Determine the force in member AB of the Indicate

Introduction

ENGINEERING MECHANICS

Spring 2020

ASSIGNMENT- 2

Solution

Solution 1

(a). It is not possible to pass a section through AB without cutting four members whose forces are unknown. Although three of these cut by

section 2 are concurrent at B and therefore the moment equation about B could be used to obtain AF, the force in AB cannot be obtained from the remaining two equilibrium principles. It is necessary to consider first the adjacent section 1 before analysing section 2. The free-body diagram for section 1 is drawn and includes the reaction of 36. 66 kN at K,

which is calculated from the equilibrium of the truss as a whole. In assigning the proper directions for the forces acting on the three cut members, we see that a balance of moments about K eliminates the effects of EA and BC and clearly requires that BE be up and to the left. A balance of moments about E eliminates the effect of the three forces concurrent at E and indicates that BC must be to the right to supply sufficient counter clockwise moment .Again it should be fairly obvious that the lower chord is under tension because of the bending tendency of the truss. Although it should also be apparent that the top chord is under compression, for purposes of illustration the force in EA will be arbitrarily assigned as tension. By the analysis of section 1, BE is obtained from

The moment of EA about B is calculated here by considering its two components

The image of the diagram is taken form J.L. Meriam, L.G. Kraige, Engineering mechanics,7th ed

as acting through A. The minus sign indicates that EA was assigned in the wrong direction.

EA = 59.64 KN (C)

From the free-body diagram of section 2, which now includes the known value of BE, a balance of moments about L is seen to eliminate AF and BC. Thus,

[∑ML = 0] 12AB + 20(16) + 20(20) – 36.66(24) – 28.28(0.707) (12) = 0

AB = 33.34 KN (T)

Again the moment of BE is determined from its components considered to be acting at B. The answer for AB is positive, so that the assumed tensile direction is correct. An alternative approach to the entire problem is to utilize section 1 to determine EA and then use the method of joints applied at A to determine AB.

Meriam, Kraige (2013). truss problem diagram. Engineering Mechanics, 7^th edition, 191,sample problem 4.