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
Contents of Cast Iron: Cast Iron or CI is prepared form melting pig iron in cupola furnace or in electric furnace. This furnace offers better quality. CI contains various


Ask question #Minimum 100 words awrite short note on the the hierarchical system structure involving various level


An experiment to determine the convection coefficient associated with airflow over the surface of a thick stainless steel casting involves insertion of thermocouples in the casting

Deficient Frame and Redundant Frame - truss: Deficien t Frame: If the numbers of member in the frame are less than (2 j -3), then the frame is called as deficient fr

write short note on''coefficient of insensitiveness''of governors.

Kineti c (Dynamic) Friction: When applied force exceeds limiting friction the body starts moving over the other body and the friction of resistance experienced by the body a

What are the reasons of attribution of raft foundations by rigid method? The overdesign of raft foundations by rigid method can be attributed to three major reasons: a. Ther

Remove cover left crank case and check for leakage: Before attending oil seal leakage check if any leak is there in the highlighted points - Neutral switch "o" ring leak, Shifter