3 COLLAPSE QUESTION A steel beam of l-section was reinforced by steel reinforcing plates welded to each flange. Some useful dimensions of the I-section and the steel reinforcing plates are given in Figure 4. The beam and reinforcing plates are made of elastic-ideally plastic material, with the yielding stress of oy. The second moment of area of the I-section (without the reinforcing plates) is known as I. i) If the moment applied on the section is M, derive an expression (in terms of oy, the dimensions given in the following figure, and ) for the moment when yielding just spreads each reinforcing plate (i.e., everywhere in the two reinforcing plates has reached the yielding stress, while the flanges haven't started to yield). ii) If the outer surfaces of the reinforcing plate (i.e., the top surface of the top reinforcing plate and the bottom surface of the bottom reinforcing plat) have just reached the yielding point, what is the stress on the outer surfaces of the I-section beam? Moreover, what is the moment (in terms of oy, the dimensions given in the following figure, and ) for this case? B C D
3 COLLAPSE QUESTION A steel beam of l-section was reinforced by steel reinforcing plates welded to each flange. Some useful dimensions of the I-section and the steel reinforcing plates are given in Figure 4. The beam and reinforcing plates are made of elastic-ideally plastic material, with the yielding stress of oy. The second moment of area of the I-section (without the reinforcing plates) is known as I. i) If the moment applied on the section is M, derive an expression (in terms of oy, the dimensions given in the following figure, and ) for the moment when yielding just spreads each reinforcing plate (i.e., everywhere in the two reinforcing plates has reached the yielding stress, while the flanges haven't started to yield). ii) If the outer surfaces of the reinforcing plate (i.e., the top surface of the top reinforcing plate and the bottom surface of the bottom reinforcing plat) have just reached the yielding point, what is the stress on the outer surfaces of the I-section beam? Moreover, what is the moment (in terms of oy, the dimensions given in the following figure, and ) for this case? B C D
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:3 COLLAPSE QUESTION
A steel beam of l-section was reinforced by steel reinforcing plates welded to each flange. Some
useful dimensions of the I-section and the steel reinforcing plates are given in Figure 4. The beam
and reinforcing plates are made of elastic-ideally plastic material, with the yielding stress of oy.
The second moment of area of the I-section (without the reinforcing plates) is known as I.
i)
If the moment applied on the section is M, derive an expression (in terms of oy, the
dimensions given in the following figure, and ) for the moment when yielding just spreads
each reinforcing plate (i.e., everywhere in the two reinforcing plates has reached the
yielding stress, while the flanges haven't started to yield).
ii) If the outer surfaces of the reinforcing plate (i.e., the top surface of the top reinforcing
plate and the bottom surface of the bottom reinforcing plat) have just reached the yielding
point, what is the stress on the outer surfaces of the I-section beam? Moreover, what is
the moment (in terms of oy, the dimensions given in the following figure, and ) for this
case?
B
C
D
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