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Old Dec 3rd 2009, 12:29 PM   #1
JAW
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Join Date: Oct 2009
Posts: 4
Tee section beam compressive and tensile stresses problem

Hi, i have the following problem to solve. Any assistance would be greatly appreciated.

A tee section beam (T) is rigidly built into a wall at one end to produce a horizontal cantilever beam. The tee section is 100mm wide at the top, has an overall vertical height of 150mm and has a uniform secton thickness of 15mm. The beam protrudes from the wall a distance of of 3m. Concentrated loads of 3 kn and 4.5kn are applied at the free end and at the mid point respectively. Assuming the modulas of elasticity for steel is 210 GN/m^2 determine

A. The max compressive and tensile stresses in the beam..
B. The resulting radius of curvature of the beam..

This is what i have so far, please advise if this is the correct way to tackle this problem....

Taking moments about R1 :-
(1.5x4.5)+(3x3)-3R2=0
5.25KN=R2

R1=4.5+3-5.25=2.25 KN

Then i have calculated shear forces and beam moments

I get SF at A = -2.25 SF at B = -2.25 +4.5=2.5 SF at C = 2.25+3-5.25=0

BM at A =0 Bm at B 1.5x-2.25= -3.375
Bm at c (3x-2.25)+(1.5x4.5)+(3x0)-(5.25x0)=0

MAx BM therefore = -3.375 KN/m

Next i have calculated y' (y bar)

(3000x15x142.5)+(150x15x7.5)=y'(3000x15)+(150x15)
6429375=y'(47250)
y'=136.071 mm

Next i have calulated Ixx by use of the parallel axis therom of rectangle

Ixx=bd^3/12

(3000x15^3/12)+(3000x15x(150-136.071)^2+(15x150^3/12)+15x150x(136.071-75)^2
=17397759.27mm^4
17.398m^4

Is this the correct way to proceed with this porblem!!!

Then i have the formula M/I=E/R=O/Y

I'm required to find O so through transposition O=MY/I
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beam, compressive, problem, section, stresses, tee, tensile



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