Given: Maximum positive shear = 3960 N Maximum negative shear = 5640 N Maximum positive moment = 20700 N-m Maximum negative moment = 2400 N-m Location of maximum shear from the left end of beam = 19 m Location of maximum moment from the left end of beam = 14 m Determine the maximum bending stress (in MEGAPASCALS on the beam) given the cross-section on figure. Exercise caution in choosing the value of "c". (Be it known obviously that for beams with irregular cross-sections, Ctop ≠ Cbottom) Note: Measurements in figure is in millimeters. Kindly Draw the Shear and Moment Diagram or FBD if necessary. Compute for all of the necessary elements, Include the proper units, use the proper formula and round-off all the answers and final answers to 2 decimal places.
Given: Maximum positive shear = 3960 N Maximum negative shear = 5640 N Maximum positive moment = 20700 N-m Maximum negative moment = 2400 N-m Location of maximum shear from the left end of beam = 19 m Location of maximum moment from the left end of beam = 14 m Determine the maximum bending stress (in MEGAPASCALS on the beam) given the cross-section on figure. Exercise caution in choosing the value of "c". (Be it known obviously that for beams with irregular cross-sections, Ctop ≠ Cbottom) Note: Measurements in figure is in millimeters. Kindly Draw the Shear and Moment Diagram or FBD if necessary. Compute for all of the necessary elements, Include the proper units, use the proper formula and round-off all the answers and final answers to 2 decimal places.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Question
Given:
Maximum positive shear = 3960 N
Maximum negative shear = 5640 N
Maximum positive moment = 20700 N-m
Maximum negative moment = 2400 N-m
Location of maximum shear from the left end of beam = 19 m
Location of maximum moment from the left end of beam = 14 m
Determine the maximum bending stress (in MEGAPASCALS on the beam) given the cross-section on figure. Exercise caution in choosing the value of "c". (Be it known obviously that for beams with irregular cross-sections, Ctop ≠ Cbottom)
Note: Measurements in figure is in millimeters.
Kindly Draw the Shear and Moment Diagram or FBD if necessary. Compute for all of the necessary elements, Include the proper units, use the proper formula and round-off all the answers and final answers to 2 decimal places.
Transcribed Image Text:Mechanics of Deformable Bodies
I =
bh3
SHEAR STRESS FORMULA
12
Mc
Mc
or
Bending Stress
I
I
Area = A'
MOVING LOADS
For more than one moving Load:
1. The bending moment under a particular load is a
maximum when the center of the beam is midway
between that load and the resultant of all loads on the
y'
A
span of the beam.
2. The maximum shear occurs at the reaction where the
resultant load is nearest. Usually, it happens if the
biggest load is over that support and as many as possible
of the remaining loads are still on the span.
PROCEDURE:
1. Determine the location of the Resultant relative
to the given loads.
2. Put the center of the load and the resultant to
coincide with the beam.
3. Calculate supports.
4. Section/cut the beam where the load in
consideration is located.
The shear stress in the
%3D
VQ
T =
It
member at the point located at a
distance
This stress is assumed to be
constant and therefore averaged
y from the neutral axis.
across the width t of the member.
MOST ECONOMIC SECTIONS
V= the shear force
I = the moment of inertia of the ENTIRE cross-
sectional area calculated about the neutral axis.
When a structural section is selected to be used as a
beam, the section modulus must be equal to or greater
than the section modulus determined by the flexure
equation;
t = the width of the member's cross section measured
at the point where the shear stress is to be determined.
|M\max
Oallow
This equation indicates that the section modulus of the
selected beam must be equal to or greater than the ratio
of the bending moment to the working stress.
A design engineer is often required to select the lightest
standard structural shape (such as a W-shape) that can
carry a given loading in addition to the weight of the
beam. Following is an outline of the selection process:
1. Determine the maximum shear and moment of
the (loaded) beam. A V-M diagram is the fastest
way to do it. Neglect beam weight at this point.
2. Determine the minimum allowable section
Q = 2ÿ'\A'j + y½A'½
modulus, Smin
3. Choose the lightest shape from the list of
structural shapes where S> Smin
4. Calculate the maximum bending stress in the
selected beam caused by the loading PLUS the
beam self weight. If ơmax < Oallow then the
selection is finished. If it is not satisfied, choose
the second lightest shape.
5. Repeat the selection process until a satisfactory,
economic shape is found.
Q = j'A'
Q = j'A'
Q = j' A', where A' is the area of the top (or bottom)
portion of the member's cross-section, above (or below)
the section plane where t is measured and y' is the
distance from the neutral axis to the centroid of A'. or
A'= Area of the section above/below t.
j' = Distance of the centroid of A' to Neutral Axis
(N.A.)
4r
E(А)
(Location of Neutral Axis) = y =
ΣΑ
(I about the Neutral Axis) I = Iy'+ Ad,?
Transcribed Image Text:150
300
25
50
25
D
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