Determine the stress in a fiber (in psi) located 1inch from the top of the beam and 4 feet from the hinge. Refer to the illustrative example in the image below. Flexure FormulaExampleA simply supported beam, 2 in wide by 4 in high and 12 ft long is subjected to a concentrated load of2000 lb at a point 3 ft from one of the supports. Determine the maximum fiber stress and the stress ina fiber located 0.5 in from the top of the beam at midspan.EMR2 = 012R₁ = 9(2000)R₁ = 1500 lbEMRI = 012R₂ = 3(2000)R₂ = 500 lbMaximum fiber stress:c = 2 in(fb)marN.A.Mm6b = 2 in(fb)maz 10, 125 psi=fb =MeIfbMm 3000 lb-ftMyI4500(12) (2)2(4³)12b= 4 in3000(12)(1.5)2(4³)12fb = 5,062.5 psianswerR₁answer2000 lb: 1500 lbStress in a fiber located 0.5 in from the top of the beam at mid-span450090.5 iny = 1.5 in3 ftN.A.12 ft4500 lb-ftb = 2 inShear DiagramMm9 ft-500 lbMoment Diagramb=4 inR₂

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Answered: Determine the stress in a fiber (in…

Determine the stress in a fiber (in psi) located 1inch from the top of the beam and 4 feet from the hinge. Refer to the illustrative example in the image below.

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Question

Determine the stress in a fiber (in psi) located 1inch from the top of the beam and 4 feet from the hinge. Refer to the illustrative example in the image below.

Flexure Formula
Example
A simply supported beam, 2 in wide by 4 in high and 12 ft long is subjected to a concentrated load of
2000 lb at a point 3 ft from one of the supports. Determine the maximum fiber stress and the stress in
a fiber located 0.5 in from the top of the beam at midspan.
EMR2 = 0
12R₁ = 9(2000)
R₁ = 1500 lb
EMRI = 0
12R₂ = 3(2000)
R₂ = 500 lb
Maximum fiber stress:
c = 2 in
(fb)mar
N.A.
Mm
6
b = 2 in
(fb)maz 10, 125 psi
=
fb =
Me
I
fb
Mm 3000 lb-ft
My
I
4500(12) (2)
2(4³)
12
b= 4 in
3000(12)(1.5)
2(4³)
12
fb = 5,062.5 psi
answer
R₁
answer
2000 lb
: 1500 lb
Stress in a fiber located 0.5 in from the top of the beam at mid-span
4500
9
0.5 in
y = 1.5 in
3 ft
N.A.
12 ft
4500 lb-ft
b = 2 in
Shear Diagram
Mm
9 ft
-500 lb
Moment Diagram
b=4 in
R₂

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