Find out horizontal and vertical components of hinge force, Mechanical Engineering

Find out horizontal and vertical components of hinge force:

The frame shown in Figure is supported by a hinge at E and a roller support at D. Find out horizontal and vertical components of hinge force at C as it acts upon member BD.

Solution

 (i)        The roller support at D is replaced by a vertical reaction VD and hinge support at E is replaced by the vertical and horizontal components of reaction VE and VH respectively as illustrated in Figure.

 (ii)       The free body diagram of the three members is illustrated in Figure.

          Figure 11.6

(iii)       For Member AB

              H A = H B ------ (a)

              VA + VB = 2400------- (b)

              M A = 2400 × 1.2 - VB × 2.2 = 0-------- (c)

           For Member DB

               H B = H C -------- (d)

               VD + VC = VB           ---------- (e)

               DC cos 45o = 1.5 and BC cos 45o = 1.1

                DC = 2.12 m; and BC = 1.55 m

                BD cos 45o = 1.5 + 1.1 = 2.6

                 or    BD = 2.6 /cos 45o

                                 = 3.67 m

                M D = VC × 1.5 + H C × 1.5 - VB × (1.5 + 1.1) - H B (1.5 + 1.1) = 0

or                VC  + H C  - VB  × 1.73 - H B  × 1.73 = 0            --------- (f)

              For Member AE

                    VE - VC - VA = 0 -------- (g)

 

                  - H E + H C - H A = 0----------- (h)

           M E = VC × 1.5 - H C × 1.5 + H A × 2.6 + VA × 2.6 = 0

or         V- H C  + H A  × 1.73 + VA  × 1.73 = 0          ---------- (i)

 (iv)      For the three members there are nine equations. The unknowns are HA, VA, VB, HB, HC, VC, VD, HE and VE also nine in numbers. Therefore, frame is statically determinate.

 (v)       From Eq. (c)

        V B   =( 2400 × 1.2 )/2.2 = 1309 N

  Therefore, from Eq. (b),

             VA = 2400 - VB

or         VA  = 2400 - 1309 = 1091 N

From Eqs. (f) and (i)

      VC + H C = 1309 × 1.73 + H B × 1.73 ------- (j)

       VC - H C = - 1091 × 1.73 - H A × 1.73-------- (k)

or         VC  - H C  = - 1091 × 1.73 - H B  × 1.73  ---------- (l)

Adding Eqs (j) and (l) :

                2VC = 218 × 1.73

or         VC  = 188.57 N         (Up side)

By Substituting for VC and VA in Eq. (i)

- H C + 1.73 H A = - 1091 × 1.73 - 188.57 = - 2076            --------- (m)

Since

H A = H B = H C

∴ 0.73 H C = - 2076

Or   H C = 2843.8 N   (Right side)

         VC = 188.57 N   (Up side )           Ans.

Posted Date: 1/29/2013 7:32:14 AM | Location : United States







Related Discussions:- Find out horizontal and vertical components of hinge force, Assignment Help, Ask Question on Find out horizontal and vertical components of hinge force, Get Answer, Expert's Help, Find out horizontal and vertical components of hinge force Discussions

Write discussion on Find out horizontal and vertical components of hinge force
Your posts are moderated
Related Questions
Resolution of a force: Sol.: When a force is resolved into two parts along the two mutually perpendicular directions, without changing the effects of it on the body, the par

what is the relation ship between tolrancr grade and manufacturing process ?

The total process of a the refining business begins at the oil field or gas field and runs all the way to the sending of processed hydrocarbon to a final user. Upstream applies

Thin wall round tube has diameter of 60mm. The end of it will be compressed to square for. How many percents torsion strenght will become lower at the end tube?

Draw shear force diagrams for the overhanging beam: Draw shear force & bending moment diagrams for the overhanging beam illustrated in Figure Figure  Solution

(i) Hydraulic press:   This can be used to lift a heavy load placed on the platform of larger piston or to press the things placed among the piston and the heavy platfor

Q. Application of hot service insulation? Provision for the expansion of hot equipment shall include the installation of expansion springs in circumferential banding securing i

Determine and illustrate about the earth pressure at rest. EARTH PRESSURE AT REST You have seen that the active pressure is the minimum lateral pressure while the passive pr

PART A A new process plant for ore processing is currently being planned. The design is only in the first stage. However, three requirements have already been clearly stated:

Diode: It allows the current to flow in one direction only and offers infinite resistance in other direction. It rectifies the alternating current that is why we call it rectifie