Secondary Structure of Amino Acids:-

Secondary structure is not just hydrogen bonds.It also includes the following

Alpha Helix: Right-handed helix with 3.6 amino acid residues per turn. Hydrogen bonds are formed parallel to the helix axis.
Beta Sheet: A parallel or antiparallel arrangement of the polypeptide chain. Hydrogen bonds are formed between the two (or more) polypeptide strands.
Beta Turn: A structure in which the polypeptide backbone folds back on itself. Turns are useful for connecting helices and sheets.

Secondary structure exists to provide a way to form hydrogen bonds in the interior of a protein. These structures  provide ways to form regular hydrogen bonds. These hydrogen bonds are just replacing those originally made with water. As a protein folds, many hydrogen bonds to water must be broken. If these broken hydrogen bonds are replaced by hydrogen bonds withinthe protein, there is no net change in the number of hydrogen bonds Because the actual number of hydrogen bonds does not change as the secondary structure is formed, it is often argued that hydrogen bonds don’t contribute much to the stability of a protein.

However, hydrogen bonds that form after the protein is already organized into the correct structure may form more stable hydrogen bonds than the ones to water. Hydrogen bonding does contribute somewhat to the overall stability of a protein; however, the hydrophobic interaction usually dominates the overall stability.Small peptides generally do not form significant secondary structure in water . For small peptides that do not form stable secondary structure, there are often other favorable interactions within the peptide that stabilize the formation of the helix or sheet structure.

The stability of secondary structure is also influenced by surrounding structures. Secondary structure may be stabilized by interactions between the side chains and by interactions of the side chains with other structures in the protein. For example, it is possible to arrange the amino acid sequence of a protein or peptide into a helix that has one face that is hydrophobic and one that is hydrophilic. The peptide backbone spirals up and around the cylinder.

In an unfolded protein, water makes hydrogen bonds to all the donors and acceptors. As the protein folds and some polar groups find themselves inside, many of the hydrogen bonds with the solvent are replaced by hydrogen bonds between the different donors and acceptors in the protein. Because hydrogen bonds are
being replaced rather than gained or lost as the protein folds, there is not a large net stabilization of the protein by the hydrogen bonds.