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

Simple harmonic motion, how to e solve motion of followers in simple harmon...

how to e solve motion of followers in simple harmonic motion. what is the angle thita?

Compare otto cycle with diesel cycle, Compare otto cycle with Diesel cycle:...

Compare otto cycle with Diesel cycle: Sol.: These two cycles can be compared on the basis of either the same compression ratio or the same maximum pressure and temperature.

What is the make group of euler operators, The Make Group of Euler Operator...

The Make Group of Euler Operators The Make group consists of four operators for adding some elements into the existing model creating a new one, and a Make-Kill operator for ad

Dynamic machine routing, Dynamic Machine Routing  Machine routing ident...

Dynamic Machine Routing  Machine routing identifies the machines that are needed for each of the operation of a given job. Within the JSP or Job Shop Scheduling Problem model,

Low lube oil pressure security in API612 , What type of low lube oil securi...

What type of low lube oil security recommended for API612 steam turbines.(Electronic/Mechanical). Please give refrences

Compound stress, Compound Stress: Define Compound Stress. Sol.: ...

Compound Stress: Define Compound Stress. Sol.:   Simple stresses mean tensile stress or compressive stress or shear stress. The tensile and compressive stresses act on p

Determine the greatest load carried by the composite springs, Determine the...

Determine the greatest load carried by the composite springs: A composite spring contain two close-coiled helical spring associated in series, each spring has 10 coils at a me

Fatigue loading on materials, what are the factors that affecting the fatig...

what are the factors that affecting the fatigue behaviour of materials?

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