Introduction:
The influence line diagram (ILD) is a graphical representation of the variation in a structural response due to a unit load moving along the structure. In this case, we need to determine the influence line diagram ordinate for the bending moment at point E when a 1 kNm load is applied at point A in the hogging condition.

Step 1: Determine the reactions at supports B and C:
To determine the bending moment at E, we first need to calculate the reactions at supports B and C. Since the load is applied at point A, the reaction at support C can be calculated as:

RA + RB + RC = 1 kN (1)

Taking moments about support B:

RA x 2 + 1 kN x 4 - RC x 1 = 0

Simplifying the equation:

2RA + 4 - RC = 0 (2)

Solving equations (1) and (2) simultaneously, we can find the values of RA and RC.

Step 2: Calculate the bending moment at E:
To calculate the bending moment at point E, we need to consider the effect of the 1 kNm load placed at point A on the beam. We can do this by drawing the influence line diagram for the bending moment at E.

Step 3: Construct the influence line diagram for bending moment at E:
To construct the influence line diagram for the bending moment at E, we consider the effect of a unit load moving across the beam. The influence line diagram is constructed by considering the deflected shape of the beam due to the unit load at different positions.

Step 4: Determine the ordinate for the 1 kNm load at E:
Once the influence line diagram is constructed, we can determine the ordinate for the 1 kNm load at point E. The ordinate represents the value of the bending moment at E due to a unit load at a specific position.

Conclusion:
In conclusion, the influence line diagram ordinate for the bending moment at point E when a 1 kNm load is applied at point A in the hogging condition can be determined by calculating the reactions at supports B and C and constructing the influence line diagram for the bending moment at E. The ordinate for the 1 kNm load at point E can then be determined from the influence line diagram.