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
MIG / CO 2 WELDING In MIG / CO 2 welding the feeding of filler wire is machanised. If the welder moves the MIG / CO 2 torch the process is called semi automatic MIG / CO 2

how to produce a design that meets the specification given: Beam Dimensions W, H and T, where H=2W and T=W/20 • Bolt Size D1 • Side Plate thickness T2 and width W2 • Cradle Plat

Sweep pattern It is used to sweep the complete casting by means of a plane sweep. These are used for generating large shapes which are axis-symmetrical or prismatic in nature s


Q. Explain caustic Stress Corrosion Cracking? Dilution of the caustic prior to injection into a relatively hot stream will minimize the potential of caustic Stress Corrosion Cr

Q. What do you mean by Levelling Procedure? The Surveyor shall calculate required field adjustment in module elevation based on data from survey in conjunction with correspondi

Determine the maximum uniformly distributed load: A timber beam 150 mm wide & 300 mm deep is supported simply over a span of 4 m. determine the maximum uniformly distribute

The crate A of weight W=27lb is being pulled to the right by the winch at B. The crate starts at x=0 and is pulled a total distance 15ft over the rough surface for which the coeffi


In general, gear drive is useful for power transmission among two shafts, which are near to each other (at most at 1m distance). In addition, it has maximum efficiency whereas tran