Two-piece continuous steel sets are to support a tunnel with a semi-circular roof having a radius of 3.5 m, and a straight leg section of 4 m. The tunnel is therefore 7 m wide by 7.5 m high. The crown is assumed hinged and the ends of the steel arch are fixed. For preliminary design assume 2.5 cm of steel rib depth for each 1 m of tunnel width and a set spacing of 1.2 m. Note that the 3.5 m radius is to the outside of the steel. Blocks 20 cm thick are placed at the crown and at the base of the arch. In addition, blocks next to these are spaced a maximum of 127 cm. Remaining blocks required should not be spaced more than 127 cm. A rock load of 3 m is expected on the basis of rock quality; rock unit weight is 26.9kN/m3.

1 Draw a neat scale diagram of the tunnel and steel set.

2 Show the position of the blocks.

3 Show the rock arch and resolution of forces (to scale) loading the set; indicate magnitudes and directions.

4 Replace the 4 m steel legs by a vertical reaction RV at the arch base.

5 Draw the cords between blocking points defining the thrust directions in the steel arch.

6 Construct the force polygon.

7 Calculate the maximum moment in the steel arch.

8 Calculate the maximum stress in the steel.

9 Estimate the safety factor for the steel arch.