Beam ABCDE has a moment release just right of joint B and has concentrated moment loads at D and E. In addition, a cable with tension P is attached at fand runs over a pulley at C (Fig, a). The beam is constructed using two steel plates, which arc welded to form a T cross section (see Fig. b). Consider ßexuralstresses only Find the maximum permissible value of load variable P if the allowable bending stress is 130 M Pa. Ignore the self-weight of the frame members and let length variable L = 0.75 m.
The maximum permissible load.
Answer to Problem 5.5.30P
The maximum permissible load is
Explanation of Solution
Given information:
The allowable bending stress is
Write the expression for the force equilibrium in x direction.
Here, the reaction at point
Write the expression for the moment at the point of release.
Here, the length of the beam is
Write the expression for the moment about point
Here, the vertical reaction at point
Write the expression for the force equilibrium in y direction.
Here, the vertical reaction at point
Write the expression for the moment at
Here the moment is
Write the expression for the moment at
Write the expression for the moment at
Write the expression for the moment at other points.
Write the expression for the area of the
Here, the width of the flange is
Write the expression for the centroid.
Here, the distance of the centroid from one end is
Write the expression for the other distance of the centroid.
Here, the distance of the centroid from other end is
Write the expression for the moment of inertia about z axis.
Here, the moment of inertia about z axis is
Write the expression for the section modulus at the top section.
Here, the section modulus at top section is
Here, the section modulus of top section is
Write the expression for the section modulus at the bottom section.
Here, the section modulus of bottom section is
Write the expression for the maximum permissible load.
Here, the allowable stress is
Calculation:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Conclusion:
The maximum permissible load is
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Chapter 5 Solutions
Mechanics of Materials (MindTap Course List)
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- Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning