{"id":557444,"date":"2024-11-05T18:18:02","date_gmt":"2024-11-05T18:18:02","guid":{"rendered":"https:\/\/pdfstandards.shop\/product\/uncategorized\/esdu-090132009\/"},"modified":"2024-11-05T18:18:02","modified_gmt":"2024-11-05T18:18:02","slug":"esdu-090132009","status":"publish","type":"product","link":"https:\/\/pdfstandards.shop\/product\/publishers\/esdu\/esdu-090132009\/","title":{"rendered":"ESDU 09013:2009"},"content":{"rendered":"

INTRODUCTION<\/strong><\/p>\n

This Data Item provides a method of calculating the initial
\nbuckling stress of a flat isosceles triangular plate of uniform
\nthickness subjected to<\/p>\n

(a) a uniform compression f<\/i> = fc<\/sub><\/i>
\nalong the base reacted by compressive stress along the two equal
\nedges of the plate (see Sketch 2.1a), or<\/p>\n

(b) a uniform compression f<\/i> = fs<\/sub><\/i>
\nalong the base reacted by shear stress q<\/i> along the two
\nequal edges of the plate (see Sketch 2.1b).<\/p>\n

The Item also provides a method of calculating the critical
\ntotal buckling stress, fcr<\/sub><\/i>, of a flat isosceles
\ntriangular plate of uniform thickness subjected to<\/p>\n

(c) a uniform compression f<\/i> = fc<\/sub><\/i> +
\nfs<\/sub><\/i> along the base of the triangular plate
\nreacted by a combination of compression fc<\/sub><\/i> and
\nshear q<\/i> along the two equal edges (see Sketch 2.1c).<\/p>\n

The boundary conditions considered are either all three edges
\nclamped (fixed in rotation and out-of-plane displacement) or all
\nthree edges simply-supported (free to rotate, fixed in out-of-plane
\ndisplacement).<\/p>\n

The data given in this Item are obtained by FEA (Derivation 3)*
\nfor loading cases (a) and (b) above and from the interaction
\nformula, Equation (2.1), for the combined case (c). The shear
\nstress is taken as positive for the load directions shown in Sketch
\n2.1.<\/p>\n

The curves in Figures 1 to 4 are applicable only to plates of
\nisotropic material and have been calculated for v = 0.3. Results
\nfor materials with other Poisson's ratios can be obtained by
\nmultiplying the values given by the curves by
\n(1-0.32<\/sup>)\/(1-v2<\/sup>).<\/p>\n

Figure 1 presents curves of Kc<\/sub><\/i> versus
\nh\/a<\/i> for uniform compression f<\/i> =
\nfc<\/sub><\/i> along the base reacted by compressive stress
\nfc<\/sub><\/i> along the two equal edges of the plate (as
\nin Sketch 2.1a).<\/p>\n

Figure 2 presents curves of Ks<\/sub><\/i> versus
\nh\/a<\/i> for uniform compression f<\/i> =
\nfs<\/sub><\/i> along the base reacted by shear stress
\nq<\/i> along the two equal edges of the plate (as in Sketch
\n2.1b).<\/p>\n

Figures 3 and 4 presents curves of K<\/i>
\nversus\u00a0fc<\/sub>\/f<\/i>\u00a0 for combined uniform
\ncompression f<\/i> = fc<\/sub><\/i> +
\nfs<\/sub><\/i> along the base reacted by a combination of
\nuniform compression fc<\/sub><\/i> and shear stress
\nq<\/i> along the two equal edges (as in Sketch 2.1c) for plates
\nwith simply-supported and clamped edge cases respectively.<\/p>\n

It may be observed that the value of Kc<\/sub><\/i> is
\nconsistently low in comparison with KS<\/sub><\/i> : this
\nis because the former corresponds to a state of biaxial compression
\nwhereas the latter condition implies a biaxial stress state in
\nwhich the transverse stress component is tensile.<\/p>\n

* The present Data Item supersedes ESDU STRUCT 02.04.06 in which
\na theoretical solution based on an approximate mode of buckling
\n(Derivations 1 and 2) was found to be insufficiently accurate, and
\nthis has now been replaced by a finite element analyis.<\/p>\n","protected":false},"excerpt":{"rendered":"

Initial Buckling of Flat Isosceles Triangular Plates Under Compression Reacted by Compression and\/or Shear<\/b><\/p>\n\n\n\n\n
Published By<\/td>\nPublication Date<\/td>\nNumber of Pages<\/td>\n<\/tr>\n
ESDU<\/b><\/a><\/td>\n2009-11<\/td>\n15<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"featured_media":557453,"template":"","meta":{"rank_math_lock_modified_date":false,"ep_exclude_from_search":false},"product_cat":[2675],"product_tag":[],"class_list":{"0":"post-557444","1":"product","2":"type-product","3":"status-publish","4":"has-post-thumbnail","6":"product_cat-esdu","8":"first","9":"instock","10":"sold-individually","11":"shipping-taxable","12":"purchasable","13":"product-type-simple"},"_links":{"self":[{"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/product\/557444","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/product"}],"about":[{"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/types\/product"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/media\/557453"}],"wp:attachment":[{"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/media?parent=557444"}],"wp:term":[{"taxonomy":"product_cat","embeddable":true,"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/product_cat?post=557444"},{"taxonomy":"product_tag","embeddable":true,"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/product_tag?post=557444"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}