GO PRACTICAL STRUCTURAL DESIGN 



Some writers use d (depth) instead of h (height), but as d is 

 used these days to indicate the depth from the top of a reinforced- 

 concrete beam to the center of gravity of the steel reinforcement 

 (the real depth of a reinforced-concrete beam) the letter h is 

 preferred when the total over-all height or depth of a beam is 

 meant. In a reinforced-concrete beam the concrete below the 

 center of the steel is used solely for bond and protection and is 

 not considered in computations to ascertain the strength of the 

 beam. 



The moment of resistance of a rectangular beam of homogeneous 

 material is said to be " the section modulus times the fiber stress." 

 This means that 



W 



: T 



is an expression denoting the effect of the shape of the beam or the 

 resistance it offers to destruction by loading. No matter what 

 the material or what the stress used, the effect of the shape is the 

 same and this is called the " section modulus," the word " modulus" 

 meaning " measure." It is, therefore, the measure of the resistance 

 of the shape. 



Every shape has a section modulus designated by S in the 

 steel manufacturers' handbooks. The calculation of the section 

 modulus for a beam with rectangular cross section has been 

 given, as it is the most simple section to handle without confusing 

 the reader with a mass of figures. 



To compute the section modulus for any shape first assume 

 some axis passing through the center of gravity. Then divide 

 the area into any number of layers desired by lines parallel to the 

 axis. Find the area of each layer and the distance from the axis 

 to the center of gravity of each layer. Multiply each layer by 

 the square of the distance from the axis to the center of gravity 

 of the layer and add the products. Thus is obtained the Moment 

 of Inertia, an expression denoting the disinclination of the body 

 to move as a whole. The Moment of Inertia divided by the distance 

 from the axis to the highest stressed fiber gives the Section 

 Modulus. 



For a rectangular beam the moment of inertia is 



bh 3 



