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Metal Structures design is the art of selecting the structure optimum sections & connections from materials which their properties are uncertain and assessing developed stresses & displacements using approximate analysis methods under probable combinations of loads that their values can only be predicted so that to have a fully safe serviceable economic structure.

by anonymous author

Structural Bolts are available with mild and high strength grads, The most recognized International Specifications for structural Bolts are:-

American ASTM A325, A490 and the recent F3125 and many others

European Bolts mechanical properties & Grades are according to EN ISO 898 while specifications for Shape & dimensions includes ISO 4015, ISO 4017, ISO 4018 and many others

Indian Standard main structural bolts specification is IS 1363.

Most specialized standard comprehensive set of Welding codes is the American welding Society AWS, European standards for welding includes EN ISO 15609, EN ISO 15614 and many others, Indian Standards for welding includes IS 817, IS 818 and many others.

Take The Control

The concept of framework analysis emerged during the period from 1850 to 1875, at this time the concepts of matrices were being introduced and defined, These concepts are the foundations of matrix structural analysis, which did not take form until nearly 80 years later to form what is know The Direct Stiffness Method.

The Demomstration of a sample simple beam stiffness matrix is as below

The strainging actions of a Simple Beam at both Ends 1 & 2 can be evaluated using the following Matrix Form as a function in the beam elastic line above deformed shape:
\begin{align*}
\begin{Bmatrix}
V_{1}\\ M_{1}\\ V_{2}\\ M_{2}
\end{Bmatrix} & =
\frac{EI}{L^{3}}
\begin{pmatrix} 12 & 6L & -12 & 6L\\
6L & 4L^{2} & -6L & 2L^{2}\\
-12 & -6L & 12 & -6L\\
6L & 2L^{2} & -6L & 4L^{2}
\end{pmatrix}
\begin{Bmatrix} v_{1}\\ \theta _{1}\\ v_{2}\\ \theta _{2}
\end{Bmatrix}
\end{align*}
The above now is in the form
$$ \{p\}=[K]\{d\} $$
The Beam stiﬀness matrix [K] is :
\[
\left[ K \right] =
\frac{EI}{L^{3}}
\begin{pmatrix} 12 & 6L & -12 & 6L\\
6L & 4L^{2} & -6L & 2L^{2}\\
-12 & -6L & 12 & -6L\\
6L & 2L^{2} & -6L & 4L^{2}
\end{pmatrix}
\]

The strainging actions of a Simple Beam at both Ends 1 & 2 can be evaluated using the following Matrix Form as a function in the beam elastic line above deformed shape:
\[
{
\begin{array}{cc} V_{1}\\ M_{1}\\ V_{2}\\ M_{2} \end{array}
}
=
\frac{EI}{L^{3}}
\left(
\begin{array}{cc} 12 & 6L & -12 & 6L \\ 6L & 4L^{2} & -6L & 2L^{2} \\ -12 & -6L & 12 & -6L \\ 6L & 2L^{2} & -6L & 4L^{2} \end{array}
\right)
\{
\begin{array}{cc} v_{1} \\ \theta _{1} \\ v_{2} \\ \theta _{2} \end{array}
\}
\]
The above now is in the form
$$ \{p\}=[K]\{d\} $$
The Beam stiﬀness matrix [K] is :
\[
\left[ K \right]
=
\frac{EI}{L^{3}}
\left(
\begin{array}{cc} 12 & 6L & -12 & 6L \\ 6L & 4L^{2} & -6L & 2L^{2} \\ -12 & -6L & 12 & -6L \\ 6L & 2L^{2} & -6L & 4L^{2} \end{array}
\right)

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