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?