(a) In the pin-supported horizontal beam structure shown in Fig. Q1(a), a transverse

force P is applied to the mid-span point C as shown. Use the finite element method

to determine the deflection and slope at points A, C, B, as well as the reaction forces

at nodes A and B. (Assume that L = 1 and El = 1. Due to structural and loading

symmetry, the slope at mid-span C can be assumed as 0)

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(b) In order to enhance the stiffness of the horizontal beam structure, a vertical spring

(k = 12) is placed below the midpoint C through a pin joint (node D is fully fixed to

the ground), as shown in Fig. Q1(b). Determine the deflection at midpoint point C

and the reactions (forces and moments) at nodes A, B and D.

MECH3361/8361/9361

A EI

ΕΙ

C

Stopper

EI

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(c) In order to further enhance the stiffness of the horizontal beam structure, a stopped is

placed below by A at the midpoint C as shown in Fig. Q1(c). Determine the deflection at

midpoint point C and the reactions (forces and moments) at nodes A, B, D and the

stopper.

Figure Q1

ΕΠ

B

El

Semester 2, 2023

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