Determine the normal stresses, Mechanical Engineering

Determine the normal stresses:

A short hollow pier 1.6 m × 1.6 m outsides as well as 1.0 m × 1.0 m intersides supports a vertical load of 2000 kN at a point located on a diagonal 0.5 m from the vertical axis of the pier. Determine the normal stresses at the 4 corners of the section of the pier, neglecting its self weight.

968_Determine the normal stresses.png



Figure illustrated the section of the pier. At point P, the load of 2000 kN is applied on the pier.

Area of cross-section A = 1.62 - 1.02 = 1.56 m2.

Section modulus, Z xx= Z yy 1.60 - 1.00 × (2/60) = 0.5875 m3

Eccentricity about XX-axis = Eccentricity around YY-axis

= 0.50 sin 45o = 0.353 m

Bending moment around XX-axis = Bending moment around YY-axis

= (2000 × 0.353)

= 706 kNm

Direct stress, f0  = P/ A =2000/1.56 = 1282.05 kN/m2  (compressive)

Bending stress around XX-axis = Bending stress around YY-axis

=± M/ Z =±     706 / 0.5785 = ± 1220.4 kN/m2

∴          Resultant stresses at corners,

f  = (P/ A) ± M xx/ Z xx ± M yy/ Z yy

Stress at corner A = 1282.05 + 1220.4 + 1220.4

                              = 3722.85 kN/m2 (compressive)

 Stress at corner B = 1282.05 - 1220.4 + 1220.4

                              = 1282.05 kN/m2 (compressive)

Stress at corner C = 1282.05 - 1220.4 - 1220.4

                           = - 1158.75 kN/m2 (tensile)

Stress at corner D = 1282.05 + 1220.4 - 1220.4

                              = 1282.05 kN/m2 (compressive)

Posted Date: 1/21/2013 7:16:25 AM | Location : United States

Related Discussions:- Determine the normal stresses, Assignment Help, Ask Question on Determine the normal stresses, Get Answer, Expert's Help, Determine the normal stresses Discussions

Write discussion on Determine the normal stresses
Your posts are moderated
Related Questions
Maintenance of Railway Line Importance of Maintenance The need for maintenance of railway lines arises out of the following considerations : (a) The track rests on

Resultant of force system: Resultant is single force that produces the same effect as produced by the number of forces jointly in the system. In equilibrium magnitude of resul

calculate the vertical reaction at A in Newtons

A straight rod of length L is released on a friction less horizontal floor in a vertical position . As it falls( also slips) , the distance of a point on the rod from the lower end

Q. What do you know about Direct welds? It is a welding method in which one or more electrodes oppose each other, contacting both sides of the work and with the current passing

how does shearing failure occurs

BASIC DEFINITIONS - Air transportation: A civil engineer dealing with airport engineering shall have to know the precise meaning of some terms. These are defined below :

maximum rpm at engine

Superheate d Steam: When the dry saturated steam is heated further at constant pressure, the temperature of it rises up above the saturation temperature. This rise in tempera