "0 turns of 10-mm wire ha%ing a mean diameter of 120 mm$ ;ompute the maximum shearing stress in the springs, using 4.$ *5-+$ eglect the mass of the rigid bar$
Solution 349
HideClick here to show or hide the solution
→ Equation (3-') or s2rin at let:
answer
or s2rin at riht:
answer
Problem 350 !s shown in 'ig$ P-520, a homogeneous 20-g rigid bloc is suspended b( the three springs whose lower ends were originall( at the same le%el$ 4ach steel spring has "& turns of 10-mm-diameter on a mean diameter of 100 mm, and 6 = 75 6Pa$ The bron8e spring has &7 turns of "0-mm-diameter wire on a mean diameter of 120 mm, and 6 = &" 6Pa$ ;ompute the maximum shearing stress in each spring using 4.$ *5-+$
Solution 350
HideClick here to show or hide the solution → Equation (1)
→ Equation ()
→ Equation (3) ro Equation (1)
u+stitute 1 to Equation (3)
→ Equation (,) ro Equation ()
u+stitute to Equation (,)
or steel at let: answer
or steel at riht: answer
or 2hos2hor +ron;e: answer
