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
Illustrate how the Rankine cycle efficiency is improved by the following : a. Lowering the condenser pressure. b. Increasing the pressure of steam. c. Superheating the ste

Space mass and weight: The geometric region occupied by bodies called as space. When body changes its position w. r.t. the other bodies, then body is known to be in motion.

Plate clutch movement on center clutch : Place plate clutch on centre clutch as shown in the picture and move the plate clutch up and down, while moving the plate clutch in the ce

Resistant Body: A body is called resistant body if this is capable of transmitting the needed forces with negligible deformation. Machine: A machine is a mechanism or a se

Explain concept of Drill Power feed of the spindle is a common feature. Also coolant system is a ordinary feature of the radial drilling machine. Radial drilling machines ca

How to determine Forces and Torque of slider crank mechanism?

Pressure - Thermodynamics: While working in the system, thermodynamic medium exerts a force on boundaries of vessel in which it is kept. The vessel may be a container, or an e

SAFETY IN TIG WELDING-Radiation Energy Hazard Radiant energy may cause injury to the welder in two areas, eye and the skin. Any personnel, whether the welder, inspection person


Q. Define Pattern draft or taper? It is also termed as "draw". It is the taper placed on the pattern surface that are parallel to the direction in which the pattern is withdraw