Calculated the magnitude of the instantaneous stress, Mechanical Engineering

Calculated the magnitude of the instantaneous stress:

While a concentrated force of 1 kN is applied at the midspan point of a simply supported beam a static deflection of 5 mm is generated. The same load generates a maximum stress of 158 MN/m2. Calculated the magnitude of the instantaneous stress generated when a weight of 10 kg is allowed to fall through a height of 12 mm onto the beam at midspan. What shall be the instantaneous deflection?

Solution                                           

Let We be the equivalent slowly applied load which generates the same static deflection δmax as that of the impact load.

Then,

We/δmax =      1 kN /0.005 m

= 200 kN/m

Now, equating the work completed by the impact load to that done by the equivalent static load, we obtain

(We/2) δ max     = W ( h + δ max )

i.e.

(We /2) × (We/200) = ((10 × 9.81)/1000) (0.012 + We /200)

 

2111_Calculated the magnitude of the instantaneous stress.png

Therefore,

1400_Calculated the magnitude of the instantaneous stress1.png

= 0.981 + 0.6932 = 0.791 kN

But

δ max     = We / 200  = 0.791 /200

= 0.003955 m = 3.955 mm ; 4 mm

 This is given that the load of 1 kN generates a maximum stress of 158 MN/m2. Thus, a load of We must produce a maximum stress, σmax equal to (158 We) MN/m2.

∴          σ max  = 158 × 0.791 = 124.978 MN/m2  ; 125 MN/m2

Therefore, the maximum stress & maximum deflection are 125 MN/m2 & 4 mm, respectively.

Posted Date: 1/21/2013 6:39:12 AM | Location : United States







Related Discussions:- Calculated the magnitude of the instantaneous stress, Assignment Help, Ask Question on Calculated the magnitude of the instantaneous stress, Get Answer, Expert's Help, Calculated the magnitude of the instantaneous stress Discussions

Write discussion on Calculated the magnitude of the instantaneous stress
Your posts are moderated
Related Questions
how to culculate stress in unsymmetrical bending

Dear Sir I would to know what is the min. time required for carbon steel tube A214 @ zero C to 50 C

Select a standard rolled steel I-section for the simply supported beam shown in figure below. Select an appropriate factor of safety and material strength. Include references for

Q. Explain working of Tubesheets? The tube and tube pitch selected shall be approved by WorleyParsons Canada. The preferred tube pitch shall be a minimum of 1.3 x tube OD and

A 6 cm diameter rubber ball weighing 5 g is used to plug a 4 cm hole in the base of a tank. The tank is in use and is gradually emptying. At approximately what depth will the ball

Determine net work done: 5 m 3   of air at 2bar, 27 0 C is compressed to 6bar pressure following PV 1. 3   = constant. It is expanded subsequently adiabaticall

Q. Flange Assembly with Torque Measurement? Select the proper bolts and gasket for the intended service. Use only new, undamaged gaskets. Lubricate the bolt threads and nut

1 Prepare an updated sketch of the electro-hydraulic system shown in Figure showing the actuators in their start position appropriate to your allocated actuator sequence. 2 By u

Volume fraction of fibres: The epoxy material is prepared to be stressed to its full strength. What must be volume fraction of fibres? Solution Here σ′ = 1200 MPa,

Consider the expansion loop displayed in the diagram below, which is part of a long pipeline.  The loop is made up of a uniform pipe section and is subjected to a temperature raise