What are Inclined Columns?
Inclined columns or slanted columns or raked columns are columns that are structurally leaned at an angle with the perpendicular. The inclination to the structure is provided intentionally to meet architectural or structural functions.
Inclined columns originated from the category of structural framing members are gravity-loaded columns and can be applied to both rigid as well as braced frames.
The design in most cases is carried out for axial force and moments by the usual method. In a condition where shear is found predominant (this is the case when the member is inclined appreciably), shear reinforcement should be designed and their provision is made.
Some examples of inclined column constructions are the rafter & struts of an RCC truss, the gable beams of a sloped roof, and the top chord of an RCC Vierendeel Girder.
The top chord (beam) of a Vierendeel girder, a horizontal member, is designed as a column, not as a beam, as compression is dominant in it.
The figure shows the free-body diagram (FBD) of an inclined column. A column that possesses a cross-section without symmetry may be subjected to torsional buckling or lateral buckling. Torsional buckling is a sudden twisting of the column. As the theories say the existence of eccentric loading would decrease column strength.
The term eccentrically loaded is defined as the situation when the axial load on the column is not concentric or in other words if the line of action of the axial load is not parallel to the central axis of the column. The eccentricity is mainly represented by the ‘e’, of the load subject to the bending of the column immediately. Hence the combined action of axial and bending would result in reduced load-carrying ability.
The reinforcement detailing is provided at the location where the inclination starts with extra care. This location is vital, and the stirrups are spaced closely at that location.
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| Fig.1. Inclined columns with Architectural Importance |
Inclined columns originated from the category of structural framing members are gravity-loaded columns and can be applied to both rigid as well as braced frames.
Loads on Inclined Columns
Mainly inclined columns are designed as any other vertical column structure, except in situations where it is subjected to the eccentricity of the axial load on a column or when they are subjected to second-order effects or P-δ effect.
For a perfectly straight column, the bending moment will be due to externally applied loads. These are first-order bending moments. When the column is inclined, there are chances that the applied axial loads become eccentric with respect to the longitudinal axis of the columns. These second-order bending moments are dependent on the geometry, stiffness, and support conditions of the structure. Pinned or fixed supports are investigated for these effects.
When we consider an inclined column (say strut) the forces it is subjected to are axial compression, moments, and shear, which can be found by any method of frame analysis. But there is no variation in the method of analysis that we perform on it.
For a perfectly straight column, the bending moment will be due to externally applied loads. These are first-order bending moments. When the column is inclined, there are chances that the applied axial loads become eccentric with respect to the longitudinal axis of the columns. These second-order bending moments are dependent on the geometry, stiffness, and support conditions of the structure. Pinned or fixed supports are investigated for these effects.
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| Fig.2.Inclined Column Construction |
When we consider an inclined column (say strut) the forces it is subjected to are axial compression, moments, and shear, which can be found by any method of frame analysis. But there is no variation in the method of analysis that we perform on it.
The design in most cases is carried out for axial force and moments by the usual method. In a condition where shear is found predominant (this is the case when the member is inclined appreciably), shear reinforcement should be designed and their provision is made.
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| Fig. 3. An Inclined Column Aligned in X, Y, and Z direction |
Some examples of inclined column constructions are the rafter & struts of an RCC truss, the gable beams of a sloped roof, and the top chord of an RCC Vierendeel Girder.
The top chord (beam) of a Vierendeel girder, a horizontal member, is designed as a column, not as a beam, as compression is dominant in it.
Load Transferring and Deflection
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| Fig.4. Tilted column subjected to eccentric axial load |
The figure shows the free-body diagram (FBD) of an inclined column. A column that possesses a cross-section without symmetry may be subjected to torsional buckling or lateral buckling. Torsional buckling is a sudden twisting of the column. As the theories say the existence of eccentric loading would decrease column strength.
The term eccentrically loaded is defined as the situation when the axial load on the column is not concentric or in other words if the line of action of the axial load is not parallel to the central axis of the column. The eccentricity is mainly represented by the ‘e’, of the load subject to the bending of the column immediately. Hence the combined action of axial and bending would result in reduced load-carrying ability.
Shear Force and Bending Moment in Inclined Columns
Figure 5 below shows an inclined column connected to a beam. We will discuss how we can determine the load in the column.
From the figure the
w = total load applied to the beam. This is the load that has to be transferred to the inclined column AB.
The axial force P can be obtained by the equation
P = wl/2
The moment due to eccentricity in the column can be given by
M = P.e
Where e is the eccentricity. From the figure, e has to be determined from the given details.
Thus
e = (L/2) cosθ
Once the column is analyzed and the loads and forces are determined the next procedure is to design the inclined column.
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| Figure.5 |
From the figure the
w = total load applied to the beam. This is the load that has to be transferred to the inclined column AB.
The axial force P can be obtained by the equation
P = wl/2
The moment due to eccentricity in the column can be given by
M = P.e
Where e is the eccentricity. From the figure, e has to be determined from the given details.
Thus
e = (L/2) cosθ
Once the column is analyzed and the loads and forces are determined the next procedure is to design the inclined column.
Design of Inclined column
- The column design is like vertical columns
- Determine the type of column by calculating the effective length and the end conditions
- For the maximum moment, the value determines the reinforcement
- Many studies have shown that inclined columns are subjected to greater moments due to eccentricity compared to vertical columns. The moment will increase with the increase in eccentricity. As the inclination of the columns is higher, the eccentricity also increases, thus the moment. The inclination in columns will result in horizontal component forces in addition to the external lateral load present.
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| Fig.6. Reinforcement Detailing for an Inclined Column R.C.C |
The reinforcement detailing is provided at the location where the inclination starts with extra care. This location is vital, and the stirrups are spaced closely at that location.
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