1. MAE 314 – Solid Mechanics Yun Jing
Combined Stresses ( ,8.4)
MAE 314 – Solid Mechanics
Yun Jing
Combined Stresses

2. Introduction
In Chapter 1 and 2, you learned how to determine the normal stress due to centric loads.
In Chapter 3, you analyzed the distribution of shearing stresses in a circular member due to a twisting couple.
In Chapter 4, you determined the normal stresses caused by bending couples.
In Chapters 5 and 6, you evaluated the shearing stresses due to transverse loads.
In Chapter 7, you learned how the components of stress are transformed by a rotation of the coordinate axes and how to determine the principal planes, principal stresses, and maximum shearing stress at a point.
In Chapter 8, you will learn how to determine the stress in a structural member or machine element due to a combination of loads and how to find the corresponding principal stresses and maximum shearing stress.

3. Principle Stresses in a Beam
Prismatic beam subjected to transverse loading
Principal stresses determined from methods of Chapter 7
Can the maximum normal stress within the cross-section be larger than

4. Principle Stresses in a Beam

5. Principle Stresses in a Beam
Cross-section shape results in large values of txy near the surface where sx is also large.
smax may be greater than sm

6. Sample Problem 8.1 SOLUTION:
Determine shear and bending moment in Section A-A’
Calculate the normal stress at top surface and at flange-web junction.
A 160-kN force is applied at the end of a W200x52 rolled-steel beam. Neglecting the effects of fillets and of stress concentrations, determine whether the normal stresses satisfy a design specification that they be equal to or less than 150 MPa at section A-A’.
Evaluate the shear stress at flange-web junction.
Calculate the principal stress at flange-web junction

7. Sample Problem 8.1 SOLUTION:
Determine shear and bending moment in Section A-A’
Calculate the normal stress at top surface and at flange-web junction.

8. Sample Problem 8.1 Evaluate shear stress at flange-web junction.
Calculate the principal stress at flange-web junction
Design specification is not satisfied.

9. Stresses Due to Combined Loads
When more than one type of load acts on a beam, the combined stress can be found by the super- position of several stress states.
Combined Stresses

10. Example Problem
Two forces are applied to the small post BD as shown. Knowing that the vertical portion of the post has a cross section of 1.5x2.4 inches, determine the principal stress, principal planes, and maximum shearing stress at point H.
Combined Stresses

11. Stresses Due to Combined Loadsy z x H y z x H
Combined Stresses

12. Example Problem
A force of 150N acts at point B on an L-shaped lug wrench as shown. The force acts vertically downward, perpendicular to the plane of the wrench. The handle of the lug wrench is a steel rod with a diameter of 12.5 mm, and its planform is shown, as well. Determine the principle stress at point A, which is on top of the wrench.
Combined Stresses

13. Example Problem
A 6-kip force is applied to the machine element AB as shown. Knowing that the uniform thickness of the element Is 0.8 in., determine the normal and shearing stresses at (a) point a, (b) point b, (c ) point c.
Combined Stresses

14. Example Problem
Member AB has a uniform rectangular cross section of 10*24 mm. For the loading shown, determine the normal and shearing stresses at (a) point H, (b) point K.
Combined Stresses