The cross section of a beam is a T with the dimension shown in Figure. The moment at the section is M = 4 kip-ft. Determine the: Location of the internal axis of the cross section; Moment of inertia with respect to the neutral axis; Maximum tensile stress and the maximum compressive stress on the cross section. y_c = sigma y_ci A_i/sigma A_i, l =bh^3/12 + Ad^2
Solution
M = moment = 4 kip-ft = 4000 lb-ft = 333.33 lb-in
Area of flage = 1x5 = 5 in2
area of web = 1x5 = 5 in2
y for flange = 5+1/2 = 5.5in
y for web = 5/2 = 2.5in
yc = [5x5.5+5x2.5]/[5+5]
yc = 4in
yt = distance between centre of gravity of section to upper fibre = 5 + 1 - 4 = 2in
I = (bd 3 /12) + Ah 2
moment of inertia for flange
I = (5x1 3 /12) + 5x(5.5-4) 2 = 11.67 in4
moment of inertia for web
I = (1x5 3 /12) + 5x(4-5/2) 2 = 21.67 in4
total moment of inertia = 11.67+21.67 = 33.34 in4
Maximum tensile stress occurs at lower extreme fibre
tensile stress = (M/I) Yc = (333.33/21.67 )4 = 61.53 psi
Maximum compression stress occurs at upper extreme fibre
compression stress = (M/I) Yt = (333.33/21.67 )2 = 30.76 psi
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The cross section of a beam is a T with the dimension shown in Figure-.docx
1. The cross section of a beam is a T with the dimension shown in Figure. The moment at the
section is M = 4 kip-ft. Determine the: Location of the internal axis of the cross section; Moment
of inertia with respect to the neutral axis; Maximum tensile stress and the maximum compressive
stress on the cross section. y_c = sigma y_ci A_i/sigma A_i, l =bh^3/12 + Ad^2
Solution
M = moment = 4 kip-ft = 4000 lb-ft = 333.33 lb-in
Area of flage = 1x5 = 5 in2
area of web = 1x5 = 5 in2
y for flange = 5+1/2 = 5.5in
y for web = 5/2 = 2.5in
yc = [5x5.5+5x2.5]/[5+5]
yc = 4in
yt = distance between centre of gravity of section to upper fibre = 5 + 1 - 4 = 2in
I = (bd 3
/12) + Ah 2
moment of inertia for flange
I = (5x1 3
/12) + 5x(5.5-4) 2
= 11.67 in4
moment of inertia for web
I = (1x5 3
/12) + 5x(4-5/2) 2
= 21.67 in4
total moment of inertia = 11.67+21.67 = 33.34 in4
2. Maximum tensile stress occurs at lower extreme fibre
tensile stress = (M/I) Yc = (333.33/21.67 )4 = 61.53 psi
Maximum compression stress occurs at upper extreme fibre
compression stress = (M/I) Yt = (333.33/21.67 )2 = 30.76 psi
![The cross section of a beam is a T with the dimension shown in Figure. The moment at the
section is M = 4 kip-ft. Determine the: Location of the internal axis of the cross section; Moment
of inertia with respect to the neutral axis; Maximum tensile stress and the maximum compressive
stress on the cross section. y_c = sigma y_ci A_i/sigma A_i, l =bh^3/12 + Ad^2
Solution
M = moment = 4 kip-ft = 4000 lb-ft = 333.33 lb-in
Area of flage = 1x5 = 5 in2
area of web = 1x5 = 5 in2
y for flange = 5+1/2 = 5.5in
y for web = 5/2 = 2.5in
yc = [5x5.5+5x2.5]/[5+5]
yc = 4in
yt = distance between centre of gravity of section to upper fibre = 5 + 1 - 4 = 2in
I = (bd 3
/12) + Ah 2
moment of inertia for flange
I = (5x1 3
/12) + 5x(5.5-4) 2
= 11.67 in4
moment of inertia for web
I = (1x5 3
/12) + 5x(4-5/2) 2
= 21.67 in4
total moment of inertia = 11.67+21.67 = 33.34 in4](https://image.slidesharecdn.com/thecrosssectionofabeamisatwiththedimensionshowninfigure-230203002030-5d304a34/85/The-cross-section-of-a-beam-is-a-T-with-the-dimension-shown-in-Figure-docx-1-320.jpg)
