Determine maximum fibre stress - beam, Mechanical Engineering

Assignment Help:

Determine Maximum fibre stress:

A beam of rectangular section of 80 mm to 120 mm carries a uniformly distributed load of 40 kN/m over a span of 2 m an axial compressive force of 10 kN. Determine

1.      Maximum fibre stress,

2.      Fibre stress at a point 0.50 m from the left end of the beam & 40 mm below the neutral axis.

199_Determine Maximum fibre stress.png

                                     (1) Loading                                          (2) Cross-section

Figure

Solution

Bending moment, M = (w × e 2) /8= (40 × 22)/8 = 20 kN-m = 20 × 106  N-mm

Section modulus, Z = (1/6) × 80 × (120)2  = 1.92 × 105  mm3

Moment of inertial, I = (1/12) × (80) × (120)3 = 11.52 × 106  mm4

Axial load, P = 10 kN = 10 × 103  N

Direct stress, f0  = P/A =10 × 103/ (80 × 120) = 1.04 N/mm2

Bending stress,  f b =± M/ Z  =( 20 × 106 )/(1.92 × 105) = ± 104.16 N/mm2

∴          Maximum fibre stress = 1.04 + 104.16 = 105.20 N/mm2 (compressive)

∴          Bending moment at 0.50 m from left end will be,

M = ( - 40 × 0.50 + 40 × 0.502 / 2)

= - 15 kN-m

= 15 × 106  N-mm (sagging)

∴          Bending stress at 40 mm below the neutral axis will be,

= (M/I) . y

= (15 × 106 )/(11.52 × 106 ) × (- 40)

=- 52.08 N/mm2  (tensile)

∴          Resultant fibre stress = 1.04 - 52.08

                                             =- 51.04 N/mm2 (tensile)


Related Discussions:- Determine maximum fibre stress - beam

Head loss, calculate the head required

calculate the head required

Determine the tension and reaction in cable - mechanics, Q:  The12m boom A...

Q:  The12m boom AB weight 1 KN, the distance of center of gravity G is 6 m from point A.  For the position given, determine the tension T in cable and reaction at B.

Material science, what is the main process to get steel hard

what is the main process to get steel hard

Thermal, how do i solve for thickness of insulation when i only have the r ...

how do i solve for thickness of insulation when i only have the r value

Radiation in welding, what is the health effects of ultraviolet ray on the ...

what is the health effects of ultraviolet ray on the eyes of welders

Strain, is strain in bending important parameter to consider?

is strain in bending important parameter to consider?

Find out the mechanical advantage of the machines, Find out the mechanical ...

Find out the mechanical advantage of the machines: A lifting machine may lift 800 N by the application of 100 N. Distance moved by the effort is 100 cm. At the same time load

What are the objectives of bearing capacity, What are the objectives of bea...

What are the objectives of bearing capacity? The objectives of bearing capacity: a. identify the possible modes of failure that a shallow foundation can undergo, b. under

What do you mean by machinibility, (a) What do you mean by machinibility ? ...

(a) What do you mean by machinibility ? Discuss the factors which come into play while evaluating the machinability of any metal. Also describe machinability index. (b) Brass co

Aluminium, ALUMINIUM Aluminium was first generated in year of 1825. Pr...

ALUMINIUM Aluminium was first generated in year of 1825. Presently it is generated in quantity second only to steel. This is the most abundant metallic element on the crust of

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