- Table method of finding deflection of beam is one of the best method of finding deflection of beam.
- This method of finding deflection is very much beneficial in case of finding slope and deflection as per superposition method.
- As per superposition method , the effect of each and every load is considered separately and finally the effect of each loading is summed up.
- This method is even very much helpful in case of analysis of indeterminate structure with the force method of analysis. By choosing the redundant , the effect of various loading is calculated at the desired position with the help of the table.
- The table consists of slope and deflection equation of some standard type of beam under various standard loadings.
1. CANTILEVER BEAM WITH POINT LOAD
- For 0 ≤ x ≤ a
Ө = (P/2EI) (X² - 2aX)
y = (P/6EI) (X³ - 3aX²)
- For a ≤ x ≤ L
Ө = - Pa²/2EI
y = (Pa² / 6EI) (a - 3x)
2. CANTILEVER BEAM WITH CONCENTRATED COUPLE
- For 0 ≤ x ≤ a
Ө = - Mx/EI
y = - Mx²/ 2EI
Ө = -Ma/EI
y = (Ma/2EI) (a - 2x)
3. CANTILEVER BEAM WITH UDL
- For 0 ≤ x ≤ a
Ө =(w/6EI)(3ax²-3a²x-x³)
y = (w/24EI)(4ax³-6a²x²-x⁴)
- For a ≤ x ≤ L
Ө = - wa³/6EI
y = (wa³/24EI) (a - 4x)
4. CANTILEVER BEAM WITH TRIANGULAR UVL
- For 0 ≤ x ≤ a
Ө = (w/24EIa)(x⁴-4ax³+6a²x²-4a³x)
y = (w/120EIa)(x⁵-5ax⁴+10a²x³-10a³x²)
- For a ≤ x ≤ L
Ө = (- wa³/24EI)
y = (wa³ /120EI)( -5x+a)
5. SIMPLY SUPPORTED BEAM WITH POINT LOAD
- For 0 ≤ x ≤ a
Ө = (Pb/6EIL)(3x²+b²-L²)
y = (Pb/6EIL)(x³+b²x-L²x)
- For a ≤ x ≤ L
Ө = (Pa/6EIL)(L²-a²-3(L-x)²)
y = (Pa(L-x)/6EIL)(x²+a²-2Lx)
6. SIMPLY SUPPORTED WITH CONCENTRATED COUPLE
- For 0 ≤ x ≤ a
Ө = (M/6EIL)(-3x²+6aL-3a²-2L²)
y = (M/6EIL)(-x³+6aLx-3a²x-2L²x)
7. SIMPLY SUPPORTED WITH UDL
- For 0 ≤ x ≤ a
Ө = (-w/24EIL)[4Lx³-6a(2L-a)x²+a²(2L-a)²]
y = (-w/24EIL)[Lx⁴-2a(2L-a)x³+a²(2L-a)²x]
- For a ≤ x ≤ L
Ө = (-wa²/24EIL)(6x²-12Lx+a²+4L²)
y = (-wa²/24EIL)(L-x)(-2x²+4Lx-a²)
8. SIMPLY SUPPORTED WITH TRIANGULAR UVL
Ө = (-w/360EIL)(15x⁴-30L²x²+7L⁴)
y = (-w/360EIL)(3x⁵-10L²x³+7L⁴x)
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