## Example 420 Propped Cantilever

Determine the support reactions and draw the bending moment diagram for the propped cantilever shown in Figure 4.80.

Figure 4.80

Solution

Fixed-End Moment for Propped Cantilever: Consider the beam fixed at both supports.

The values of the fixed-end moments for encastre beams are given in Appendix 2. The moment MB must be cancelled out by applying an equal and opposite moment at B which in turn produces a carry-over moment equal to-(0.5xMB) at support A. Examples in structural analysis 314 (i) Fixed Support Reactions

Consider the rotational equilibrium of the beam:

Consider the rotational equilibrium of the beam: Consider the vertical equilibrium of the beam:

Equation (1)

Consider the vertical equilibrium of the beam:

Equation (2) Consider the rotational equilibrium of the beam:

+ (10 x 8.0 x 4,0) - (8.0 x f[W) = 0 .■- Kbh»- + 4A.0 fcN J Equation

Beams 315 Consider the vertical equilibrium of the beam:

Equation (2)

The final vertical support reactions are given by (i)+(ii):

The final vertical support reactions are given by (i)+(ii):

Check the vertical equilibrium: Total vertical force =+50.0+30.0 =+80 kN

MO.OlNm

MO.OlNm Note the similarity between the shape of the bending moment diagram and the final deflected shape as shown in Figure 4.82.

Figure 4.82

The position of the maximum bending moment can be determined by finding the point of zero shear force as shown in Figure 4.83. Figure 4.83

+3 -6

### Responses

• verdiana
How to analyse propped cantilever?
4 years ago
• nazario
What are propped cantilever structures?
4 years ago
• Abeba
What is propped cantilever slab?
3 years ago
• petronio
What is propped cantilever beam?
3 years ago
• sanelma
How to find reactions in proped cantilever beam?
3 years ago
• rebecca
What i prpped cantilever?
3 years ago
• rorimac
How to solve propped cantilever beam?
3 years ago
• anne pfaff
How to find reaction of propped cantilever?
3 years ago
• valentina
How to solve propped cantilever structure with a fixed end?
3 years ago
• Uta
What is propped cantilever and how it is analysed?
3 years ago
• alfonsina
How do we calculate reactions in a propped cantilever beam?
3 years ago
• petra
What is propped cantilever beam and draw the diagram?
3 years ago
• Panu Raila
What is propped cantilever beam explain with diagram?
3 years ago
• Christopher Maclean
What is propped canteler beam?
3 years ago
• kibra
How to find a reaction of proped cantilever beam?
3 years ago
• morgan
How to solve a beam with prop?
3 years ago
• ELIAS
What is propped cantilever and fixed beam?
3 years ago
• JUHANA SINERVO
How to design propped cantlivear?
3 years ago
• faramir
How to solve proped cantilever?
1 year ago
• elias
What is propped cantilever moment at fixed end?
5 months ago
• Chantelle
How to draw the bending moment diagram for a propped cantilver?
3 months ago
• quintina
What is a prop cantilever?
2 months ago