Building Structures (Lecture 6)

1. Lecture 6. Building Structures

P R E PA R E D B Y: S . N I Y E T B AY

2. Structural and Analytical Models

Structural Model of a
Beam
Represents real
physical
characteristics:
Material
cross-sectional shape
and dimensions
support conditions
joints and connections
Analytical Model of a
Beam
Simplified
representation used
for calculations:
beam replaced by its
geometric axis
secondary factors
neglected
only essential loads
and constraints
considered
Purpose → correct
determination of
internal forces and
reactions.

3. Basic Assumptions of the Analytical Model

When idealizing the structure:
Beam replaced by an axial line
Section properties not directly considered
Loads applied to the axis
Friction at supports neglected
Consequence:
Internal forces depend only on loading and boundary
conditions.

4. Concept of the Effective Span

The effective span l0l₀l0​ is used in calculations:
determined by support locations
depends on support conditions
may differ from geometric dimensions
General definition:
Effective span → distance between points of action
of support reactions.

5. Idealization of Supports

Analytical models use ideal supports.
Pinned Roller Support
prevents vertical displacement
allows horizontal movement
produces one reaction
Pinned Support
prevents vertical and horizontal displacement
allows rotation
produces two reactions

6. Determination of the Design Span of a Beam

Key geometric
parameters:
l – distance between
grid (layout) axes
l₀ – design span of the
beam
l_sv – clear distance
between supports
l_op – length of
support zone
δ – distance from axis
to edge of element
Engineering principle:
The design span l₀ is
defined considering
the actual support
conditions rather than
nominal dimensions.

7. Hinged–Fixed Support (Pinned Support)

Mechanical characteristics:
Prevents vertical and
horizontal translations
Allows rotation at the
support
Generates two reaction
components: H_A and V_A
Modeling assumption:
In the analytical model, the
support is represented by
constraints eliminating
linear displacements while
preserving rotational
freedom.

8. Structural vs Design (Analytical) Beam Schemes

• Important distinction:
• Structural scheme → reflects real detailing,
connections, dimensions
• Design scheme → idealized mechanical
representation for analysis
• Why simplification is required:
• Internal forces and reactions cannot be
determined directly from construction details;
idealization ensures solvable static models.

9. Beam Anchorage and Load Direction Effects

PRACTICAL
OBSERVATION:
IF LOAD
DIRECTION OR
POTENTIAL
HORIZONTAL
ACTIONS ARE
SIGNIFICANT:
SUPPORT ROLES
MAY NEED
RECONSIDERATIO
N
ANCHORAGE
DEVICES MUST
BE INTRODUCED
DESIGN
IMPLICATION:
BOLTED OR
WELDED
RESTRAINTS MAY
BE REQUIRED
SUPPORTS MUST
ENSURE
STABILITY FOR
ALL REALISTIC
LOAD
COMBINATIONS,
NOT ONLY

10. Beam Anchorage and Load Direction Effects

11. Beam Bearing on Masonry Walls

Real behavior of beams:
Beam deformation reduces effective end distance
Small gaps may exist between beam and masonry
Friction often prevents horizontal movement
Engineering simplification:
Depending on conditions, the beam may be modeled with:
One fixed support
Two movable supports
Hinged support assumptions
Correct modeling depends on structural behavior, not only geometry.

12. Cantilever Beam: Structural and Design Schemes

Definition of a cantilever:
A beam with one end rigidly fixed and the other end free
Widely used in slabs, canopies, balconies, cornices
Support characteristics:
Restrains vertical, horizontal, and rotational displacements
Generates reactions V_A, H_A, and fixing moment M_A
Design simplification:
Rigid fixing is modeled by eliminating translations and rotation
Design span l₀ is measured from the face of the fixing to the free end

13. Beam Bearing on Masonry Walls & Modeling Assumptions

Beam Bearing on Masonry Walls &
Modeling Assumptions
Practical behavior:
Supports may be
idealized depending on
actual behavior
Perfect rigid fixing is
rarely achieved in
masonry supports
Rigid fixing may be
replaced with hinged
assumptions
Small embedment
depths lead to partial
restraint
Analytical model must
reflect real working
conditions
Friction and local
deformations influence
structural response
Engineering modeling
approach:
Key principle:
The design scheme
must represent the
structural behavior with
rational accuracy rather
than purely geometric
assumptions.

14. Columns: Structural vs Design Schemes

General principle:
Modeling approaches used for beams also apply to
columns
Structural scheme → reflects real connections and
details
Design scheme → idealized analytical representation
Engineering objective:
Accurate idealization of boundary conditions governs
reliability and correctness of internal force evaluation.

15. Steel Column Base Connections

Column
connected via
base plate and
anchor bolts
Such systems
possess
rotational
flexibility
Full rigid fixing is
not ensured
Design
interpretation:
Base is
commonly
modeled as
pinned (hinged)
support
Rotation allowed,
moment transfer
neglected
Only force
reactions
considered
Typical practical
solution:

16. Rigid Column Fixing to Foundations

When rigid
behavior is
required:
More complex
base details are
introduced
Increased
stiffness of the
base zone
Rotation of the
column base is
restrained
Analytical
implication:
Support modeled
as fixed (rigid)
support
Moment M_A
develops
Rotational degree
of freedom
eliminated

17. Beam-to-Column Connections

Two
fundamental
connection
types:
Hinged
connection
Allows end
rotation of beam
No moment
transfer
Simplifies force
distribution
Rigid
connection
Prevents
relative rotation
Transfers
bending
moments
Key modeling
rule:
Connection
stiffness — not
visual detailing
— defines the
design scheme.
Alters internal
force patterns

18. Reinforced Concrete Columns: Fixing to Foundations

Typical structural solution:
Columns embedded into the foundation socket
Monolithic concrete ensures load transfer
Base rotation may be restrained
Design interpretation:
For large foundation dimensions → fixed support
model
Column base assumed rigid
Moment transfer considered

19. Influence of Foundation Stiffness on Column Behavior

Practical observation:
Small foundations may rotate with the column
Full rigid fixing is not always realistic
Structural stiffness governs support behavior
Analytical implication:
For flexible foundation systems → pinned support
model
Base moment may be neglected
Only force reactions considered

20. Beam-to-Column Connections in RC Frames

• Common detailing approaches:
• Anchorage bolts
• Embedded steel plates
• Welded connections
• Engineering assumption:
• Many such joints behave as hinged
connections
• Beam end rotation allowed
• Simplified force distribution

21. Rigid Beam-to-Column Connections

When rotational restraint is required:
Special reinforcement detailing applied
Embedded elements ensure stiffness
Rotation of beam end restricted
Design consequence:
Joint modeled as rigid node
Bending moments transferred
Internal forces significantly altered

22. Masonry (Brick) Columns: Structural Behavior

Typical support
conditions:
Rotational
restraint is
minimal
Columns rest on
foundations
Beams often
supported without
special fixings
Modeling rule:
Masonry columns
are usually
treated as
pinned systems
Moment
resistance limited
Stability depends
on geometry and
loading