Question

A man of mass 91 kg, is bungee jumping by using an elastic steel cable can be modeled as an elastic spring without damping as shown in Figure (below). The cable is stretched to a length such that vertical stretched length under static conditions is 16 mm as a SDOF system of vibration. The wind generates the vibration to excite the bridge that can be considered as harmonic motion with frequency 7 Hz and amplitude 5.0 mm. a) What is the level of vibration felt by the man hanging with the bridge? It is required to perform the severity analysis in terms human comfort and building/structural damage.

Answer 1

Solo: weight of the man = 91129 Scable = 16mm Sco var en avant = 24-76 wad (sve) Wn = 84:76 Padsen stay = 24.76 K=55,794, 325 Nm wind Suites the bridge with W: 21*F Colla co=21TY (7) F=7H2 = 43.9 Sad Isec. y = 5 sincat modeled as Harmonic motion at base: - Sot maximum displacement Cal 2 = V1 + (26650 co (Alb damping) Veitor (28) Son X El-BY 4 cl -1-7763 mm = 43.98 w 24-76 و 5 x = +1 2.1554) Scanned with CamScanner L - 2-3197 mm Steady state ampibende of vibration am

But, man skeleton may damage during transient also so for man transient i => 1%C250)%y'n be co X = 16 2 1554 x=74232 mm force, Experience by mam= kx = 55.794.375x7.4232 1000 = 414.17N 100 Be cause steady state Fx = laxa. = 55794.375x_/0 79 63 = 99.10 N so tatal face expert ole = Firen + Asteady - [5131277n] tatal x = a trou tastedy 19.1995 mm cam be dangerous to man at the same time can damage the bridge the vibration level can be controlled by providing dumping materials near the bridge and also the protective cauipment the mas is having coll the suit to which be is tied to sope should have good resistant and damping quality a TH It o be on © cs Scanned with CamScanner