Determine the maximum stress developed in the beam, Mechanical Engineering

Determine the maximum stress developed in the beam:

An I section in Figure is utilized as a beam. The beam is subjected to a bending moment of 2.5 kN m at its neutral axis. Determine the maximum stress developed in the beam.

 1648_Determine the maximum stress developed in the beam.png

Beam Section                                 Bending Stress Distribution

Figure

Solution

 Assume 1713_Determine the maximum stress developed in the beam1.png be the distance of centroid from the bottom face.

Then, 1713_Determine the maximum stress developed in the beam1.png  =∑ ay / ∑ a

   1713_Determine the maximum stress developed in the beam1.png= ((100 × 20) ×10 + (20 ×100) × 70 + (60 × 20) ×130) /((100 × 20) + (20 ×100) + (60 × 20))

= 60.8 mm

 Moment of inertia of the section around the horizontal axis passing through the centriod,

I = [(1/12) ×100 × (20)3 + (100 × 20)(60.8 - 10)2 ]

+[ (1/12) × 20 (100)3 + (20 ×100)(70 - 60.8)2 ]

+ [(1/12) × 60 (20)3 + (60 × 20)(130 - 60.8)2 ]

= 1285.04 × 104 mm4

Topmost layer distance, yt = 140 - 60.8 = 79.2 mm

Bottommost layer distance, yb = 60.8 mm

∴          ymax = yt = 79.2 mm

 Through the relation,  M/ I = σ/ y

We obtain,       σmax = ( M/ I) × ymax

Bending moment,  M = 2.5 kN m

                                   = 2.5 × 106 mm

∴          σmax =  (2.5 × 10 6/1285.04 × 104)  × 79.2 = 15.41 N/mm

∴  The maximum bending stress in the beam = 15.41 N/mm2.

Posted Date: 1/21/2013 7:32:21 AM | Location : United States







Related Discussions:- Determine the maximum stress developed in the beam, Assignment Help, Ask Question on Determine the maximum stress developed in the beam, Get Answer, Expert's Help, Determine the maximum stress developed in the beam Discussions

Write discussion on Determine the maximum stress developed in the beam
Your posts are moderated
Related Questions
We shutdown our furnace and always encountered crack on our piping at the weld joints. I investigated that upon shutdown the furnace cracking, our maintenance immediately remove th


Keywords used in appropriate technology: Hill Roads : Roads in hilly and mountainous terrain. Landslides : The slippage of mass of hill face. Retaining Walls : Str

(a) What is the function of a clutch in an automobile? Illustrate the principle of friction clutches with the help of neat diagrams. (b) Discuss the working and construction of

hiw can i fix the maximum temp of the aluminium

Q.What is Erosion-Corrosion in Steam Service? Depending on the steam quality, Let-down valves are subject to erosion-corrosion when pressure drop exceeds 1000kPa. Hard facing i

Determine tension in horizontal rope: Q:  A 500N cylinder, 1 m in diameter is loaded between cross pieces AE and BD that make an angle of 60º with each other and are pinn

Determine the maximum value of the coefficient of friction: A force of 200 N inclined at 60 o to the horizontal is applied to the block A weighing 400 N. find out whether blo

Flux Cored Arc Welding (FCAW) This is a variation of GMAW where solid wire is replaced by flux cored wire. The equipments and accessories are the same. Generally, flux cored wi

Write down the energy balance for a vapor stream going through a throttling valve (a valve that just reduces the pressure).  State your assumptions. Suppose a nonvolatile materi