Loads on Structures(Part II)
College of Technological Studies
CE 278 Structural Analysis
Department of Civil Engineering Technology
Tutorial (8)
Example (1): Use the approximate method to convert the trapezoidal load on the beam to a uniform load.
39.6 kN/m
12 m
5m, 12mx L A B
12 m 12 m
A1 – B15 m
22 2 5m1 2 11 1 0.769
3 3 12m
x
L
5m1 1 0.583
12m
x
L
30.45 kN/m
Equivalent uniform load (Bending Moment):
Equivalent uniform load (Reactions + Shear Force):
(M)
kN kN0.769 39.6 30.45
m meq uw w
39.6 kN/m
12 m
(R +V)
kN kN0.583 39.6 23.09
m meq uw w
23.09 kN/m
39.6 kN/m
12 m
5m, 10mx L
22 2 5m1 2 11 1 0.667
3 3 10m
x
L
5m1 1 0.50
10m
x
L
Equivalent uniform load (Bending Moment):
Equivalent uniform load (Reactions + Shear Force):
(M)
kN kN0.667 79.2 52.83
m meq uw w
(R +V)
kN kN0.50 79.2 39.6
m meq uw w
Example (2): Use the approximate method to convert the trapezoidal load on the beam to a uniform load.
1
2
C D E
10 m
10 m
12 m 12 m
5 m5 m
79.2 kN/m
12 m
79.2 kN/m
10 m
79.2 kN/m
10 m
52.83 kN/m
10 m
39.6 kN/m
10 m
D1 – D2
Does it work?!
39.6 kN/m
12 m5 m 2 m 5 m
Original Beam
12 m
6 m 6 m
277.2 kN
138.6 kN 138.6 kN
Reactions + Shear Beam
23.09 kN/m
12 m
6 m 6 m
277.08 kN
138.54 kN 138.54 kN
Reactions and Shear Force39.6 kN/m
12 m
Original Beam
Reactions + Shear Beam
23.09 kN/m
12 m
Exact
Approximate
Bending Moment39.6 kN/m
12 m
Original Beam
Bending Moment Beam
30.45 kN/m
12 m
Exact
Approximate
Questions?