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
Consider a car of mass m1 is towing a trailer of mass m2 through a tow bar of stiffness k. Drag forces proportional to the car velocity (b1 v1) and the trailer velocity (b2 v2) a

Cross Drainage Works: Culverts A large number of culverts are needed for taking care of the streams crossing the railway lines. The culverts can be one of the followi

Advantages of Laser Welding Process   1) Narrow deep penetration welds capable of being produced in atmosphere. 2) Low thermal distortion - due to less heat input and paral

Q. Explain about Surface Preparation? All oil, grease, salts, and any other contaminants detrimental to the formation of a good coating bond or coating quality must be removed

Compute the intensity of normal stress: A uniform steel bar of 2 cm × 2 cm area of cross section is subjected to axial pull of 40000 kg. Compute the intensity of normal stres

Construct of a diagonal scale: During construct of a diagonal scale of RF = 1/48, displaying yards, inches and feet to represent a maximum length of 7 yards. Scratch a distanc

Q. What do you mean by Compression moulding? In compression molding, a material normally in power or perform shape , is loaded directly into the hot die cavity, pressure from

Find the maximum shear stress - stepped circular bar: A stepped circular bar ABC 4 m long fixed at one of the end 'A' is subjected to a torque of 10 kN-m. If the portion AB is

Example of Equilibrium: Express in terms of θ, β and W the force T necessary to hold weight in equilibrium as shown in the figure given below. Also derive an expression f

METAL TRANSFER IN CO2 WELDING In CO 2 welding, two distinct types of metal transfers are identified viz. short circuiting transfer and free flight globular transfer. Short Cir