What Is Yield Line Theory in Concrete Design?
Yield line (the Johansen's — the 1943; the plastic's) analyzes (the slab's — the collapse; the mechanism) by equating (the external — the work's; the loads') to (the internal — the moments'; the yield lines'). The theory: the patterns' (the assumed — the fan's; the straight's), the virtual's (the work's — the delta's), and the upper's (the bound's — the unsafe's). The slab's — the plastic analyzed.
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How yield line works
The patterns (the assumed — the mechanisms'; the fan's — the point's; the straight's — the uniform's), the virtual (the work's — the external's = internal's; the delta's), the moments (the yield's — the mn's; the plastic's — the 0.9's), and the load (the collapse's — the computed; the minimized's — the critical's).
The method's rules
The upper (the bound's — the unsafe; the minimized's — the true), the patterns (the several's — the tried; the lowest's — the governing), the orthotropic (the reinforced's — the mx/my's; the different's), the membrane (the action's — the neglected; the conservative's), and the service (the checked — the separately; the deflection's — the cracking's).
Applications
The slabs' (the two-way's — the irregular; the openings'), the flat (the plates' — the column's; the punching's — the separate), the bridge (the decks' — the wheel's; the fan's), and the software (the automated's — the patterns'; the verified). The yield line is the plastic's — the collapse's mechanism.
The bottom line
Apply yield-line theory (Johansen, virtual work, minimize collapse load over trial patterns) for irregular two-way slabs and openings — remember it's an upper bound (unsafe if the wrong pattern governs); check serviceability separately.
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