Analyse the state of stress at the critical section, Civil Engineering

Analyse the state of stress at the critical section:

A prismatic bar of circular section with 80 mm diameter is subjected to bending moment of 5 kN-m and a torque of 7 kN-m. Analyse the state of stress at the critical section.

Solution

Moment of the inertia, I = πD4/64 = π×804/64 = 2.016×106 mm4

Polar moment of inertia, J = πD4/32 = π/32 ×804 = 4.032×106 mm4

Maximum bending stress, σx = Mymax/I = 5×106×40/2.016×106 = 99.206 N/mm2

Maximum shear stress τxy  = 7 × 106 × 40/4.032×106 =69.444 N/mm2

Determination of Principal Stress

992_Analyse the state of stress at the critical section.png

Thus, we get

σ1  = 134.944 N/mm2  and σ2 = -35.737 N/mm2

τmax =σ1 -σ 2/2 = 85.34 N/mm2

Note

While the cross-section of the bar is hollow circular along with outer and inner diameters D and d respectively the analysis of stresses is to be carried through the similar procedure except for using the expressions,

 I = π/64 (D4 -d4) and J =π/32 (D4 -d4)

Posted Date: 1/30/2013 6:31:32 AM | Location : United States







Related Discussions:- Analyse the state of stress at the critical section, Assignment Help, Ask Question on Analyse the state of stress at the critical section, Get Answer, Expert's Help, Analyse the state of stress at the critical section Discussions

Write discussion on Analyse the state of stress at the critical section
Your posts are moderated
Related Questions
Define the Categories of Scaling? Scaling is classified into following three categories: i. Light scale - loss of surface mortar up to 5 mm deep, with surface exposure of co

what is the theory of roof trusses practical?

Define the Precedence Diagramming Methods a) Activity on Node (AON) with arrows for dependencies b) Uses all forms of precedence relationships

Resultant Force on a Given Area of an Inclined Plane The resultant force is calculated from the average pressure:    R = (AVERAGE P)(A)

Classification of beam

You wish to buy a house and you can afford to make a down payment of $50,000. Your monthly mortgage payment cannot exceed $2,000. If 30-year loans are available at 7.5% annual inte

Q. What is Rail Lubrication? Rail Lubrication is done on sharp curves where lateral wear is considerable. The function of Rail Lubrication is to lubricate or oil the running fa

Q. What is Multiple-cell box girder? Multiple-cell box girder: cells connected by top flanges vs. cells connected both by top and bottom flanges When the depth of a box gi

A retaining wall is battered away from the fill from bottom to top at an angle of 15° with the vertical. Height of the wall is 6 m. The fill slopes upwards at an angle 15° away fro