Concept explainers
Two cover plates, each 7.5 mm thick, are welded to a W460 × 74 beam as shown. Knowing that σall = 150 MPa for both the beam and the plates, determine the required value of (a) the length of the plates, (b) the width of the plates.
Fig. P5.144 and P5.145
(a)
Find the length of the plates.
Answer to Problem 145P
The length of the plates is
Explanation of Solution
The length of the cover plate is
The thickness of the cover plate is
The width of the cover plate is
The allowable normal stress in the beam is
Show the free-body diagram of the prismatic beam as in Figure 1.
Determine the vertical reaction at point B by taking moment at point A.
Determine the vertical reaction at point A by resolving the vertical component of forces.
Show the free-body diagram of the section AD as in Figure 2.
Determine the moment at point D by taking moment about point D.
Refer to Appendix C “Properties of Rolled-Steel Sections” in the textbook.
The section modulus of the
Determine the moment at point D
Here, the allowable stress of the beam is
Substitute 150 MPa for
Find the length of the plate using trial and error method.
Therefore, the length of the plates is
(b)
Find the width of the plates.
Answer to Problem 145P
The width of the plates is
Explanation of Solution
The length of the cover plate is
The thickness of the cover plate is
The width of the cover plate is
The allowable normal stress in the beam is
Show the free-body diagram of the prismatic beam as in Figure 3.
Determine the vertical reaction at point B by taking moment at point A.
Determine the vertical reaction at point A by resolving the vertical component of forces.
Show the free-body diagram of the section AC as in Figure 4.
Determine the moment at point C by taking moment about point C.
Show the cross section of the beam as in Figure 5.
Determine the section modulus (S) of the beam using the relation.
Here, the allowable normal stress in the beam is
Substitute
Refer to Appendix C “Properties of Rolled-Steel Sections” in the textbook.
The depth of the
The moment of inertia of the
Determine the moment of inertia (I) of the beam using the relation;
Here, the moment of inertia of the beam is
Refer to the cross section of the beam;
Substitute
Determine the distance from the neutral axis (c) to outer most fibre as follows;
Determine the width of the plates (b) using the relation.
Substitute
Therefore, the width of the plates is
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Chapter 5 Solutions
Mechanics of Materials, 7th Edition