Find out the reactions at point, Mechanical Engineering

Assignment Help:

Find out the reactions at point:

A beam AB is hinged at A and is supported at C. It is loaded as revealed in Figure. Find out the reactions at A and C.

2314_Find out the reactions at point.png

Solution

Let the reaction components at A be HA and VA as illustrated in Figure. The reaction at C shall be acting vertically upwards. As the beam is at rest under the action of the forces, the conditions of equilibrium may be applied.

Taking moments of all of forces about A, we obtain

∑ M A  = 0

18 × 3 × (3/2) + (40 sin 60o ) × 5 - Rc × 7 + 24 × 9 = 0

∴ 81 + 173.2 - 7 Rc + 216 = 0

∴ Rc = (81 + 173.2 + 216) /7

= 67.171 kN

 [Note : Moments because of HA, VA and 40 cos 60o regarding A are zero as they pass through point A. Clockwise moments are taken as +ve.]

Now, ∑ Fx  = 0

∴ H A - 40 cos 60o  = 0

∴ H A = 40 × 0.5 = 20 kN

and, ∑ Fy  = 0

∴ VA  - (18 × 3) - 40 sin 60o  + Rc  - 24 = 0

∴ VA  = 54 + 34.64 - 67.171 + 24

= 45.469 kN

1555_Find out the reactions at hinge2.png

 = 49.673 kN

tan θ= VA / H A = 45.469/20  = 2.2734

∴ θ = 66.257o  = 66o 15′ 25′′

The reaction at A contain a magnitude of 49.673 kN and is inclined at 66o 15′ 25′′ with respect to horizontal whereas reaction at C is working vertically upwards and has a magnitude of 67.171 kN.


Related Discussions:- Find out the reactions at point

Combined rules- priority rules-conventional priority rules, Combined Rules ...

Combined Rules           MOD (modified operation due date)                                 PN j = max (t + o j , t dj ) (SPT-Tr) (Truncated SPT)

Design loading - unloading facilities in plant layout, Q. Design Loading - ...

Q. Design Loading - Unloading Facilities in plant layout? Loading and unloading areas should be separated. These facilities should be situated on the edge of the site near road

Efficiency and mean effective pressure of a dual cycle, Draw TS and pv diag...

Draw TS and pv diagrams of a dual cycle. Why this cycle is also named limited pressure or mixed cycle ? Derive the mathematical expressions for the efficiency and mean effective pr

Evaluation of specific volume of steam - thermodynamics , Evaluation of Spe...

Evaluation of Specific Volume of Steam: Specific volume of steam means the volume which is occupied by unit mass of steam. It is expressed in m3 /kg. Specific volume of steam

Calculations for force, Calculations for force: A square block having...

Calculations for force: A square block having 25cm side and weighing 20N is hinged at point A and rests on rollers at point B as shown in the figure given below. It is pu

Thermodynamics, The attached figure depicts an indirectly fired gas turbine...

The attached figure depicts an indirectly fired gas turbine engine. In the gas turbine engine, air is compressed to a high pressure and then heat is added. The high pressure, high

Define conceptual engineering phase for project, Q. Define Conceptual Engin...

Q. Define Conceptual Engineering Phase for project? The primary objective of this stage is to include and clearly define the economic feasibility of the project, sensitivity to

Find out load lifted by the machine, Find out load lifted by the machine: ...

Find out load lifted by the machine: An effort of 400 N is applied in a lifting machine. The distance moved through effort is 4 m and that by load is 40 cm. If the efficiency

Molecular structure, Molecular Structure The polymers have three disti...

Molecular Structure The polymers have three distinct arrangements of molecular chain, hence resulting in three structures. In amorphous structure the molecular chain are ar

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd