Name : (Englist'\ Class : EG114101/2\ Name : (Chines\ Student No. :\ Test 1\ Q.1 A simply supported beam

ABCD

with an overhang

AB

and

CD

is shown in Figure

Q1

. The\ flexural rigidity of the beam segments

ABCD

is

EI

. Given that the modulus of elasticity

(E)

is\ 300GPa and the moment of inertia

(I)

is

400^(**)10^(-6)m^(4)

. It is required to use "Energy Method"\ to determine the vertical deflection at point

D

:\ (a) Draw the bending moment diagram of the beam

ABCD

caused by real loads. Indicate in\ the diagram all equations of the bending moment

M(x)

and the relevant coordinate\ system(s) adopted.\ (25 marks)\ (b) Draw the bending moment diagram of the beam

ABCD

caused by virtual load of

1kN

.\ Indicate in the diagram all equations of the bending moment

m(x)

and the relevant\ coordinate system(s) adopted.\ (17 marks)\ (c) Calculate the vertical deflection at point

D

.\ Ans.

34.11mm

\ (8 marks)\ sigure Y1

Q. 1 A simply supported beam ABCD with an overhang AB and CD is shown in Figure Q1. The flexural rigidity of the beam segments ABCD is EI. Given that the modulus of elasticity (E) is 300GPa and the moment of inertia (I) is 400106m4. It is required to use "Energy Method" to determine the vertical deflection at point D : (a) Draw the bending moment diagram of the beam ABCD caused by real loads. Indicate in the diagram all equations of the bending moment M(x) and the relevant coordinate system(s) adopted. (25 marks) (b) Draw the bending moment diagram of the beam ABCD caused by virtual load of 1kN. Indicate in the diagram all equations of the bending moment m(x) and the relevant coordinate system(s) adopted. (17 marks) (c) Calculate the vertical deflection at point D. Ans. 34.11mm (8 marks) Figure Q1