# Shear Modulus

Written by Jerry Ratzlaff on . Posted in Thermodynamics Shear modulus, abbreviated as G, also called modulus of rigidity or shear modulus of elasticity, is the ratio of the tangential force per unit area applied to a body or substance to the resulting tangential strain within the elastic limits.

## Shear Modulus formulas

 $$\large{ G = \frac { \tau } { \gamma } }$$ $$\large{ G = \frac { F\;l } { A\;\Delta x } }$$ $$\large{ G = \frac { E }{ 2 \; \left( 1 \;+\; \mu \right) } }$$ $$\large{ G = \frac { 8 \; k_s \; n_a \; D^3 } { d^4 } }$$ (spring)

### Where:

$$\large{ G }$$ = shear modulus

$$\large{ A }$$ = area on which the force acts

$$\large{ E }$$ = elasticity

$$\large{ F }$$ = force that acts

$$\large{ l }$$ = lateral length of the material without force applied

$$\large{ D }$$ = mean coil diameter

$$\large{ n_a }$$ = number of active coils

$$\large{ \mu }$$  (Greek symbol mu) = Poisson's Ratio

$$\large{ \gamma }$$  (Greek symbol gamma) = shear strain

$$\large{ \tau }$$  (Greek symbol tau) = shear stress

$$\large{ k_s }$$ = spring constant

$$\large{ \Delta x }$$ = transverse displacement

$$\large{ d }$$ = wire size
{"ft_lang_label":"__label__en","ft_lang_prob":0.74236995,"math_prob":1.0000006,"size":1186,"snap":"2021-04-2021-17","text_gpt3_token_len":378,"char_repetition_ratio":0.20050761,"word_repetition_ratio":0.046511628,"special_character_ratio":0.36593592,"punctuation_ratio":0.07650273,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":1.0000088,"pos_list":[0,1,2],"im_url_duplicate_count":[null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-01-17T21:28:28Z\",\"WARC-Record-ID\":\"<urn:uuid:3bdc990e-f899-4b19-a4fe-03cb1beb2f7a>\",\"Content-Length\":\"27988\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:1bdcf70a-c744-4102-b69c-494cccc5ea90>\",\"WARC-Concurrent-To\":\"<urn:uuid:0267b131-58a2-4e52-95e8-bb8c11d64694>\",\"WARC-IP-Address\":\"23.235.195.68\",\"WARC-Target-URI\":\"https://www.piping-designer.com/index.php/properties/thermodynamics/557-shear-modulus\",\"WARC-Payload-Digest\":\"sha1:JG4EVDKJ2XMTEXAJGHIA25VTWBD5QO6Z\",\"WARC-Block-Digest\":\"sha1:PGG6LWWCP7HMOAG27IS5OS7Q3APOOO5O\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-04/CC-MAIN-2021-04_segments_1610703513194.17_warc_CC-MAIN-20210117205246-20210117235246-00176.warc.gz\"}"}