STRUCTURAL THEORY-FORMULA
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THREE MOMENT EQUATION
$M_1L_1 + 2M_2(L_1 + L_2) + M_3L_2 + \dfrac{6A_1\bar{a}_1}{L_1} + \dfrac{6A_2\bar{b}_2}{L_2} = 0
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BEAMS STATIC DETERMINACY
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TRUSSES INTERNAL STABILITY
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TRUSSES STATIC DETERMINACY
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FRAMES STATIC DETERMINACY
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Deflection of Simply Supported Beam
directly below the Single Pointload
directly below the Single Pointload
$\delta\ =\ \frac{P\ a^{2\ }b^2}{3(a+b)\ EI}\ $
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BEAMS STATIC DETERMINACY
$r\ \left[\begin{matrix}>\\=\\<\\\end{matrix}\right]\ \ 3+e_c\ $
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TRUSSES INTERNAL STABILITY
$m\ \left[{<\atop\geq}\right]\ 2j-3\ \ \ \ \ \ $
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TRUSSES STATIC DETERMINACY
$m\ +\ r\ \left[\begin{matrix}<\\=\\>\\\end{matrix}\right]\ 2j$
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FRAMES STATIC DETERMINACY
$3m\ +\ r\ \left[\begin{matrix}<\\=\\>\\\end{matrix}\right]\ 3j\ +\ \ e_c\ \ \
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CANTILEVER HACKS
$\delta_{\ after\ the\ \ Con.\ Load}=\frac{Pa^2(3L-a)}{6EI}$
$\delta_{\ before\ the\ \ Con.\ Load}=\frac{Px^2(3a-x)}{6EI}$
$\delta_{\ before\ the\ \ Con.\ Load}=\frac{Px^2(3a-x)}{6EI}$
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CANTILEVER HACKS
DEFLECTION FREE END
DEFLECTION FREE END
$\delta=\frac{M_R\ L^2}{\left(n+2\right)\ EI}$
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CANTILEVER HACKS
ROTATION FREE END
ROTATION FREE END
$\theta=\frac{M_R\ L}{\left(n+1\right)\ EI}$
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FIXED END MOMENTS
can point load analogous P=(A+Bx)
${\rm FEM}_{\ left}=\ \frac{P\ a\ b^2}{L^2}$
${FEM\ }_{ryt}=\ \frac{P\ a^2\ b}{L^2}$
${\rm FEM}_{\ left}=\ \frac{P\ a\ b^2}{L^2}$
${FEM\ }_{ryt}=\ \frac{P\ a^2\ b}{L^2}$
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$Virtual\ Work\ Method$
Deflection of Trusses
due to EXTERNAL LOADINGS
Deflection of Trusses
due to EXTERNAL LOADINGS
$\delta\ =\ \sum\frac{S\ u\ L}{A\ E}$
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$Virtual\ Work\ Method$
Deflection and Slope of Beams
Deflection and Slope of Beams
$\delta\ or\ \theta\ =\ \sum\int{\frac{Mm}{EI}\ dx}$
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Muller Breslau
Create IL Diagram for Reaction B
Create IL Diagram for Reaction B
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Muller Breslau
Create IL Diagram for Reaction D
Create IL Diagram for Reaction D
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Muller Breslau
Create IL Diagram for Vertical Reaction F
Create IL Diagram for Vertical Reaction F
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Muller Breslau
Create IL Diagram for Moment Reaction F
Create IL Diagram for Moment Reaction F
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Muller Breslau
Create IL Diagram for internal shear in the
beam at a point 2m
to the right of point D (shown as point D')
Create IL Diagram for internal shear in the
beam at a point 2m
to the right of point D (shown as point D')
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Muller Breslau
Create IL Diagram for internal shear in the
beam at a point 6m
to the right of point C (shown as point C')
Create IL Diagram for internal shear in the
beam at a point 6m
to the right of point C (shown as point C')
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Muller Breslau
Create IL Diagram for internal moment in the beam at a point 2m to the right of
point D (shown as point D')
Create IL Diagram for internal moment in the beam at a point 2m to the right of
point D (shown as point D')
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Muller Breslau
Create IL Diagram for internal moment in the beam at a point 6m to the right of
point C (shown as point C')
Create IL Diagram for internal moment in the beam at a point 6m to the right of
point C (shown as point C')
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$MEANING$
in
$AREA-MOMENT\ METHOD$
$t_{B/A}$
in
$AREA-MOMENT\ METHOD$
$t_{B/A}$
the DEVIATION of B
with RESPECT to the
TANGENT EXTENDED/ DRAWN
at A
$sample\ unit\ \left(kN\ -\ m^3\right)$
with RESPECT to the
TANGENT EXTENDED/ DRAWN
at A
$sample\ unit\ \left(kN\ -\ m^3\right)$
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$Virtual\ Work\ Method$
Deflection of Trusses and Frames
due to TEMPERATURE
Deflection of Trusses and Frames
due to TEMPERATURE
$\sum\left( \alpha\bullet\ u\ \bullet L\ \bullet ∆T \right)$
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$Virtual\ Work\ Method$
Deflection of Trusses and Frames
due to FABRICATION ERRORS
Deflection of Trusses and Frames
due to FABRICATION ERRORS
$\delta\ =\ \ \sum\left(u\bullet\ \Delta L\right)$
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REVISED
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CONCEPT
DETERMINACY and STABILITY
in FRAMES
DON'T CUT on JOINTS, CUT on MEMBERS
SEPERATE all the SUPPORT REACTIONS,
using VERTICAL CUTTING SECTION ONLY,
TRAVERSING ALL HORIZONTAL MEMBERS
DETERMINACY and STABILITY
in FRAMES
DON'T CUT on JOINTS, CUT on MEMBERS
SEPERATE all the SUPPORT REACTIONS,
using VERTICAL CUTTING SECTION ONLY,
TRAVERSING ALL HORIZONTAL MEMBERS
CONCEPT
DETERMINACY and STABILITY
in FRAMES
DON'T CUT on JOINTS, CUT on MEMBERS
SEPERATE all the SUPPORT REACTIONS,
using VERTICAL CUTTING SECTION ONLY,
TRAVERSING ALL HORIZONTAL MEMBERS
DETERMINACY and STABILITY
in FRAMES
DON'T CUT on JOINTS, CUT on MEMBERS
SEPERATE all the SUPPORT REACTIONS,
using VERTICAL CUTTING SECTION ONLY,
TRAVERSING ALL HORIZONTAL MEMBERS
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DEGREE of INDETERMINACY
3D FRAMES
3D FRAMES
$DI\ =\ 6\ \left( \# \ of\ LOOPS \right)$
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