2. In a laboratory test of a beam loaded by end couples, the fibers at layer AB inFigure below are found to increase 60 x 10-3 mm whereas those at CD decrease100 x 10-3 mm in the 200-mm-gage length. Using E=70 GPa, determine theflexural stress in the top and bottom fibers.200 mm30 mm| 120 mm30 mmPlease solve according tothe exporters of a typicalsolution.4. Stress in BeamsThe beam in figure (1) shows two sectionEF, -0* fo. •da = o(ab) and (cd) that separate by distance (dx).leNeutealfecedA-oFigure (2) show the deflected shapeof the beam.Since the (vtA) is the momentof the differential area (A4) aboutthe neutral axis, the integral6 = hk = ydÐFig.1Fig 3f ydA ) is the total moment of areaAy' -oyd0efef pd0hence :Strain =%3Donly (y) can be equal zero, Le. the neutral axis must contain the centroid ofthe cross-sectional area .EF, -0that leads to the shear stress formula (V, = |t, *dA)Neutral surfaceydeEF,-0That leads to the formula of shear (t.dA=0)EM, - 0 = S z(0, * d4) - opd02y• da - 0O = E * ɛ(Hook's law)deThe integral =y dA is the product of inertia (P). which is zeroonly if ) or (2) is an axis of symmetry or principal axis.O = ELd'dE M, - 0.M - M,M - fy (o. • dA)Fig.2

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2. In a laboratory test of a beam loaded by end couples, the fibers at layer AB in Figure below are found to increase 60 x 10-3 mm whereas those at CD decrease 100 x 103 mm in the 200-mm-gage length. Using E=70 GPa, determine the flexural stress in the top and bottom fibers. 200 mm 30 mm 120 mm 30 mm

2. In a laboratory test of a beam loaded by end couples, the fibers at layer AB in Figure below are found to increase 60 x 10-3 mm whereas those at CD decrease 100 x 103 mm in the 200-mm-gage length. Using E=70 GPa, determine the flexural stress in the top and bottom fibers. 200 mm 30 mm 120 mm 30 mm

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Slope and Deflection

The slope in a deflected beam is described as an angle in radians made by the tangent of the section with the original axis of the beam. The deflection at any point on the axis of the beam is defined as the lateral displacement of the point before and after loading.

Question

2. In a laboratory test of a beam loaded by end couples, the fibers at layer AB in
Figure below are found to increase 60 x 10-3 mm whereas those at CD decrease
100 x 10-3 mm in the 200-mm-gage length. Using E=70 GPa, determine the
flexural stress in the top and bottom fibers.
200 mm
30 mm
| 120 mm
30 mm
Please solve according to
the exporters of a typical
solution.
4. Stress in Beams
The beam in figure (1) shows two section
EF, -0
* fo. •da = o
(ab) and (cd) that separate by distance (dx).
le
Neuteal
fece
dA-o
Figure (2) show the deflected shape
of the beam.
Since the (vtA) is the moment
of the differential area (A4) about
the neutral axis, the integral
6 = hk = ydÐ
Fig.1
Fig 3
f ydA ) is the total moment of area
Ay' -o
yd0
ef
ef pd0
hence :
Strain =
%3D
only (y) can be equal zero, Le. the neutral axis must contain the centroid of
the cross-sectional area .
EF, -0
that leads to the shear stress formula (V, = |t, *dA)
Neutral surface
yde
EF,-0
That leads to the formula of shear (t.dA=0)
EM, - 0 = S z(0, * d4) - o
pd0
2y• da - 0
O = E * ɛ
(Hook's law)
de
The integral =y dA is the product of inertia (P). which is zero
only if ) or (2) is an axis of symmetry or principal axis.
O = EL
d'd
E M, - 0.M - M,
M - fy (o. • dA)
Fig.2

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