Pallet rack is a system used to store materials. A company employed a modular steel rack

system for the storage of materials produced by its factory. The modular rack system consisted

of four parallel columns spaced at $1\mathrm{.}4m$ and connected to each other through tie beams as

shown in Figure $1.$ The height of columns is $9\mathrm{.}8m$ and they are made of a steel tube having

dimensions of $120120mm$ and a thickness of $2\mathrm{.}5mm.$ The columns sit on a square base plate

with the size of $300mm$ and a thickness of $10mm.$ The connection between the columns and

the base plate is fixed. Base plates are connected to a $200mm$ thick concrete slab through $4$

high strength bolts with the diameter of $16mm.$ The tie beams are connected to columns

through bolts providing a fixed beam$-$to$-$column connection. The tie beams are made of a steel

tube profile with the dimensions of $6060mm,$ and a thickness of $3mm.$ The modular rack

system has been designed to carry safely six pallets each of which $10000N$ in weight. Pallets

sits on four steel brackets each of which $8mm$ thick and $300mm$ in length. Brackets are

installed at the four corners of each level as shown in Figure $1.$ There is a $150mm$ gap between

the pallets and the columns when pallets are installed on brackets. The lateral load resisting

system of the rack system along axes $1$ and $2$ is a braced system made of $40mm$ tube profiles

having $2\mathrm{.}5mm$ thickness. As shown in Figure $1,$ along the A and B axes, the rack system relies

on a moment frame that has only one tie beam installed on the roof level to resist against lateral

deformations. The yield strength of the employed steel materials is $280$MPa and its modulus

of elasticity equals $200$GPa.

After few weeks being in operation safely, as shown in Figure $2,$ the rack system experienced

a sudden collapsed when workers were adding new pallets to a half$-$filled rack system. The

rack system collapsed suddenly along the moment frame $($i$.$e$.,$ axis A and B$)$ and imposed

significant monetary loss to the company.

Figure $1.$ Details of the modular rack system

QUESTION

Assume the rack system is empty but is hit by a lift truck at $1\mathrm{.}4m$ height, estimate the

minimum truck load that can lead to the collapse of the rack system.