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Combined Loadings

Chapter 6 discusses the combined effects of multiple loadings on structures, focusing on axial force, shear force, torsional moment, and bending moment. It reviews the stresses caused by normal force, shear force, and bending moment, explaining how they can be combined to determine the overall state of stress at specific points. The chapter includes examples to illustrate the calculation of stress in various scenarios.

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Abathar Al-Hamrani
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33 views15 pages

Combined Loadings

Chapter 6 discusses the combined effects of multiple loadings on structures, focusing on axial force, shear force, torsional moment, and bending moment. It reviews the stresses caused by normal force, shear force, and bending moment, explaining how they can be combined to determine the overall state of stress at specific points. The chapter includes examples to illustrate the calculation of stress in various scenarios.

Uploaded by

Abathar Al-Hamrani
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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CH#6: Combined loadings

In preceding chapters, we studied four basic types of loading: axial force, shear force
torsional moment, and bending moment. Each of these types was discussed on the
assumption that only one of these loadings was acting on a structure at a time. The
present chapter is concerned with cases in which two or more of these loadings act
simultaneously on a structure.

.‫ القوة المحورية وقوة القص وعزم االلتواء وعزم االنثناء‬:‫ درسنا أربعة أنواع أساسية من األحمال‬،‫في الفصول السابقة‬
‫ في هذا الفصل‬.‫وقد تمت مناقشة كل نوع من هذه األنواع على افتراض أن أحد هذه األحمال فقط كان يؤثر في وقت واحد‬
.‫سنقوم بدراسة الحاالت التي تؤثر فيها اثنتان أو أكثر من هذه األحمال في وقت واحد‬
To better understand this concept, we will make a quick review on the stresses that we
have obtained from 2-D problems, which were caused by the following three loadings:
1- Normal force (N)
2- Shear force (V)
3- Bending moment (M)

M
N

Each one of these forces will cause a certain type of stress as follows:
𝑁
1- Normal force (N) → Normal stress = 𝜎=
𝐴
𝑉𝑄
2- Shear force (V) → Shear stress = 𝜏=
𝐼𝑡

𝑀𝑦
3- Bending moment → bending stress = 𝜎=
𝐼

Important note: It can be noticed that we give the same notation of stress for the normal
and bending stresses, which is (𝜎). This is because both stresses are acting
perpendicular to the cross-section, which means that both stresses are creating either a
compressive or tensile stresses. Therefore, we can consider the bending stress as a
normal stress, and they can be combined together. As a result, the state of stress in an
element located at a specific point on the cross-section can be represented as follows:
𝑃 𝑀𝑦
For normal stresses → 𝜎 = +
𝐴 𝐼
where each term will have a negative sign in case of compressive stresses and a positive
sign in case of tensile stresses.
𝑉𝑄
For shear stresses → 𝜏 =
𝐼𝑡
Example: The member shown in the figure below has a rectangular cross section.
Determine the state of stress that the loading produces at point C.
For 3-D problems, we will have three forces in a section and three moments as shown in
the figure below:

Normal force (Ny) Shear force (VX)


Shear force (Vz)

Moment (Mz) Torsional moment (My)


Moment (Mx)
Example: A force of 15 kN is applied to the edge of the member shown in Figure. Neglect
the weight of the member and determine the state of stress at points B and C.

Y
X
Example: The rectangular block of negligible weight in the figure below is subjected to a
vertical force of 40 kN, which is applied to its corner. Determine the largest normal stress
acting on a section through ABCD.
Example: The solid rod shown has a radius of 7.5 mm. If it is subjected to the force of 500
N, determine the state of stress at point A.
Example: The solid rod shown has a radius of 7.5 mm. If it is subjected to the force of
800 N, determine the state of stress at point A.

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