Experimental analysis of limitations in the strut-and-tie method

Abstract

One of the overall main purposes for a structural engineer is to design structures and structural
elements so that they meet society’s safety requirements, yet use as little material as possible. In
order to do so, the designer has to understand and simplify a complex reality. The strut-and-tie
method is such a simplification model which allows engineers to design reinforced concrete
structures where basic beam theory is not applicable, e. g. high beams or discontinuity regions near
supports and loads.
When designing according to the strut-and-tie method, several assumptions have to be made
regarding the structural behavior. Questions exists whether current recommendations regarding
these assumptions are conservative – the assumed internal truss system for ultimate limit state
calculations is usually based on the linear-elastic stress field. This despite stress redistribution due
to cracking and plastic deformations is possible. Accounting for the stress redistribution would
yield a higher load-bearing capacity in the ultimate limit state. The conservative approach derives
from uncertainties regarding the materials plastic deformation capacities and serviceability limit
state considerations.
The aim of this report is to investigate the effects on the stress distribution of a simply supported
high concrete beam when loaded to failure, investigating the redistribution capacity of the member.
In the design of the specimen, extreme cases were chosen, e.g. a structure with a very small amount
of reinforcement. Thus, the scope of the project also includes limitations in the strut-and-tie
method.
Studies were performed on four specimen with different amount of reinforcement; three members
with increasing amount of reinforcement and a fourth reinforced with a minimum reinforcement
mesh in accordance with Eurocode. The beams were simply supported and subjected to two-point
loading. Laboratory results were compared with computer simulations and hand calculations.
Analyzing the results from the simulations indicated a rise of the internal lever arm, in three out
of four cases. The laboratory test results clearly showed two types of behavior; a brittle failure for
the ‘insufficiently reinforced’ and a ductile response from the one with minimum reinforcement
installed. Comparing the results from the lab and the model gave diverse results in terms of
stiffness.

Popular Abstract

Structural engineers often face design situations which are too advanced to analyze in a simple
way. In this case a simplification method such as the strut-and-tie method may be of use. After
assuming the internal stress flow a fictive truss may be assumed and then designed according to
the code. If caution not is taken however dangerous failures may occur and lives might be at stake.
Concrete structures with non-linear stress
variations are rather common, and conventional
dimensioning techniques cannot be applied.
Therefore simplifications such as the strut-andtie
method are introduced. Regions containing
non-linear stress distribution, e.g. Figure 1, are
known as discontinuity regions, and may
appear close to concentrated loads or
geometrical discontinuities.
Figure 1: Stress field and internal truss [Engström, Björn,
Design and analysis of deep beams, plates and other
discontinuity regions, 2011)
This project consisted of three main parts:
initiating calculations using the strut-and-tie
method, a laboratory practical and computer
simulation. The aim was to evaluate the internal
stress behavior and hopefully rationalize the
usage of the strut-and-tie method. Limitations
of the method as well as the risks were also
evaluated.
Four specimens were designed, casted, tested
and simulated in a finite element software
called Brigade/Plus, Figure 2. There were three
specimens with increasing reinforcement and
one with additional minimum reinforcement.
Unfortunately the results did not coincide in
terms of stiffness and only one out of four
beams could be tested all the way to failure. The
failure that did occur, in the least reinforced
beam, however was brittle and aggressive, and
if being a member of a real structure, this could
cause a major hazard.
Evaluating the load-deflection response from
each of the specimens, the beam equipped with
minimum reinforcement, i.e. highest amount of
reinforcement, surprisingly cracked at a lower
load. However its ductile behavior is far more
desirable in a structure than the brittle behavior
of the insufficiently reinforced beam.
Figure 2: Beam, computer model
Conclusions drawn from the project are:
• Minimum reinforcement serves a well
motivated purpose
• When using high design angles the
tension strength of the concrete should
be considered
• The strut-and-tie method is made for
cracked cases
• It is hard to model the behavior of
concrete accurately

• author: Wahlgren, Mikael and Bailleul, Niels
• supervisor: Oskar Larsson
• organization: Division of Structural Engineering
• course: VBK920 20161
• year: 2016
• type: H3 - Professional qualifications (4 Years - )
• subject: Technology and Engineering
• keywords: Strut-and-Tie method, Reinforced concrete, Concrete Damaged Plasticity, Fracture energy
• report number: TVBK-5249
• ISSN: 0349-4969
• language: English
• additional info: examinator: Annika Mårtensson
• id: 8882138
• date added to LUP: 2016-06-20 09:03:22
• date last changed: 2016-06-20 09:03:22