# m4l8 - Module 4 Doubly Reinforced Beams Theory and Problems...

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Module 4 Doubly Reinforced Beams – Theory and Problems Version 2 CE IIT, Kharagpur

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Lesson 8 Doubly Reinforced Beams – Theory Version 2 CE IIT, Kharagpur
Instructional Objectives: At the end of this lesson, the student should be able to: explain the situations when doubly reinforced beams are designed, name three cases other than doubly reinforced beams where compression reinforcement is provided, state the assumptions of analysis and design of doubly reinforced beams, derive the governing equations of doubly reinforced beams, calculate the values of f sc from (i) d'/d and (ii) calculating the strain of the compression reinforcement, state the minimum and maximum amounts of A sc and A st in doubly reinforced beams, state the two types of numerical problems of doubly reinforced beams, name the two methods of solving the two types of problems, and write down the steps of the two methods for each of the two types of problems. 4.8.1 Introduction Version 2 CE IIT, Kharagpur

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Concrete has very good compressive strength and almost negligible tensile strength. Hence, steel reinforcement is used on the tensile side of concrete. Thus, singly reinforced beams reinforced on the tensile face are good both in compression and tension. However, these beams have their respective limiting moments of resistance with specified width, depth and grades of concrete and steel. The amount of steel reinforcement needed is known as A st , lim . Problem will arise, therefore, if such a section is subjected to bending moment greater than its limiting moment of resistance as a singly reinforced section. There are two ways to solve the problem. First, we may increase the depth of the beam, which may not be feasible in many situations. In those cases, it is possible to increase both the compressive and tensile forces of the beam by providing steel reinforcement in compression face and additional reinforcement in tension face of the beam without increasing the depth (Fig. 4.8.1). The total compressive force of such beams comprises (i) force due to concrete in compression and (ii) force due to steel in compression. The tensile force also has two components: (i) the first provided by A st , lim which is equal to the compressive force of concrete in compression. The second part is due to the additional steel in tension - its force will be equal to the compressive force of steel in compression. Such reinforced concrete beams having steel reinforcement both on tensile and compressive faces are known as doubly reinforced beams. Doubly reinforced beams, therefore, have moment of resistance more than the singly reinforced beams of the same depth for particular grades of steel and concrete. In many practical situations, architectural or functional requirements may restrict the overall depth of the beams. However, other than in doubly reinforced beams compression steel reinforcement is provided when: (i) some sections of a continuous beam with moving loads undergo
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m4l8 - Module 4 Doubly Reinforced Beams Theory and Problems...

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