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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P-
E.
D.
Transcribed Image Text:P- E. D.
The simply supported beam with an overhang shown in the enclosed sketch is subjected
to a concentrated force "P" at point A of a 150 kN and a distributed force "w" of 75 kN/m
between points E and B. Please notice that the sketch is not at scale, the distances between
points A, C, D, E, and B are labelled on the sketch. The beam is a prismatic beam with a
rectangular cross-section 100 mm wide and 300 mm tall The beam is made of ASTM A36 steel
with the following properties: yield stress in tension 250 MPa, yield stress in shear 145 MPa, and
a modulus of elasticity of 200 GPa It is desired to obtain the following information:
1.) Reactions at the supports D and B, magnitude and direction
2.) Internal shear force diagram from A to B
3.) Internal bending moment diagram from A to B
4.) Maximum tensile bending stress along the beam such as magnitude and sign and in
what beam section does it occur, and within the cross section where will the
maximum occur. Is the design safe based on yield tensile stress?
5.) Maximum shear stress along the beam and in what section does it occur and within
the cross section where it will occur. Based on the yield shear stress is the design
safe?
6.) In section C, it is desired to calculate the normal and shear stresses at a point "a"
within the section located midway between the top fiber and the neutral fiber, please
plot the stresses (normal and shear) on an briented element including the vertical and
horizontal planes; you need to include magnitude and directions for all the stresses
acting on these two planes
7.) Calculate the Principal stresses at the same point "a" of the section C indicating
magnitudes and signs
8.) Calculate the orientations of the principal planes and show these on an element
appropriately oriented showing the principal stresses on the corresponding planes
9.) Calculate the angle of rotation 8 of the section at "D" using superposition and the
tables included with the FE reference manual, and
Calculate the deflection v of section "C" using superposition and the tables
10.)
included with the FE reference manual
Transcribed Image Text:The simply supported beam with an overhang shown in the enclosed sketch is subjected to a concentrated force "P" at point A of a 150 kN and a distributed force "w" of 75 kN/m between points E and B. Please notice that the sketch is not at scale, the distances between points A, C, D, E, and B are labelled on the sketch. The beam is a prismatic beam with a rectangular cross-section 100 mm wide and 300 mm tall The beam is made of ASTM A36 steel with the following properties: yield stress in tension 250 MPa, yield stress in shear 145 MPa, and a modulus of elasticity of 200 GPa It is desired to obtain the following information: 1.) Reactions at the supports D and B, magnitude and direction 2.) Internal shear force diagram from A to B 3.) Internal bending moment diagram from A to B 4.) Maximum tensile bending stress along the beam such as magnitude and sign and in what beam section does it occur, and within the cross section where will the maximum occur. Is the design safe based on yield tensile stress? 5.) Maximum shear stress along the beam and in what section does it occur and within the cross section where it will occur. Based on the yield shear stress is the design safe? 6.) In section C, it is desired to calculate the normal and shear stresses at a point "a" within the section located midway between the top fiber and the neutral fiber, please plot the stresses (normal and shear) on an briented element including the vertical and horizontal planes; you need to include magnitude and directions for all the stresses acting on these two planes 7.) Calculate the Principal stresses at the same point "a" of the section C indicating magnitudes and signs 8.) Calculate the orientations of the principal planes and show these on an element appropriately oriented showing the principal stresses on the corresponding planes 9.) Calculate the angle of rotation 8 of the section at "D" using superposition and the tables included with the FE reference manual, and Calculate the deflection v of section "C" using superposition and the tables 10.) included with the FE reference manual
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