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International Journal of Engineering & Technology, 7 (4.20) (2018) 251-258
International Journal of Engineering & Technology
Website: www.sciencepubco.com/index.php/IJET
Research paper
Applying Various Types of Loading on Continuous Deep
Beams Using Strut and Tie Modelling
Khattab Saleem Abdul-Razzaq
1
*, Ali Mustafa Jalil
2
, Abbas H. Mohammed
3
1
University of Diyala, Civil Engineering, Diyala, Iraq
2
University of Diyala, Civil Engineering, Diyala, Iraq
3
University of Diyala, Civil Engineering, Diyala, Iraq
*Corresponding author E-mail: dr.khattabsaleem@yahoo.com
Abstract
This work aims at presenting detailed procedures companied by numerical examples for designing reinforced concrete two span continuous
deep beams under various types of loading; one concentrated force, two concentrated forces and uniform load for each span. Analysis and
design was conducted based on Strut and Tie modeling (STM) of ACI 318M-14 since they contain significant extents of D-regions and
they show a marked truss or tied arch action. It was found that changing the loading type has a significant impact on the capacity for the
same specimen that has the same dimensions, concrete and steel properties, in addition to the same amount and arrangement of steel
reinforcement. In more detail, the increase in the number of concentrated forces causes an obvious increase in ultimate capacity due to the
reduction in span to overall height (a/h) ratio and the increase in the value of the strut-tie angle, which causes shortening in the length of
the strut. Therefore, the ultimate capacity increased by about (44-70) % when the applied load was changed from 1-concentrated force to
2-concentrated forces or to uniformly distributed load.
Keywords: Reinforced concrete, Continuous deep beams, Strut and Tie, one and two concentrated forces, Uniform load, Design procedures.
1. Introduction
Deep beams are loaded on one face and supported on the opposite
face such that strut-like compression elements can develop between
the loads and supports and that satisfies (a) or (b) [1]: (a) Clear span
ln does not exceed four times the overall member depth h. (b)
Concentrated loads exist within a distance 2h from the face of the
support. Many investigators have suggested empirical and semi-
empirical expressions to determine the ultimate load capacity of
conventionally reinforced concrete deep beams [2, 3]. Some
researchers studied the parameters that affect deep beams such as
effect of heating, existence of openings, strengthening of openings,
amount and type of web reinforcement, types of loading, concrete
and steel strengths [4-10]. Furthermore, Abdul-Razzaq and Jebur
suggested alternatives for reinforced concrete deep beams by
reinforcing struts and ties only as compressive and tensile members,
respectively [11]. Since 2002, the ACI- 318 Code procedure is
based on empirical equations for the design of deep beams.
According to ACI 318M-14 [1], STM is defined as "a truss model
of a structural member or of a D- region in such a member, made
up of struts and ties connected at nodes, capable of transferring the
factored loads to the supports or to adjacent B-regions". Provisions
for STM have been also taken into considerations by many authors
for the design purposes. STM complies with the plasticity lower
bound theory, which needs that only yield conditions in addition to
equilibrium to be satisfied. Plasticity lower bound theory states that
if the load has such a value that it is possible to find a distribution
of stress corresponding to stresses that keep internal and external
equilibrium within the yield surface, then this load will not cause
failure of the body. In other words, the capacity of a structure as
estimated by a lower bound theory will be less than or equal to the
real failure load of the body in question [12].
2. STM Analysis and Design Procedure
An emerging methodology for the design of all types of D-Regions
is to predict and design an internal truss. This truss is consisting of
steel tension ties and concrete compressive struts that are
interconnected at nodes, to support the imposed loading through the
regions of discontinuity. The STM design procedure includes the
general steps summarized below [1]:
i. Define the D-Region boundaries and determine the imposed
sectional and local forces.
ii. Draw the internal supporting truss, find equivalent loadings,
and calculate the truss member forces.
iii. Choose the reinforcing steel to provide the necessary capacity
of the tie and ensure that this tie reinforcement is adequately
anchored in the nodal zones.
iv. Evaluate the dimensions of the nodes and struts, such that the
capacities of these components are adequate to carry the values
of the design forces.
v. Select the distributed reinforcement to guarantee the ductile
behavior of the D-Regions. It is important to note that both
hydrostatic and non-hydrostatic nodes are idealizations of
reality. The use of either hydrostatic or non-hydrostatic nodes
is an assumption that a design tool intended to provide a simple
method for proportioning STM. The classical method of node
dimensioning is by node shape arranging so that the applied
stresses on all sides of the node are equal. The stress biaxial