How to Determine Reactions at Points in Beam Analysis?

In summary, the conversation is about finding the reactions at point A and C in order to draw shear and bending moment diagrams for beam AB. The first step is to find the reactions at A and C, which can be done using three equations and three unknowns. However, the member CD is pinned at both ends and has no internal transverse applied load, making it a truss member. This means that the reaction at C will be in line with the line segment CD, which is an exception to the general rule that pin connections have a reaction with unknown direction. Meeting condition 1 does not define a truss member, it must also meet condition 2.
  • #1
zzinfinity
47
0

Homework Statement



Neglecting the size of the pulley at G, draw the shear and bending moment diagrams for beam AB.



Homework Equations


Fxnet=0
Fynet=0
Netmoment=0


The Attempt at a Solution

\

What I want to do first is figure out the reactions at A and C, however I'm not sure how to do that since there seem to be four unknowns and only three equations. Is this the correct first step, or should I try it another way? Thanks!
 

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  • #2
zzinfinity: Yes, that is the correct first step. No, there are three equations and three unknowns. Hint 1: Is member CD a so-called truss (axial force) member? Give it a try.
 
  • #3
So does that mean the reaction at c is in the direction of cd? I thought pin connections always had a reaction with unknown direction. Is this not always the case?
 
  • #4
Since member CD is apparently pinned at both ends, the reaction at C will be in line with the line segment CD.
 
  • #5
zzinfinity said:
So does that mean the reaction at c is in the direction of cd?
Yes.
zzinfinity said:
I thought pin connections always had a reaction with unknown direction. Is this not always the case?
zzinfinity: You are correct. Pin connections generally have a reaction force with (initially) unknown direction. However, this is not the case if a member is (1) pinned at both ends, and (2) has no internal transverse applied load. (Notice, there is no load applied to member CD between points C and D. It thus meets both conditions 1 and 2, making it a truss member.)

Meeting condition 1, alone, does not define a truss (axial force) member.
 

1. What is a shear moment and how is it different from a bending moment?

A shear moment is a force that acts parallel to a material, causing it to slide against an adjacent material. On the other hand, a bending moment is a force that causes a material to bend or deform. Both types of moments can occur simultaneously, but they act in different directions and have different effects on the material.

2. What causes shear and bending moments to occur?

Shear moments are caused by forces that are parallel to a material, such as wind or sliding objects. Bending moments are caused by forces that are perpendicular to a material, such as weight or pressure. Both types of moments can also be caused by the internal forces within a material, known as internal stresses.

3. How are shear and bending moments calculated?

Shear and bending moments can be calculated using mathematical equations and formulas, based on the type and magnitude of the forces acting on a material. These calculations are commonly used in structural engineering and mechanics to determine the strength and stability of a structure.

4. What are the units of measurement for shear and bending moments?

Shear and bending moments are typically measured in units of force, such as newtons or pounds. The units can also be converted to other units of force, such as kilonewtons or kilopounds, depending on the specific requirements of the project or calculation.

5. How do shear and bending moments affect the design of structures?

Shear and bending moments play a crucial role in the design of structures, as they determine the strength and stability of a material. Engineers must consider the magnitude and direction of these moments when designing structures to ensure they can withstand the forces that will act upon them.

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