May 2015

Situation
The three-hinged arch shown below is loaded with symmetrically placed concentrated loads as shown in the figure below.
 

The loads are as follows:
$$P_1 = 90 ~ \text{kN} \qquad P_2 = 240 ~ \text{kN}$$
 

The dimensions are:
$$H = 8 ~ \text{m} \qquad S = 4 ~ \text{kN}$$
 

Calculate the following:
 

1.   The horizontal reaction at A.

2.   The total reaction at B.

3.   The vertical reaction at C.

Problem
The digits of a three-digit number are in arithmetic progression. If you divide the number by the sum of its digits, the quotient is 26. If the digits are reversed, the resulting number is 198 more than the original number. Find the sum of all the digits.

Situation
The truss shown in is made from timber Guijo 100 mm × 150 mm. The load on the truss is 20 kN. Neglect friction.

1.   Determine the minimum value of x in mm.

2.   Determine the minimum value of y in mm.

3.   Calculate the axial stress of member AC in MPa.