Determine the normal stresses, Mechanical Engineering

Assignment Help:

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

Solution

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)


Related Discussions:- Determine the normal stresses

Determine the deflection of the spring, Determine the deflection of the spr...

Determine the deflection of the spring: A close coiled helical spring deflects 25 mm under a certain axial load. Determine the deflection of the second spring under the simila

Calculate required tractive effort, how can i calculate tractive effort for...

how can i calculate tractive effort for jet ski to start move and how much power necessary ?

Average force of resistance, Average force of resistance: A gun weighi...

Average force of resistance: A gun weighing 500 kN is utilized to fire a shell weighing 10 kN in a horizontal direction with a velocity of 500 metres/sec. With what initial ve

How to calculate total hysteresis loss?, Q.  The area of the hysteresis lo...

Q.  The area of the hysteresis loop of a given magnetic material is 50cm 2 with the two axes scaled as 1cm = 20AT and 1cm = 50mWb, for 50Hz frequency find the total hysteresis

Piston rings-basic components of engine , Piston Rings: Piston rings (Fig...

Piston Rings: Piston rings (Figure), fitted into the grooves around the piston, provide a tight sealing effect between the piston and the cylinder wall thus preventing leakage of

Equilibrium in concurrent force system - mechanics, Equilibrium in concurre...

Equilibrium in concurrent force system:   Sol.: The steps for solving problems of equilibrium in concurrent force system are as follows: 1.  First draw free body diagram

Solve the equations by factorization method, a) Answer the following equati...

a) Answer the following equations by Factorization method 10x+y+z =12 ; 2x+10y+z =13 ; 2x+2y+10z=14 b) Apply Gauss-Seidal Iteration method to solve the equations 20x+y-2z

Find out the effort required to run this machine, Find out the effort requi...

Find out the effort required to run this machine: The efficiency of a machine is 75% while an effort of 20 N is required to lift a load of 160 N. Compute the velocity ratio an

Determine strap beam with suitable demonstration, Determine strap beam with...

Determine strap beam with suitable demonstration. Here observe that R e becomes greater than P e by a magnitude of V while R i becomes less than P i by a magnitude equal to

The same magnitude as it did at the bottom, For the normal force in Figure ...

For the normal force in Figure to have the same magnitude at all points on the vertical track, the stunt driver must adjust the speed to be different at different points. Suppose,

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd