The representative frame shown below is subjected to a wind pressure of 1.5kPa. The frames are spaced 6m apart and the coefficients of wind pressure are given for each member as shown. Assume that A and E are hinged and that C is pin-connected. Solve the reactions and draw the shear, moment, and axial diagrams of each member.
The wind pressure is first converted into equivalent uniformly distributed loads on each member by multiplying it by the frame spacing. A positive wind pressure coefficient indicates that the load acts toward the member, whereas a negative coefficient represents a suction effect, causing the load to act away from the member (see the directions of the load on member CD and DE).
A useful technique in solving the reactions when there are distributed loads acting perpendicular to the inclined members of a frame is to split the load into two uniformly distributed loads acting over the horizontal and vertical components of the distances.
For example, the 2kN/m and 5kN/m uniform loads acting on BC and CD are broken into two separate loading acting over the 4-m horizontal distance and the 3-m vertical distance.
We only revert this once we draw the shear, moment, and axial diagrams since we generally want the external loads to act perpendicular to the member.
In our solution, we combine the forces with the same moment arms. For example, the 30kN resultant on AB and the 15kN resultant on DE each have a moment arm of 2.5m about point E, so we join the two as (30+15) multiplied by the common moment arm. Note that we still follow our sign convention here. Both the 30kN and 15kN loads cause a clockwise rotation about point E, so we use a positive sign for both. In the case where, for example, the 15kN load will cause a counterclockwise rotation, we use (30-15) multiplied by the moment arm.
For the purpose of uniformity, we draw our shear, moment, and axial diagrams from top to bottom or left to right and use rotated reference axes for inclined members (BC and CD). We must also obtain the components of the original external and internal reactions along the rotated axes.
